CE 4030 Hydraulics Lab Manual

8/19/2019 CE 4030 Hydraulics Lab Manual

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CE 4030

Hydraulics Engineering Laboratory Manual

Environmental and Water Resources Engineering Division

Department of Civil Engineering

Indian Institute of Technology Madras

Chennai – 600036


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List of Experiments

1 BERNOULLI’S EQUATION 5

1.1 THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1.1 Bernoulli’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1.2 Bernoulli’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1.3 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.4 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2 EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.3 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.4 Technical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.5 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.6 Observing Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.7 Observation Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.9 Precautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 CENTRIFUGAL PUMP CHARACTERISTICS CURVE 11

2.1 THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.2 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.3 Performance Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.4 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.5 Pumps in series and parallel . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13


2.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2.6 Precautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 ENERGY LOSSES IN PIPES 17

3.1 THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.2 Major Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.3 Minor Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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3.2.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.3 Technical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2.4 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20


3.2.6 Model Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2.7 Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2.9 Precautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 FLOW OVER WEIRS 22

4.1 THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.1.2 Rectangular Weir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.1.3 Triangular Weir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.1.4 Depressed and Clinging Nappe . . . . . . . . . . . . . . . . . . . . . . 244.2 EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2.4 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2.5 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2.6 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2.9 Precautions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5 GUELPH PERMEAMETER 29

5.1 THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.1.2 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.2 EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.2.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.2.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.2.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.2.4 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.2.5 Observation Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.2.6 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.8 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6 HYDRAULIC JUMP 36

6.1 THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

6.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

6.1.2 Analysis of hydraulic jump in horizontal rectangular channel . . . . . . 36

6.2 EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

6.2.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376.2.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

6.2.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

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6.2.4 Observations and Calculations . . . . . . . . . . . . . . . . . . . . . . 38

6.2.5 Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6.2.6 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 39

6.2.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6.2.8 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

7 IMPACT OF JET 41

7.1 THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

7.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

7.1.2 Effect of height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

7.1.3 Impact of Jets apparatus . . . . . . . . . . . . . . . . . . . . . . . . . 43

7.2 EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

7.2.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

7.2.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

7.2.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7.2.4 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467.2.5 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

7.2.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

7.2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

7.2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

8 PIPE SURGE AND WATER HAMMER 48

8.1 THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

8.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

8.1.2 Analysis of Water Hammer . . . . . . . . . . . . . . . . . . . . . . . . 49

8.2 EXPERIMENT - ANALYSIS OF PIPE SURGE CHARACTERISTICS US-

ING SURGE TANK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

8.2.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

8.2.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

8.2.3 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

8.2.4 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

8.2.5 Results and Calculations . . . . . . . . . . . . . . . . . . . . . . . . . 55

8.2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

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List of Figures

1.1 F1-15 Bernoulli’s Theorem demonstration . . . . . . . . . . . . . . . . . . . . 6

1.2 F1-10 Basic Hydraulics Bench . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Equipment dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1 F1-27 Centrifugal Pump Characteristics . . . . . . . . . . . . . . . . . . . . . 12

3.1 Moody’s Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2 Head loss vs Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 F1-18 Energy losses in pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1 Different shapes of notches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2 Rectangular Notch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.3 Triangular Notch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.4 Nappe along the hydraulic structure . . . . . . . . . . . . . . . . . . . . . . . 24

4.5 F1–13 Flow over Weirs-Vee notch weir . . . . . . . . . . . . . . . . . . . . . 25

4.6 Q vs H 5/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.1 The Guelph Permeameter Kit(2800KI) components in carrying case . . . . . . 30

5.2 Guelph Permeameter Support Kit . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.3 Guelph Components (detailed) . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.1 Hydraulic Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

7.1 Different target vanes (flat, conical and semi-spherical from left to right) . . . . 42

7.2 Cussons P6233 Impact of Jets apparatus . . . . . . . . . . . . . . . . . . . . . 44

7.3 F1–16 Impact of a jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

8.1 Macro-cavitation occurring due to pump trip . . . . . . . . . . . . . . . . . . . 508.2 Effect of sudden valve closure on elasticity of water visualized as a spring, it

has to be noted that the regions indicated by red lines are compression zones

where the velocity of the spring/water is zero. . . . . . . . . . . . . . . . . . . 50

8.3 Pressure and velocity waves in a single-conduit, frictionless pipeline following

its sudden closure. The areas of steady-state pressure head are shaded medium

dark, those of increased pressure dark, and those of reduced pressure light. The

expansion and contraction of the pipeline as a result of rising and falling pres-

sure levels, respectively, are shown. To give an idea of the relationship in-

volved: With a 100 bar pressure rise, the volume of water will decrease by

about 0.5 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

8.4 Simple Harmonic Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

8.5 C7-MK Pipe Surge and Water Hammer apparatus . . . . . . . . . . . . . . . . 54

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1

BERNOULLI’S EQUATION

1.1 THEORY

1.1.1 Bernoulli’s TheoremBernoulli’s theorem is basically the law of conservation of energy as applied to a fluid flow sys-

tem. It states that for an inviscid, incompressible, irrotational and steady flow along a streamline

the total energy remains the same.

1.1.2 Bernoulli’s Equation

In its most practical form the theorem can be represented by the following equation, according

to which the total energy per unit weight at any point in a fluid flow system remains a constant.

P

γ + V 2

2g + z = constant (1.1)

where P = static pressure measured at a side hole, V = fluid velocity, z = vertical elevation of the

fluid. Each term of the above equation represents energy per unit weight and has the dimension

of length and hence is known as the energy head. Here P γ

is called pressure head and represents

the pressure energy per unit weight, V 2

2g is called velocity head and represents the kinetic energy

per unit weight, z is called potential head or datum head and represents the potential energy per

unit weight. Sum of all these components is known as the total energy head. When the equation

is applied to any two points, along a streamline in the flow we get:

P 1

γ + V 2

12g + z 1 = P 2

γ + V 2

22g + z 2 = H = constant (1.2)

where subscripts 1 and 2 refer to any two points (1) and (2) If the tube is horizontal, the difference

in height can be disregarded. So the above equation becomes:

P 1

γ +

V 212g

= P 2

γ +

V 222g

(1.3)

since z 1 = z 2

1.1.3 Continuity Equation

For an incompressible fluid, conservation of mass requires that volume is also conserved.

A1V 1 = A2V 2 (1.4)

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1.1.4 Measurements

Static Pressure Head

With the armfield F1-15 apparatus shown in the Figure 1.1, the static pressure head h in meters,

is measured using a manometer directly from a side hole pressure tapping. The static pressurehead is related to the pressure by the following relation (tube is horizontal):

h = P

ρg (1.5)

This allows Bernoulli’s equation to be written in a revised form:

h1 + V 212g

= h2 + V 222g

(1.6)

Figure 1.1: F1-15 Bernoulli’s Theorem demonstration

Total Pressure Head

The total pressure head, ho, can be measured can be measured from a probe with an end hole

facing into the flow such that it brings the flow to rest locally at the probe end. Thus ho = h + V 2

2g

and from Bernoulli’s equation it follows that ho1 = ho2. The term

V 2

2g is called dynamic head.

Velocity

The velocity of the flow is measured by measuring the volume of the flow, V, over a time period.Volumetric measurement is generally done using F1-10 hydraulics bench apparatus as shown

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in Figure 1.2. This gives the rate of volume flow as: Qv = V t

which in turn gives the velocity

of flow through a defined area A.

V = Qv

A (1.7)

Figure 1.2: F1-10 Basic Hydraulics Bench

1.2 EXPERIMENT

1.2.1 Aim

To investigate the validity of the Bernoulli equation when applied to the steady flow of water

in a tapered duct.

