1

Experiment 1 CENTRE OF PRESSURE ON A PLANE SURFACE

I. THE OBJECTIVES OF EXPERIMENT

To determine the position of the centre of pressure on the rectangular face of the torroid.

II. APPARATUS

Hydrostatic Pressure Apparatus

III. ANALYSIS

Hydrostatic force acting on the rectangular face: AghP Cρ= (1)

and its center Ay

IyyC

CD += (2)

♦ Partial immersion

m

L

a

y d

b

yD yC

Water surface

2

2yyh CC == ; A = by (3)

Hence 2

21 gbyP ρ= (4)

6

2

122

3

yby

byyy CD ==− (5)

Moment M of P about knife-edge axis is given by:

⎟⎠⎞

⎜⎝⎛ +−+=

6221 2 yydagbyM ρ (6)

and then ⎟⎠⎞

⎜⎝⎛ −+=

321 2 ydagbyM ρ (7)

Also M = gmL Where m = mass added to balance pan L = distance from knife-edge axis to balance pan suspension rod axis Thereby,

⎟⎠⎞

⎜⎝⎛ −+=

321 2 ydabymL ρ (8)

♦ Complete immersion

2dyyh CC −== ; A = bd (9)

Hence bddygP ⎟⎠⎞

⎜⎝⎛ −=

2ρ (10)

( ) ( )2/122/12 2

3

dyd

dybd

bdyy CD −

=−

=− (11)

Moment M of P about knife-edge axis is given by:

m

L

a

y d

b

yD yC

Water surface

3

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−

++⎟⎠⎞

⎜⎝⎛ −=

2/1222

2

dyddadygbdM ρ (12)

and thereby,

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−

++⎟⎠⎞

⎜⎝⎛ −=

2/1222

2

dyddadybdmL ρ (13)

IV. PROCEDURE

(a) Locate the torroid on the dowel pins and fasten to the balance arm by the central screw. (b) Measure the dimensions a, b, and d, and the distance L from the knife – edge axis to the balance pan axis. (c) Position the perspex tank on work surface and locate the balance arm on the knife edges. (d) Attach a length of hose to the drain cock and direct the other end of hose to the sink. Attach a length of hose to tap V3 and place the free end in the triangular aperture on the top of the perspex tank. Level the tank, using the adjustable feet in conjunction with the spirit level. (e) Adjust the counter - balance weigh until the balance arm is horizontal. This is indicated on a gate adjacent to the balance arm. (f)Fill water to the perspex tank until the water is level with the bottom edge of the torroid. (g) Place a mass on the balance pan and fill water to the tank until the balance arm is horizontal. Note the water level on the scale. Fine adjustment of the water level may be achieved by over – filling and slowly draining, using the drain cock. (h) Repeat the procedure under section (g) for different masses : 5 masses for water levels y > d (complete immersion) and 5 masses for y < d (partial immersion) (i) Repeat readings for reducing masses on the balance pan. All record data can be arranged as shown in table 1 and 2 Table 1.

a(cm) b( cm) d(cm) L (cm)

Table. 2

Case m (g) y (cm) Complete immersion y > d

4

2ym

2ym

⎟⎠⎞

⎜⎝⎛ −+

ρ=

3yda

L2b

ym2

L6bρ

−

L2)da(b +ρ

Patital immersion y < d

V. REPORT

For y< d (partial immersion) Tabulate and plot against y From (8) It is found that the slope of this graph should be And the intercept should be

Comparison between the experimental results and theory

For y> d (complete immersion)

Tabulate ⎟⎠⎞

⎜⎝⎛ −=

2dyy ,

ym and

y1

Plot ym against

y1

From (13), it is found that the slope of this graph should be ρbd3/(12L)

And the intercept should be ⎟⎠⎞

⎜⎝⎛ +

2da

Lbdρ

Comparison between the experimental results and theory

V. CONCLUSIONS

Give reasons for the discrepancies, if any, between the measured and predicted values of the above expressions for the graph parameters.

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Experiment 2 FLOW OVER A WEIR I. THE OBJECTIVES OF EXPERIMENT

− To investigate the characteristics of flow over a vee notch and a rectangular notch. − To determine the velocity coefficient and discharge coefficient.

II. EQUIPMENT SET – UP

- Hydraulics Bench, Point Gauge, stop watch. - Basic Weir: 1 - Triangular weirs of 900 notch. 2 - Rectangular weirs.

III. SUMMARY OF THEORY

The discharge flowing over the weir can be determined by formula: Triangular weir

Q = C d Η⎟⎠⎞

⎜⎝⎛

2tan2

158 θg 5/2 (1)

Rectangular weir

Q = C’d HgB 2

32 3/2 (2)

Where: Cd, C’

d : discharge coefficient

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IV. PROCEDURE Ensure that the hydraulic bench is located on a level floor, as the accuracy of the results will be affected if the bench top is not level. Set up the equipment as shown in the diagram. Set Vernier Height Gauge to a datum reading, by placing the point on the crest of the weir. Take extreme care not to damage the weir plate with the point gauge.

Position the gauge about half way between the notch plate and stilling baffle. Admit water to channel, adjust flow control valve to obtain heads, H, increasing in step of about 1cm. For each flow rate, stabilize conditions, measure and record H. Take reading of volume and time using the volumetric tank to determine the flow rate.

Regulate the flow rate over the V - notch by adjusting the control valve of pump. For each flow rate, stabilize conditions, measure (Zb) to determine the head above notch bottom (H), and take reading of volume (V) and time (T) to determine the flow rate. In order to increase the degree of accurate of flow rate measurement, it should be taken at least three sets of reading of volume and time. Replace triangular weir by rectangular weir and repeat procedure above for rectangular weir.