1.2.2 Method

To measure flow rates and both static and total pressure heads in a rigid convergent/divergent

tube of known geometry for a range of steady flow rates.

1.2.3 Apparatus

• F1-10 Hydraulics Bench which allows us to measure flow by timed volume collection.

• F1-15 Bernoulli’s Apparatus Test Equipment

• A stopwatch for timing the flow measurement

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1.2.4 Technical Data

The following dimensions from the equipment are used in the appropriate calculations. If re-

quired these values may be checked as part of the experimental procedure and replaced with

your own measurements.

Figure 1.3: Equipment dimensions

1.2.5 Procedure

(i) Level the Apparatus

Set up the Bernoulli equation apparatus on the hydraulic bench such that its base is hori-

zontal. This is necessary for accurate height measurement from the manometers.

(ii) Set the directions of test section

Ensure that the test-section has the 14o tapered sections converging in the direction of flow.If you need to reverse the test-section, the total pressure head probe must be withdrawn

before releasing the mounting couplings.

(iii) Connect the water inlet and outlet

Ensure that the rig outflow tube is positioned above the volumetric tank in order to facil-itate timed volume collections. Connect the rig inlet to the bench flow supply; close the

bench valve and the apparatus flow control valve and start the pump. Gradually open the

bench valve to fill the test rig with water.

(iv) Bleeding the manometers

In order to bleed air from pressure tapping points and manometers, close the bench valve,

the rig flow control valve and open the air bleed screw and remove the cap from the adja-

cent air valve. Connect a length of small bore tubing from the air valve to the volumetric

tank. Now, open the bench valve and allow flow through the manometers—to purge all

air from them; then, tighten the air bleed screw and partly open the bench valve and testrig flow control valve. Next, open the air bleed screw slightly to allow air to enter the

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top of the manometers (you may need to adjust both valves in order to achieve this); re-

tighten the screw when the manometer levels reach a convenient height. The maximum

volume flow rate will be determined by the need to have the maximum (h1) and minimum

(h5) manometer readings both on scale. If required, the manometer levels can be adjusted

further by using the air bleed screw and the hand pump supplied. The air bleed screw

controls the air flow through the air valve, so, when using the hand pump, the bleed screwmust be open. To retain the hand pump pressure in the system, the screw must be closed

after pumping.

1.2.6 Observing Results

Readings should be taken at 3 flow rates. Finally, you may reverse the test section in order to

see the effects of a more rapid converging section.

(i) Setting the flow rate

Take the first set of readings at the maximum flow rate, and then reduce the volume flowrate to give the h1-h5 head difference of about 50 mm. Finally repeat the whole process

for one further flow rate, set to give the h1–h2 difference approximately half way between

that obtained in the above two tests.

(ii) Reading the flow rate

Take readings of the h1-h5 manometers when the levels have steadied. Ensure that the

total pressure probe is retracted from the test-section.

(iii) Timed Volume Collection

You should carry out a timed volume collection, using the volumetric tank, in order todetermine the volume flow rate. This is achieved by closing the ball valve and measuring

(with a stopwatch) the time taken to accumulate a known volume of fluid in the tank, which

is read from the sight glass. You should collect fluid for at least one minute to minimize

timing errors. Again the total pressure probe should be retracted from the test-section

during these measurements. If not using the F1-15-301 software, enter the test results into

the data entry form, and repeat this measurement twice to check for repeatability. If using

the software, perform the collection as described in the walkthrough presentation.

(iv) Reading the total pressure head distribution

Measure the total pressure head distribution by traversing the total pressure probe along

the length of the test section. The datum line is the side hole pressure tapping associated

with the manometer h1. A suitable starting point is 1 cm upstream of the beginning of

the 14° tapered section and measurements should be made at 1 cm intervals along the

test-section length until the end-of the divergent (210) section.

(v) Reversing the test section

Ensure that the total pressure probe is fully withdrawn from the test-section (but not pulled

out of its guide in the downstream coupling). Unscrew the two couplings, remove the test-

section and reverse it; then re-assemble by tightening the coupling.

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1.2.7 Observation Table

Volume Collected,V(m3) Time to collect,t(sec) Flow rate,Qv (m3/sec) Area of duct,A(cm2) Static head,h(m) Velocity,v(m/sec) Dynamic head(m) Total head(m)

6.16

4.34

2.69

1.54

2.69

4.34

6.16

Note: Total Head = Static head + Dynamic head

1.2.8 Discussion

(i) What are the conditions under which the Bernoulli’s equation is valid and are they being

fulfilled in the experiment?

(ii) Practical application of Bernoulli’s theorem in real life.

(iii) Is there any restriction to the cross-sectional area that you can have at the junction of the

converging and diverging portions?

1.2.9 Precautions

(i) It is to be ensured that there are no air bubbles in the manometer

(ii) Each reading be taken only when the steady state conditions are established

(iii) There should be no leakage between upstream and downstream end of the conduit

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2

CENTRIFUGAL PUMP CHARACTERISTICS

CURVE

2.1 THEORY2.1.1 Introduction

In centrifugal pump, the fluid is drawn into the centre of a rotating impeller and is thrown

outwards by centrifugal action. As a result of the high speed of rotation, the liquid acquires a

high kinetic energy. The pressure difference between the suction and delivery sides arises from

the conversion of this kinetic energy into pressure energy. This conversion process of energy

into pressure is done by two main parts:

(i) Impeller: Rotating part that converts the driver energy into kinetic energy.

(ii) Volute (diffuser): The stationary part that converts the energy into pressure.

The impeller is a high speed rotary element with radial vanes integrally cast in it. Liquid flows

outward in the spaces between the vanes and leaves the impeller at a considerably greater ve-

locity with respect to the ground than at the entrance to the impeller. The amount of energy

given to fluid is directly proportional to the velocity of the flow at the edge of the vanes of the

impeller; the faster the impeller is (v = ω ∗ r) or the larger it was the larger kinetic energy istransformed to the fluid. This kinetic energy of the fluid coming out of an impeller is harnessed

by creating a resistance to the flow. The first resistance is created by the pump volute (casing)

that catches the liquid and slows it down. The liquid then leaves the pump through a tangential

discharge connection. In the volute the velocity head of the liquid from the impeller is con-verted into pressure head. In the discharge nozzle, the liquid further decelerates and its velocity

is converted to pressure according to Bernoulli’s principle. The power is applied to the fluid by

the impeller. The impeller is directly connected through a drive shaft to an electric motor. The

work performed in changing the energy stages of a unit mass of the fluid may be expressed as

the total dynamic head (H) of the pump.

H = (v22 − v21)/2g + (z 2 − z 1) + ( p2 − p1)/ρg (2.1)Since the pipe diameters are similar, the first term is negligible and the above equation reduces

to:

H = (z 2 − z 1) + ( p2 − p1)/ρg = (z 2 − z 1) + (h2 − h1) (2.2)

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The relative vertical distance between the inlet and outlet may then be expressed as head dif-

ference:

H d = (z 2 − z 1) = hd(outlet)− hd(inlet) = 0.15m (2.3)

Substituting the above equation in Equation 2.2 gives head generated across the pump asfollows:

H = H d + (h2 − h1) (2.4)In the laboratory, centrifugal pump characteristics are investigated using the armfield F1-27

apparatus as shown in the figure below:

Figure 2.1: F1-27 Centrifugal Pump Characteristics

2.1.2 PrincipleThe centrifugal pump is a rotodynamic machine, which increases the pressure energy of a liquid

with the help of centrifugal action. In this type of pump the liquid is imparted a whirling motion

due to the rotation of the impeller which creates a centrifugal head or dynamic pressure. This

pressure head enables the lifting of liquid from a lower level to a higher level.The fluid flows

from the inlet to the impeller centre and out along its blades. The centrifugal force hereby

increases the fluid velocity and consequently also the kinetic energy is transformed to pressure.

Centrifugal pumps are fluid- kinetic machines designed for power increase within a rotating

Impeller. Therefore it is also called the hydrodynamic pumping principle. According to this

principle, the fluid is accelerated through the impeller. In the outlet connection of the centrifugal

pump, the resulting increase in speed is converted into delivery head.

2.1.3 Performance Curve

Every pump’s performance is represented by the pump performance curve which is a plot of

the developed head against the flow rate. The curve also shows the efficiency of the pump, the

speed of the impeller and its size. These curves are generated according to tests performed by

the manufacturer.

2.1.4 Efficiency

The efficiency is an important factor in selecting a pump and it represents the ratio betweenenergy inputs (from motor) to energy output (to the flow) of the pump.

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2.1.5 Pumps in series and parallel

Sometimes the required head for a system can’t match any single pump performance curve or

the suitable pump is not in stock. In such cases two or more pumps can be connected in series

to increase the head coming out of pumps. Pumps are connected in series by attaching one of

the pump’s discharge to the other one’s suction. When larger flow rate is required and no single pump is available for use, then two or more pumps can be connected in parallel. Pumps are

connected in parallel when their discharge is connected to a common pipe. In the experiment

we deal with single pumps and pumps in parallel.

2.2 EXPERIMENT

2.2.1 Aim

• To investigate the operating characteristics of a centrifugal pump used to transport water

• Explore characteristic curve of varying head versus the volumetric flow rate

• Obtain a head-flow curve for a centrifugal pump operating at inherent speed

• To study the performance of centrifugal pumps by plotting the performance charts

2.2.2 Apparatus

• Hydraulics bench which provides one of the two pumps used during this experiment, and

allows the volume flow rate to be measured by timed volume collection

• Centrifugal Pump

• Stopwatch

• Pressure Gauges

• Digital Tachometers which read the rotation speed in rpm

2.2.3 Procedure

Single Pump Operation

(i) Empty the tank and set the inverter to the value of 50 Hz and run the machine.

(ii) Note down the initial readings for inlet head, outlet head and also the pump power input

(watts)

(iii) Now open the valve a little and allow some water to flow into the tank.

(iv) Note down the time taken to fill the tank by 5 litres from the measuring tube on the side

of the equipment.

(v) At this point also note down the values from the for inlet head, outlet head and the pump

power input values.

(vi) Now increase the flow more by opening the valve further and repeat steps 4 to 6.

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(vii) Repeat this procedure 5 times for Frequency of 50 Hz.

(viii) Perform the above steps 1-7 for frequencies: 45, 40, 35, and 30 Hz.

Parallel Pump Operation

• Change the setup by switching on the second pump in parallel.

• Perform steps 1-7 for frequency 50 Hz for parallel pump operations.

Conversion of frequency into RPM: The frequency of the pump is multiplied by 56 to know

the RPM of the pump. The following table gives the speed of the pump for the corresponding

frequency:

Frequency (Hz) Speed (rpm)

50 2800

45 252040 2240

35 1960

30 1680

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2.4 Observation Table

No. Speed(rpm) Volume of water(L) Time to collect(s) Inlet head(mm of Hg) Outlet Head(m) Power input(KW) Inlet head(m) Discharge(cms) Total head(m) Power(KW) Efficiency(%)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

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2.2.5 Discussion

(i) Explain how the pump characteristics curves will help in choosing the pump?

(ii) By comparing the curves of head against flow rate and overall efficiency against flow rate

determine the optimum operating point for different speeds of the pump.

(iii) Discuss about the performance curves of single pump and parallel pumps for same speed.

Do we get double the flow rates for parallel pump? Give reasons for any differences

observed.

(iv) Discuss the nature of the characteristic curves obtained.

2.2.6 Precautions

(i) Prime the pump to remove the air completely before starting the pump.

(ii) After each change in the valve opening let the flow stabilize before taking readings.

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3

ENERGY LOSSES IN PIPES

3.1 THEORY

3.1.1 IntroductionThere is a pressure drop when a fluid flows in a pipe because energy is required to overcome

the viscous or frictional forces exerted by the walls of the pipe on the moving fluid. In addition

to the energy lost due to frictional forces, the flow also loses energy as it goes through fittings,

such as valves, elbows, contractions and expansions. This loss in pressure is often due to the

fact that flow separates locally as it moves through such fittings. The pressure loss in pipe flows

is commonly referred to as head loss. The frictional losses are referred to as major losses while

losses through fittings, etc, are called minor losses. Together they make up the total head losses

for pipe flows.

3.1.2 Major Losses

While the nature of flow depends upon Reynolds Number, the frictional resistance offered to

the flow of fluids depends essentially on the roughness of the surface of the conduit carrying

the flow. This frictional resistance causes the loss of head, hf , which is given by Darcy and

Weisbach equation:

hf = f

L

D

v2

2g (3.1)

where L = length of the pipe, d = diameter of the pipe, v = average fluid velocity of the pipe, f

= friction factor.In general, the friction factor is a function of the Reynolds Number (Re) and the non-dimensional

surface roughnessK sd

and is determined experimentally. v in terms of volume flow rate Qt is

given by:

v = 4Qtπd2

(3.2)

Reynolds Number (Re) is given by:

Re = vd

ν (3.3)

where ν is the kinematic viscosity of fluid.

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The plot of f versus Re is usually referred to as Moody diagram and is shown below:

Figure 3.1: Moody’s Diagram

Two types of flow may exist in pipe: Laminar and Turbulent. In laminar flow frcitional

resistance is mostly due to viscous resistance of fluid to flow and h ∝ u. In turbulent flow,frictional resistance is due to resistance offered by viscosity of fluid and surface roughness of

the conduit and h ∝ un.

Figure 3.2: Head loss vs Velocity

where h = head loss and u = fluid velocity.

The theoretical formulation for laminar flow is:

f = 64

Re(3.4)

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For turbulent flow in a smooth pipe, a well-known curve fit to experimental data is given

by:

f = 0.316 ∗ R−0.25e (3.5)

3.1.3 Minor Losses

Minor losses in pipe flow occur due to pipe entrance or exit; sudden expansion or contraction;

bends, elbows, tees, and other fittings; valves, open or partially closed; gradual expansions or

contractions.

The most common equation used to determine these head losses is:

hL = ∆ p

ρg = K L

v2

2g (3.6)

where K L is loss co-efficient. Although K L is dimensionless, it is not correlated with Reynolds

number and roughness ratio but is correlated with the size of the pipe only.

In laboratory, we determine head loss or friction factor using armfield F1-18 apparatus as

shown below:

Figure 3.3: F1-18 Energy losses in pipes

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3.2 EXPERIMENT

3.2.1 Aim

To investigate the head loss due to friction when the water through a pipe and to determine the

associated friction factor. Both variables are to be determined over a range of flow rates andtheir characteristics identified for both laminar and turbulent flows.

3.2.2 Apparatus

• F1-10 Hydraulics Bench which allows to measure flow by timed volume collection.

• F1-18 Pipe Friction Apparatus.

• Stopwatch to allow us to determine the flow rate of water.

• Thermometer

• Measuring cylinder for measuring very low flow rates

3.2.3 Technical Details

The following dimensions of the equipment are to be used in the appropriate calculations. If

required these values may be checked as part of the experimental procedure and replaced with

your own measurements.

• Length of test pipe L = 0.5 m

• Diameter of test pipe d = 0.003 m

3.2.4 Procedure

(i) Check for a constant head in the reservoir tank.

(ii) Change head and try to make it constant by opening the valve.

(iii) Allow a minimum flow to occur when the head is constant by opening the tap.

(iv) Collect volume of water for t seconds and note down the readings for Head 1 and Head 2

(mercury levels)

(v) Repeat the step 4 for 12 different (increasing) flows through the valve.

(vi) Make sure that there are no fluctuations in the readings of the two: h1 and h2. If there is

fluctuation, take average of the top and bottom readings of the fluctuation.

(vii) Measure the temperature of the water in the tank using a thermometer by placing it in

water for 10 seconds.


Temperature of the water:Kinematic Viscosity (Search for corresponding value from internet with respect to temperature):

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Volume,V(*106m3) Ti me t o col lect ,t (sec) h1(mm) h2(mm) Head l oss(mm) F low rat e, Q(*106m3/sec) Velocity,v(m/sec) Friction factor,f Reynolds number,Re

3.2.6 Model Calculation

Do a single calculation of the above work.

3.2.7 Graph

(i) Plot graph between ln(Reynolds number) vs ln(friction factor)

(ii) Plot graph between ln(head loss) vs ln(velocity)

3.2.8 Discussion

(i) What is the reason behind the fluctuations in the readings of the heads?

(ii) What is the effect of temperature on head loss?

(iii) What are the practical applications of this experiment?

(iv) What is the dependence of head loss upon flow rate in the laminar and turbulent regions

of flow?

(v) Identify the laminar and turbulent flow regimes. What is the critical Reynolds number?

(vi) Assuming a relationship of the form f = KRne , calculate these values from graphs youhave plotted and compare these with the accepted values.

(vii) What is the cumulative effect of experimental errors on the values of K and n?

(viii) Why head in the tank is kept constant?

3.2.9 Precautions

(i) There should be no leakage from any of the pipe fittings.

(ii) Ensure that there is no air bubble in the manometer.

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4

FLOW OVER WEIRS

4.1 THEORY

4.1.1 IntroductionA weir is a device used for measurement of flow in open channels and rivers. It is nothing but a

partial obstruction placed across the flow in the channel causing the liquid to backup, upstream

of the obstruction and then flow over it. Thus the discharge thorugh an open channel can be

obtained by the measurement of a single parameter i.e., the head of liquid above the crest of

the weir. In open channel hydraulics, weirs are commonly used to either regulate or to measure

the volumetric flow rate. They are of particular use in large scale situations such as irrigation

schemes, canals and rivers. For small scale applications, weirs are often referred to as notches

and invariably are sharp edged and manufactured from thin plate material. There are different

shapes of weirs that can be used to measure the volumetric flow rate. These shapes with their

dimension are shown below:

Figure 4.1: Different shapes of notches

4.1.2 Rectangular Weir

A rectangular notch is a thin square edged weir plate installed in a weir channel as shown in Fig

4.2. The head H on the weir is defined as the vertical distance between the weir crest and theliquid surface taken far enough upstream of the weir to avoid local free-surface curvature.

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Figure 4.2: Rectangular Notch

The discharge equation for the weir is derived using velocity of approach method i.e., by

integrating V dA = V Ldh. over the total head on the weir. Here, L is the length of the weir andV is the velocity at any given distance h below the free surface. Neglecting streamline curvature

and assuming negligible velocity of approach upstream of the weir, one obtains an expression

for V by writing the Bernoulli equation between a point upstream of the weir and a point in the

plane of the weir. Assuming the pressure in the plane of the weir is atmospheric, this equation

is:

p1

γ + H = (H − h) + V

2

2g (4.1)

Here the reference elevation is the elevation of the crest of the weir, and the reference pres-

sure is atmospheric pressure. Therefore p1 = 0 and the above equation reduces to:

V =√

2gh (4.2)

dQ =√

2ghLdh and the discharge equation becomes:

Q =

∫ H 0

√ 2ghLdh =

2

3L√

2gH 3/2 (4.3)

In the case of actual flow over a weir, the streamlines converge downstream of the plane of the

weir, and viscous effects are not entirely absent. Consequently, a discharge coefficient, C d must

be applied to the basic expression on the right-hand side of the equation to bring the theory in

line with the actual flow rate. Thus the rectangular weir equation is:

Q = 2

3C dL

√ 2gH 3/2 (4.4)

4.1.3 Triangular Weir

The discharge equation for the triangular weir is derived in the same manner as that for the

rectangular weir using velocity of approach method and Bernoulli’s equation.

Q = 8

15C d tanθ

2√ 2gH 5/2 (4.5)

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Figure 4.3: Triangular Notch

The coefficient of contraction of a notch depends upon the length of the wetted perimeter.

In a triangular notch there is no base to contraction. The contraction is due to sides only. Con-sequently the coefficient of discharge is nearly constant in a triangular notch for all heads. A

triangular notch is very accurate for the measurement of low discharges.

4.1.4 Depressed and Clinging Nappe

When a weir discharges freely at a reasonably high flow rate the nappe springs clear of the

downstream face of the weir and the nappe is surrounded by air at atmospheric pressure. In

a suppressed weir discharging between the walls of a discharge channel of the same width,

the nappe will remain in contact with the discharge channel walls. If no provision is made to

ventilate the space under the nappe by supplying air, then a partial vacuum will be produced.

The discharge will then be increased due to the lower pressure under the nappe and the nappewill also be depressed or drawn towards the weir. In extreme cases the whole of the volume of

air behind the nappe will be ejected and a turbulent recirculating volume of water will occupy

the space under the nappe. This condition is known as a drowned nappe or underwetted nappe.

With very low heads, particularly if the head is increasing from zero, the nappe will adhere

or cling to the downstream face of the weir with an increased discharge which may be 30 percent

higher than for the same head with the nappe discharging freely. The nappe will spring clear

of the weir when the head increases to an extent where the liquid surface tension and the local

pressure at the weir downstream face allows the admission of air or the release of vapour.

(a) Springing Clear (b) Depressed Nappe (c) Drowned Nappe (d) Clinging Nappe

Figure 4.4: Nappe along the hydraulic structure

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4.2 EXPERIMENT

4.2.1 Aim

• To determine the characteristics of open channel flow over triangular and rectangular

weirs.

• To determine the coefficient of discharge for each type of weir.

4.2.2 Apparatus

(i) Hydraulic bench which is used to measure flow by timed volume collection

(ii) Triangular(Vee) notch with an angle of 90o

(iii) Vernier height gauge to measure the head difference

(iv) Stop watch for timed collection of water

(v) Spirit level to check the surface horizontality

(vi) Stilling baffle to reduce the turbulence of the flow

Figure 4.5: F1–13 Flow over Weirs-Vee notch weir

4.2.3 Experimental Setup

It consists of one hydraulic bench with a flow channel in it. Make sure that the hydraulic bench is

positioned so that its surface is horizontal. Mount the Vee notch plate into the flow channel at theoutlet and also position the stilling baffle at the inlet to reduce the turbulence of the flow. Then

mount the instrument carrier with vernier height gauge and it should be located approximately

half the way between stilling baffle and Vee notch plate, to avoid surface curvature and end

contractions near the Vee notch plate and turbulence near the inlet.

4.2.4 Procedure

(i) Measure the datum height of base of the Vee notch with the help of height gauge. Height

gauge is provided with one drop adjustment screw and one fine adjustment screw. First

lower the gauge using coarse adjustment screw until its tip is just above the datum height

and then use fine adjustment screw for accurate adjustment.

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(ii) Start the pump and control the flow using bench regulating valve to get the required head

in the flow channel. Once the flow height is stabilized, measure the height of the flow

(water level) using height gauge.

(iii) While taking the readings of water level, adjust the height gauge till tip of the gauge

coincides with its reflection in the water.

(iv) Close the outlet valve of volumetric tank and measure timed volume of the flow.

(v) Repeat the steps (2) to (4) for different flows, which can be adjusted using bench regulating

valve.

(vi) Take care not to allow spillage over the plate top adjacent to the notch and also clinging

to the notch.

4.2.5 Observations

Angle of Vee Notch =

Flow number Notch type Datum height,ho(m) Water level,h(m) Volume collected,V(m3) Time taken for collection,t(sec)

1

2

3

4

5

6

4.2.6 Calculations

Volume flow rate (m3/sec) = Volume collected / Time takenHeight above the notch = (h − ho), (m)Discharge Coefficient C d =

Q815

tanθ2

√ 2gH 5/2

For flow number 1,

Volume flow rate =

Height above the notch =

Discharge Coefficient C d =

Similarly, note the other observations as follows:

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Flow number Volume flow rate,Qt(m3/sec) Height above notch,H = h − ho(mm) H 5/2 C d1

2

3

4

5

6

Plot the graph (Q vs H 5/2) which looks like below:

Figure 4.6: Q vs H 5/2

From the graph plotted above,

The best fit line equation is, y =

Slope (theoretical value) =

Slope (experimental value) =

C d (theoretical value) =

C d (experimental value) =

4.2.7 Results

Theoretical C d value =

Experimental C d value =

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4.2.8 Discussion

(i) Compare the experimental results to the theory.

(ii) What are the limitations of the theory?

(iii) Why would you expect wider variations of C d values at lower flow rates?

(iv) In what situations, a rectangular notch is used and a V notch is used?

4.2.9 Precautions

(i) Each reading be taken only when the steady state conditions is established and the head

remaining constant

(ii) Preferably flow rate for each reading be recorded over the same time period which being

sufficiently large

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5

GUELPH PERMEAMETER

5.1 THEORY

5.1.1 IntroductionThe determination of the steady state infiltration rate and hydraulic conductivity of soils in the

field is an important measurement in order to determine the hydraulic properties of the soil

and to track the fate of infiltrating rain and irrigation water. Borehole permeameters are used

to determine in-situ saturated hydraulic conductivity in soils, when steady state infiltration is

achieved i.e., the rate of infiltration is constant.

The Guelph permeameter provides a good estimation of the field saturated hydraulic con-

ductivity, matrix flux potential and soil sorpitivity in the field. The Guelph Permeameter works

by creating constant head permeability test within the hole according to the Marriotte Principle.

At the start of a test, the hole is flooded with water to create a constant head inside the hole. Theoutflow of water from the reservoir and into the hole creates a partial vacuum above the water

level in the reservoir. The sum of the pressures of the head height of the water reservoir and the

partial vacuum will equilibrate to the atmospheric pressure acting on the water in the hole.

When the user raises the upper air tube to the chosen height, the lower air tube will be also

be raised by that height. When the lower air tube is raised, water will fill the hole until it reaches

the air inlet tip. As water infiltrates through the soil, it will cause the water level in the hole to

fall. Once the water level has fallen below the Air inlet Tip then the now exposed Air Inlet Tip

will allow air to rush into the reservoir and relieve the partial vacuum. This in turn causes the

water in the reservoir to run out and back into the hole, where it will rise up to the level of theAir Inlet Tip.

5.1.2 Principle

The Guelph Permeameter is an in-hole constant-head permeameter, employing the Marriote

principle. The method involves measuring the steady-state rate of water recharge into unsatu-

rated soil from a cylindrical well hole, in which a constant depth (head) of water is maintained.

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5.2 EXPERIMENT

5.2.1 Aim

To determine the field saturated hydraulic conductivity K f s(cm/sec), matrix flux potential

φ(cm2/sec) and macroscopic capillary length parameter (α∗) of soil with the help of in-holeconstant head permeameter (Guelph Permeameter) set-up. The experiment is performed for

two different head levels.

5.2.2 Apparatus

(i) Toothed and flat bottomed augers for hole preparation

(ii) Guelph Permeameter setup

(iii) Small water tank

(iv) Measuring scale

Figure 5.1: The Guelph Permeameter Kit(2800KI) components in carrying case

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Figure 5.2: Guelph Permeameter Support Kit

Figure 5.3: Guelph Components (detailed)

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It is advisable to do all the setup away from the test hole because spilled water could affect the

test results.

Base

To construct the base of the Permeameter, take the three tripod legs and stick them into therubber tripod base. As the base is rubber rather than rigid, it is advisable to use the chain to

create more stability and prevent the legs from splaying out.

Support Tube

The Support tube fits into the bottom of the reservoir tube. However, before that step,

you must add in the Lower Air Tube and the Tripod Bushing. The Lower Air Tube connects

to the Middle Air Tube by one of the black rubber tubes found with the kit. According to

the documentation, this connection should be made with a different connector that has fins to

provide stability within the support tube, but that piece appears to be missing. The Tripod

bushing should be added to the exterior of the support tube with the smaller end pointing down

before connecting the support tube to the reservoir. The support tube can then be joined to the

reservoir.

Top

First, add the Well Head Marker to the top of the middle air tube. This is used to mark the

height of the water in the hole. Next, connect the Upper Air Tube to the Middle Air Tube via

one of the black rubber tubes. Like the other connector, in the documentation this piece appears

to have fins for stability, but the piece described in the documentation appears to be missing.

Finally, add the Well Height Scale to the top. The Well Head Marker should be adjusted so that

it sits at 0 when the Air Tube Assembly is pushed all the way down such that the Air Inlet Tip

is at the bottom of the Support Tube.

Test Preparation

Set up the Guelph Permeameter by threading the support tube through the hole in the tripod base. The Tripod Bushing should sit on the tripod base, and the end of the support tube should

be in the air or on the ground. Next, remove the cork from the top of the Reservoir tank and

fill the reservoir to the desired height. (It is unclear if the height of the water in the reservoir

affects the test in any way) It is useful to bring both a large water carrying container for water

storage and a smaller container such as a 500 mL graduated cylinder for pouring the water into

the reservoir. If the notch on the knob at the bottom of the reservoir is pointing upwards, then

both reservoirs will fill. If it is pointing down, only the inner reservoir will fill. According to

the documentation, using only the inner reservoir is preferable for soils with a lower hydraulic

conductivity, although only the Combination Reservoir method has been tested. It is extremely

important that the cork be replaced once the reservoir has been filled or else the test will notwork and the hole will flood.

Hole Preparation

Once a site has been selected, dig down to roughly 15 cm (∼6 inches) above the desireddepth of the hole. The Auger head provided in the Guelph Permeameter kit appeared badly

damaged with the ”teeth” flattened. It was not useful for digging, so a different auger was

used for the initial hole. It may be useful to save the soil from the freshly dug hole for later lab

analysis. Once the initial depth has been reached, switch auger heads to the flat-bottomed auger.

This Auger head creates a smooth and flat bottomed hole that is more uniform than the other

auger. Dig down approximately 15 cm (∼6 inches) with this head. Once the hole is finished,

take the brush and brush up and down several times in the hole. This is designed to eliminatesmearing on the side of the hole that may have occurred during digging.

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Testing

At this point, the Guelph Permeameter is placed into the hole. The bottom of the outlet

tip should be in contact with the bottom of the hole. Once the Permeameter is situated, the

Tripod bushing should be pushed down to fit into the Tripod Base for stability. The legs on the

Tripod can also be splayed out if the hole is especially deep, or, if the hole is extremely deep, thedocumentation says that the Tripod bushing can be used as the base and the tripod legs can be

done away with entirely. Once the Permeameter is situated properly, pull up the upper air tube

so that the Well Head Marker is at the appropriate height. The water should fill the hole up to the

bottom of the Air Inlet Tip. (If the water fills higher than that, this could be a sign of a seal issue

within the Guelph Permeameter. More info on this and other problems is in the Troubleshooting

page.) Take height measurements of the water level at the proper intervals (generally 2 minutes,

but adjustable depending on the soil) and record the data. The test is complete when the drop

in the reservoir is maintained at a steady rate for three straight intervals. This indicates that the

soil has reached saturation and you are observing the saturated conductivity.

5.2.4 Procedure

(i) Set up the Guelph Permeameter by threading the support tube through the hole in the tripod

base.

(ii) Next, remove the cork from the top of the reservoir tank and fill the reservoir to the desired

height.

(iii) If the notch on the knob at the bottom of the reservoir is pointing upwards, then both reser-

voirs will fill. If it is pointing down, only the inner reservoir will fill. In this experiment

we perform Combination Reservoir method.

(iv) Pull the air tube up to 5 cm mark to create a constant head of 5 cm in the hole.

(v) Start the stop watch and record the water level in the reservoir at regular intervals.

(vi) Calculate rate of change of head at each interval and continue the experiment till a constant

rate of change in head is obtained.

(vii) Now pull up the air tube to 10 cm mark and perform the similar experiment for 10 cm

constant head.

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Depth of hole:

Radius:

Water level in well = 5cm

Time,t(min) ∆t(min) Water level in reservoir,h(cm) ∆h(cm) Rate of change, R1 = ∆h/∆t(cm/min)

Steady state for 3 consecutive readings (R1):

Water level in well = 10cm

Time,t(min) ∆t(min) Water level in reservoir,h(cm) ∆h(cm) Rate of change, R2 = ∆h/∆t(cm/min)

Steady state for 3 consecutive readings (R2):

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5.2.6 Calculations

(i) Field Saturated Hydraulic Conductivity K fs(cm/sec) = A×10−5(6.8R2−9R1)(cm/sec)

(ii) Matrix flux potential φ(cm2/sec) = A × 10−4(9.5R2 − 3.9R1)(cm2/sec)

(iii) Macroscopic Capillary length parameter α∗ = K fsφ (cm−1)

where A is the cross-sectional area of the outer reservoir tube and is equal to 28.274 cm2

5.2.7 Discussion

Soil texture-structure categories for site-estimation of α:

Soil Texture - Structure Category α∗ (cm−1)

Compacted, structureless, clayey or silty materials such as landfill caps and liners, lacustrine or marine sediments, etc. 1.01

S oi ls whi ch are bot h fine t extured (cl ayey or sil ty) and unstructured; may also i nclude some fine sands. 0.04

Most structured soils from clays through loams; also includes unstructured medium and fine sands. The category most frequently applicable for agricultural soils. 0.12

Coarse and gravelly sands; may also include some highly structured soils with large and/or numerous cracks, macro pores, etc. 0.36

Macroscopic capillary length parameter α∗ represents the ratio of gravity to capillary forces

during infiltration or drainage. Large α∗ values indicates dominance of gravity over capillarity,

which occurs primarily in coarse textured and/or highly structured porous media. Small α∗

values indicate dominance of capillarity over gravity which occurs primarily in fine textured

and/or unstructured porous media. Although , K fs and φ can individually range over many

orders in magnitude in a porous medium, α∗ generally varies from about 0.01 cm−1 to 0.5

cm−1

.

5.2.8 Applications

• The Guelph Permeameter can be used wherever a hole can be augured in soil. The above

instructions present a generalized method for determining field-saturated hydraulic con-

ductivity, matric flux potential, and α∗ parameter.

• Guelph Permeameter is ideally suited for involving analysis and design of irrigation sys-

tems, drainage systems, canals, reservoirs, sanitary landfills, land treatment facilities,

tailings areas, hazardous waste storage areas, septic tank systems, soil and hydrologic

studies and surveys

• The Guelph Permeameter can be used to investigate changes in the hydraulic properties

of soils with depth.

• A soil profile description and soil survey report will greatly enhance the value and under-

standing of data obtained with the Guelph Permeameter.

• Because of the ease and simplicity of the Guelph Permeameter and its depth profiling

capability, it is a very useful method for understanding the three-dimensional distributions

of the water transmission properties of soils.

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6

HYDRAULIC JUMP

6.1 THEORY

6.1.1 IntroductionThe sudden, turbulent passage of water from a super-critical state to a sub-critical state causes

the formation of hydraulic jump. Hydraulic jump frequently occurs in a canal below a sluice,

at the foot of a spillway or when a steep channel slope meets a flat slope. Hydraulic jump is a

very useful means of dissipation of energy which otherwise, would cause damages downstream.

Hydraulic jump analysis can be carried out by making the following assumptions:

• The flow is uniform and hence the pressure distribution is hydrostatic, before and after

the formation of jump.

• The length of jump is small so that frictional losses can be neglected.

• The weight component of the water mass in the direction of flow is negligible.

• Channel bed is horizontal.

6.1.2 Analysis of hydraulic jump in horizontal rectangular channel

Consider the flow situation, shown in Figure 7.2 below, in which section 1 is in supercritical

zone and section 2 is in sub-critical zone. Two equations can be used to describe the hydraulic

jump with the above assumptions. One is conservation of mass and other is conservation of

linear momentum.

Conservation of mass

Since the flow rate is constant in sections 1 and 2, we have:

Q1 = Q2 (6.1)

V 1A1 = V 2A2 (6.2)

For constant width:

V 1h1 = V 2h2 (6.3)

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Figure 6.1: Hydraulic Jump

Conservation of linear momentum

Newton’s second law states that the net force acting on a body in any fixed direction is equal

to the rate of increase of momentum of the body in that direction. Using relation obtained from

conservation of mass:

ΣF x = F 1 − F 2 = ρgh212 − ρg h

22

2 = qρ(v2 − v1) (6.4)

h2h1

= 12

1 + 8v21gh1

− 1 (6.5)

where q is flow rate per unit width. The above equation is known as Belorngers equation. Here,

we define F r1 = v1√ gh1

and F r1 is called Froude number at section 1.

Energy Loss

Applying Bernoulli’s equation between section 1 and section 2 and taking bed of channel as

datum equation for energy loss in hydraulic jump can be derived. The equation for energy loss

is:

hL =

(h2−

h1)3

4h1h2 (6.6)

6.2 EXPERIMENT

6.2.1 Aim

To study charateristics of hydraulic jump


(i) Hydraulic jump setup (glass-walled rectangular flume), with ogee and step spill ways oneither side, of 5m long, 0.4m wide and 0.8m deep. This setup also consists of sluice gate

at inlet end and tail gate at the downstream end.

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(ii) Calibrated meter scale, mounted on the top with a roller and with a sharp end, to measure

the heights of the flow just before and after the jump.

(iii) Another meter scale, to measure length of jump i.e. distance between the points the height

is measured.

(iv) A piece of chalk, to mark the points at which the height is measured.

6.2.3 Procedure

(i) By adjusting the supply valve, sluice gate, and the tail gate, we need to form a stable

hydraulic jump in the flume.

(ii) Take the pointer gauge readings for the bed levels and water surface elevations at pre-jump

section (1) and post-jump section (2) to get heights (h1, h2) of jump.

(iii) Measure the discharge using head measured at top of notch.

(iv) Repeat steps (1) to (3) for other positions of valve, sluice gate, and tail gate.

6.2.4 Observations and Calculations

S.No. Height above notch, H ′

(cm) Length of Jump, L(cm) H ′

1(cm) H ′

2(cm)

Ogee Spillway

1

2

3

4Step Spillway

1

2

3

4

Bottom value of notch = a

Bottom value of channel bed = b

Width of flume =

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S .No Lengt h of Jump, L Hei ght over Weir,H = H ′

− a H 1 = H ′

1 − b H 2 = H

′

2 − b Flow Rate,Q V 1 V 2 F r1 E1 E2 hL hj hj/E1 hL/E1

(cm) (cm) (cm) (cm) (m3/s) (m/s) (m/s) (m) (m) (m) (m)

gee Spillway

1

2

3

4

tep Spillway

1

2

3

4

2.5 Graphs(i) Plot h2/h1v/sF rl on a simple graph paper. On the same plot also draw the line.

ii) Plot hL/E 1 and h j/E 1 for various values of F r1.

2.6 Results and Discussions

bserve graphs and discuss your observations.

2.7 Applications

(i) Usually hydraulic jump reverses the flow of water. This phenomenon can be used to mix chemicals for water purification.

ii) Hydraulic jump usually maintains the high water level on the downstream side. This high water level can be used

for irrigation purposes.

ii) Hydraulic jump can be used to remove air from water supply and sewage lines to prevent the air locking

v) It prevents the scouring action on the downstreamside of the dam structure

v) It is most commonly used choice of design engineers for energy dissipation below spillways and outlets.

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6.2.8 Questions

(i) Identify different types of jumps that were occurred while doing experiments?

(ii) If channel is not rectangular, then what is your observation on this experiments?

(iii) What are all practical applications of hydraulic jump?

(iv) What are all your observations on jumps occurred in both types of spillways?

(v) What are all different types of conditions for hydraulic jump to occur?

(vi) How hydraulic jump can be classified based on Froude number?

(vii) Explain briefly phenomenon of hydraulic jump?

(viii) What is the other way of deriving Belongers equation?

(ix) The equation given for energy loss in above theory, can it applicable for jump occurred incompound channel?

(x) What is approximate time to be waited to get proper jump after adjusting sluice gate?

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7

IMPACT OF JET

7.1 THEORY

7.1.1 IntroductionWater turbines are widely used throughout the world to generate power. In the type of water

turbine referred to as a Pelton wheel, one or more water jets are directed tangentially on to vanes

or buckets that are fastened to the rim of the turbine disc. The impact of the water on the vanes

generates a torque on the wheel, causing it to rotate and to develop power. Although the concept

is essentially simple, such turbines can generate considerable output at high efficiency. Pow-

ers in excess of 100 MW, and hydraulic efficiencies greater than 95 percent, are not uncommon.

To predict the output of a Pelton wheel, and to determine its optimum rotational speed, we

need to understand how the deflection of the jet generates a force on the buckets, and how the

force is related to the rate of momentum flow in the jet. In this experiment, we measure theforce generated by a jet of water striking a flat plate or a hemispherical cup, and compare the

results with the computed momentum flow rate in the jet. A jet of water striking a solid surface

will exert a force on the surface and continue to flow along the surface. For a jet of steady

velocity which is not highly turbulent the rebound of water from the surface will be negligent.

If we neglect the frictional forces by assuming water as an inviscid fluid and neglect the energy

losses due to shocks and turbulence, we can see that the velocity of the fluid stream does not

change in magnitude after striking the solid surface. Hence the change in momentum at surface

is not from the change in magnitude of the jet but from change in direction.

Considering typical target vanes as shown in Fig 7.1 (flat, conical and semi-spherical), thewater deflects at a different angle from each of them along its surface. For the flat target vane

the water deflects at an angle of 90o. For the conical target vane the water deflects by an angleof 45o. For the semi-spherical target vane the water is deflected by an angle of 135o. To find theforce exerted by the water jet we have to find the change in momentum of the water jet upon

incidence on the target vane. We have already established that the change in momentum occurs

only in direction and not in magnitude.

Applying Newton’s Second Law of Motion along the direction of the water jet,

Force = Rate of change of momentum

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Figure 7.1: Different target vanes (flat, conical and semi-spherical from left to right)

As velocity is constant in magnitude and time independent,

Force = Mass×Change in VelocityForce,F = M∆V

where M is mass of waternd and V is the impact velocity of the jet.

Relation between the total Mass of water with density ρ and volumetric flow rate Q is given

by:M = ρQ (7.1)

The change in velocity of a water jet with impact velocity V i when deflected by an angle θ

is given by:

∆V = V i − V i cos θ = V i(1 − cos θ) (7.2)Hence force on impact is given by:

F = ρQV i(1 − cos θ) (7.3)

F

ρQV i= (1

−cos θ) (7.4)

In all cases of vanes it is assumed that there is no splashing or rebound of the water from the

surface so that the exit angle is parallel to the exit angle of the target.

7.1.2 Effect of height

The jet velocity can be calculated from the measured flow rate and the nozzle exit area.

V n = Q

A (7.5)

However, as the nozzle is below the target, the impact velocity will be less than the noz-

zle velocity due to interchanges between potential energy and kinetic energy. Applying the

Bernoulli equation between nozzle and plate:

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P

γ +

V 2n2g

+ Z n = P i

γ +

V 2i2g

+ Z i (7.6)

Since the jet is open to the atmosphere, we have:

P γ − P i

γ = 0 (7.7)

Z n − Z i = 0 (7.8)Therefore,

V 2i = V 2n − 2gh (7.9)

where h is the height of target above the nozzle exit.

Impact on normal plane target

For the normal plane target θ is 90 degrees. Therefore cos θ = 0

F

ρQV i= (1 − cos θ) = 1 (7.10)

Impact on conical and 30 degree plate

The cone semi-angle θ is 120 degrees. Therefore cos θ = 0.5

F

ρQV i= (1 − cos θ) = 0.5 (7.11)

Impact on semi-spherical target

The target exit angle θ is 180 degrees. Therefore cos θ = −1

F

ρQV i= (1 − cos θ) = 2 (7.12)

By using the above equation, we can compare the theoretical and experimental force value of

target with different angles.

Theoretically,

F = mg

Experimentally,

F = ρQV i(1 − cos θ) (7.13)

7.1.3 Impact of Jets apparatus

Cussons P6233 Impact of Jets apparatus (as shown in Fig 7.2) enables experiments to be carried

out on the reaction of a jet of water on vanes of various forms. The apparatus is supported on

a PVC base into which a vertical water supply pipe is fitted. Surrounding the supply pipe is a

transparent plastic shield fitted with a top PVC flanged cover assembly. The force of the jet is

balanced by the addition of masses. A vertical shaft, which passes through a plain bearing inthe top flange assembly, has provision for attaching the target vane at its lower end.

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Figure 7.2: Cussons P6233 Impact of Jets apparatus

The reaction vane is held within the transparent shield approximately 20 mm above the

vertical water supply pipe nozzle by a rod which passes through the top cover and supports a

flat tray, onto which masses may be placed. In operation, water from the Hydraulics Bench is

fed into the unit and a vertical jet is produced through the supply pipe and its interchangeable

nozzle. The water from the jet is deflected by the reaction vane under test, and drains away

through the large aperture in the base of the chamber. The force produced by the jet impinging

on the target is transmitted by the rod, to the flat tray where weights are placed in order to

balance this transmitted force. Three different types of reaction vane are supplied with the

apparatus and the types are flat, hemispherical cup and 45 cone form. Each vane can be secured

to the pivot arm by a set screw and when not in use is stored on pegs on the unit base plate.

Two interchangeable nozzles for the supply pipe are supplied, one of 8 mm and one of 5 mm

diameter.

7.2 EXPERIMENT

7.2.1 Aim

To investigate the reaction force produced by the impact of a jet of water on to various target

vanes.

7.2.2 Apparatus

(i) Hydraulics Bench which allows us to measure flow by timed volume collection.

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(ii) Impact of Jets Apparatus with interchangeable target vanes such as flat, conical, semi

spherical and nozzles.

Figure 7.3: F1–16 Impact of a jet

(iii) Stopwatch for timing the flow measurement

(iv) Scale for measuring the height differences

(v) Weights

7.2.3 Procedure

(i) Screw on the 5mm nozzle and the Flat Target Vane

(ii) In free condition adjust the pointer to align with the base of the weight platform

(iii) Measure the height difference between the tip of the nozzle and the target vane

(iv) Add a known weight to the weight platform. The platform will move downwards

(v) Start the pump in the hydraulic bench and adjust the flow rate so that the water jet velocity

from the nozzle changes and it raises the weight platform back to its original position

(vi) Measure the volumetric flow rate used timed collection using a stopwatch from the hy-

draulic bench

(vii) Further add a known weight to the platform

(viii) Adjust the flow rate again so that the platform moves back to its original position

(ix) Measure the volumetric flow rate

(x) Switch off the pump

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Repeat this procedure for all combinations of nozzles and target vanes, namely, 5mm and 8mm

nozzles and flat, conical and semi-spherical target vanes.

7.2.4 Observations

Observations for first nozzle:

Nozzle Diameter = Flat Target Conical

Target

Semi-

Spherical

Target

Total Weight (kg)

Quantity of Water Collected (m3)

Time to Collect Water (s)

Volumetric Flow Rate, Q (m3/s) Nozzle Velocity, V n (m/s)

Height of Target above Nozzle (m)

Impact Velocity, V i (m/s)

Impact Force, F (N)

Incident Momentum, ρQV i (kgm/s)

F/ ρQV i% Error

Observations for second nozzle:

Nozzle Diameter = Flat Target Conical

Target

Semi-

Spherical

Target

Total Weight (kg)

Quantity of Water Collected (m3)

Time to Collect Water (s)

Volumetric Flow Rate, Q (m3/s) Nozzle Velocity, V n (m/s)

Height of Target above Nozzle (m)

Impact Velocity, V i (m/s)

Impact Force, F (N)

Incident Momentum, ρQV i (kgm/s)

F/ ρQV i% Error

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7.2.5 Calculations

Calculations procedure used to complete the above tables:

V olumetric f low rate = (Quantity of water collected)/(T ime taken f or collection)

Nozzle velocity = (V olumetric f low rate)/(Area of cross – section of nozzle)

Impact velocity =√

(Nozzle V elocity)2 − 2 × (Acceleration due to gravity)× (Height of target)

Impact force = Total Weight ×Acceleration due to gravity

7.2.6 Results

(i) The theoretical value of vanes such as flat, semi spherical and conical target are ……………

respectively.

(ii) The experimental value of vanes such as flat, semi spherical and conical target are ……………

(iii) The percentage of error involved in theoretical an experimental value of vanes (flat, con-

ical and semi spherical) are ……………… respectively.

7.2.7 Discussion

(i) Is there any deviation between theoretical and experimental value? If yes, why it occur?

(ii) How to minimize the error involved between theoretical and experimental value?

(iii) If you want to implement the vane to the turbine, then which kind of vane you would

prefer? And why?

(iv) Why the energy of the water jet is used differently by each body?

(v) Why the efficiency of semispherical is best to use energy of water jet?

7.2.8 Conclusion

Conclude whether the theoretical and experimental forces do or do not have significant percent-

age of error.

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8

PIPE SURGE AND WATER HAMMER

8.1 THEORY

8.1.1 IntroductionFluid distribution systems (hydropower plants, pumping facilities, jet fueling systems, and

wastewater collection systems) and hydropower plants can be severely damaged by pipe surge

and water hammer. The first thing to understand is that surge is very different from pulsation

or water hammer. Water hammer can destroy turbo machines and cause pipes and penstocks to

rupture. Water hammer can be solved by designing and/or operating these systems such that un-

favorable changes in water velocity are minimized. The damage caused by water hammer by far

exceeds the cost of preventive analysis and control measures (surge tank, air vessel, fly wheel,

air valve). But surge is less predictable and can also cause severe damage to pipes, valves,

fittings and pumps. Water systems never operate at a constant pressure. Pumps going on and

off line, changes in temperature, demand and tank levels, alter system flow rate and pressure atany given time. A mild change called a surge, results from water pressure oscillations within

the system and can damage pipes, valves and fittings. A gradual closing of valve in a pipeline

creates pipe surge while quick closing sets in water hammer.

More severe water hammer, on the other hand, comes about when there is a sudden change

at either the inlet or outlet of a system. Pumps suddenly going on or off line or valves rapidly

closing are the most common causes. In other words, it is the forceful slam, bang, or shudder

that occurs in pipes when there is a sudden change in fluid velocity creating a significant change

in fluid pressure. When an outlet valve suddenly closes, the energy contained in the water

flow compresses the water nearest the valve. Like a spring, this energy then reverses flow,sending a shockwave at the speed of sound back upstream until it hits an obstruction: a joint,

another closed valve or the impeller in the pump. Most of the energy from that shockwave then

bounces off that obstruction and returns to hammer the valve. The wave travels back and forth

between the obstruction and valve until friction finally dissipates the energy. Under unfavorable

circumstances, damage due to water hammer may occur in pipelines measuring more than one

hundred meters and conveying only several tenths of a litre per second. But even very short,

unsupported pipelines in pumping stations can be damaged by resonant vibrations if they are

not properly anchored. By contrast, the phenomenon is not very common in building services

systems, e.g. in heating and drinking water supply pipelines, which typically are short in length

and have a small cross-section.

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8.1.2 Analysis of Water Hammer

The mass inertia of fluid, elasticity of pipe wall and fluid, frictional resistance of the pipe wall

have to be analyzed to understand the water hammer phenomenon.

Inertia

The sudden closure of a valve in a pipeline causes the mass inertia of the liquid column toexert a force on the valve’s shut-off element. This causes the pressure on the upstream side

of the valve to increase; on the downstream side of the valve the pressure decreases. Let us

consider an example: for a 200mm diameter pipe, L = 900 m, v = 3 m/s, the volume of water

in the pipeline is calculated by,

mwater = 0.22π

4 ∗ 900 ∗ 1000 = 28274kg (8.1)

This is more or less the same as the weight of a truck; v = 3 m/s corresponds to 11 km/h. In

other words, if the flow is suddenly stopped, our truck – to put it in less abstract terms – runs

into a wall (closed valve) at 11 km/h (water mass inside the pipe). In terms of our pipeline, thismeans that the sequence of events taking place inside the pipe will result in high pressures and

in high forces acting on the shut-off valve. As a further example of inertia, Figure 8.1 shows a

pump discharge pipe. At a very small moment of inertia of pump and motor, the failing pump

comes to a sudden standstill, which has the same effect as a suddenly closing gate valve. If

mass inertia causes the fluid flow on the downstream side of the pump to collapse into separate

columns, a cavity containing a mixture of water vapour and air coming out of solution will be

formed. As the separate liquid columns subsequently move backward and recombine with a

hammer like impact, high pressures develop. The phenomenon is referred to as liquid column

separation or macro-cavitation.

Macro-cavitation in pipelines is not to be confused with microscopic cavitation causing pit-

ting corrosion on pump and turbine blades. The latter always strikes in the same place and is

characterised by local high pressures of up to 1000 bar or more that develop when the micro-

scopically small vapour bubbles collapse. With macro-cavitation, repetitive strain of this kin

Documents

CE 4030 Hydraulics Lab Manual