All record data can be arranged as shown in Table I.

Table I

Weir type No. of

Experiment Zb

(cm) Z cr

(cm) Volume (V)

(litre) Time (T)

(s)

Triangular weir

1

2

3

4

H: Water head Triangular weir

900 H

Rectangular weir

on the weir H

B =101mm

7

2/3g22Q3ΗΒ

Table 2

Weir type No. of

Experiment Zb

(cm) Z cr

(cm) Volume (V)

(litre) Time (T)

(s)

Rectangular weir

1

2

3

4

V. REPORT

1. From Table 1, calculate the water head (H) on the weirs and the discharge in each experiment.

2. For the triangular weir: a) Compute and tabulate Q and Q2/5. b) Plot Q2/5 against H. c) Find Cd from the slope of the graph. d) Are Cd, C’

d constant for the condition of the flow? e) What are the advantages and disadvantages of plotting Q2/5 against H instead of Q against H5/2.

3. For the rectangular weir:

a) Compute and tabulate: Q,H3/2, C’

d = ,Q2/3, log Q, log H b) Plot:

- Q 2/3 against log H. - Log Q against log H. - C’

d against H. c) Is C’

d constant for this weir? Can the Q – H relationship be described by an empirical formula Q = KHn, if so, find the values of K and n.

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Experiment 3 FRICTION LOSS IN PIPE I. OBJECTIVES OF EXPERIMENT

- To investigate the variation of friction head along a circular pipe with the mean flow velocity in the pipe. - To investigate the friction factor against Reynolds number and roughness.

II. EQUIPMENT SET – UP

A pipe of 10.64cm diameter is supplied by water a centrifugal pump. Five test sections

with interval of 3 m are connected to a bank of pressurized manometer tubes. Water from the pipe flow into the concrete channel, and at the end of channel a vee-notch, is installed to measure the flow rate in the channel, this flow rate is equal to the flow rate in the pipe. Water level over the vee-notch is measured by a point gauge mounted on a small tank which is opened to the channel.

The flow rate over the vee-notch is calculated by formula as follow:

2/50.2

2158 hgCtgQ D⎟

⎠⎞

⎜⎝⎛=α (1)

Where: α = 90o CD = 0.58 g = 9.81 m/s2 ho = ZCR – z Where z is water level, ZCR is the elevation of the crest of Vee-notch, ZCR = 28.335cm The flow rate over the Vee-notch is regulated by a control valve of pump, and an ampere meter mounted on an electric box will show the current intensity of motor corresponding to the flow

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rate in the pipe. The difference of pressure between the test sections in the pipe are measured by reading the water level in the tubes of manometer. III. SUMMARY OF THEORY Considering flow at two sections i,j in a pipe, Bernouilli’s equation may be written as:

ijjjj

iii hZ

Pg

VZ

Pg

V+++=++

γγ 22

22

(2)

Where: Vi, Vj : velocity at section i, j respectively Pi, Pj : pressure at section i, j respectively Zi, Zj : elevation at of water surface section i, j hi,j : friction loss from section i to section j For this apparatus, Zi = Zj, Vi = Vj, hence

jiji

ji hPP

h ,, Δ=−

=γ

(3)

Δhi,j : the difference of manometer reading at section i and section j. On the other hand, the friction factor can be determined by Darcy’s formula :

g

VDLfh ji 2

2

, = (4)

Where : f : friction factor L : the distance between section i and j D : diameter of pipe V : velocity of pipe The friction coefficient depends upon the Reynolds number of flow and upon the ratio e/D, the relative roughness of the pipe.

⎟⎠⎞

⎜⎝⎛=

DeRFf e , (5)

Where : Re : Reynolds’ number Re = VD/ν (ν : viscosity coefficient) e : size of roughness

De : relative roughness

For a given pipe, De is a constant

IV. PROCEDURE

1. Open the control valve (1) to discharge water into pumping chamber. When the pumping chamber is full of water, close control valve (1).

2. Open the valve at the end of the pipe (2). 3. Turn on power to start pump and use the control valve to regulate the flow rate in the pipe

according to the current intensity shown in ampere meter. 4. For 3 large flow rates corresponding to current 20A < I < 22A :

- Closing the valves on the tubes 3, 4 and 5 of manometer. - Reading the water level in the tubes 1 and 2, and measuring the water level before

the Vee-notch in the channel by point gauge.

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5. For 5 flow rates corresponding to current I < 20.5A, repeat the same procedure above. The data table may be arranged as follows :

Table 1

No I Manometer reading (mm) Water Ampere (1) (2) (3) (4) (5) Level (z)

(cm) 1 21.5 2 21 3 20.5

1 20 2 19.5 3 19 4 18.5 5 18

V. REPORT

For 3 large flow rates

1. Compute the flow rates in the pipe from the measured data in Table 1. 2. Compute the head loss between section (1) and (2). And then plot the head loss against flow

rates. Conclude the relationship between the head loss and flow rates.

For 5 small flow rates

3. Determine 7 small flow rates by using the measured data in Table 1. 4. Compute the head loss between sections 2-1, 3-1, 4-1 and 5-1. And then plot the graph of the

friction loss against the distances. Give the conclusions about the relationship between the friction loss and the distances.

For 8 flow rates (3 large flow rates and 5 small flow rates)

5. Determine the friction factors f by using the Darcy’s formula. Plot the curve of log (f) against log (Re) and give the conclusion about the regime of the flow in the pipe.

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Experiment 4 MEASUREMENT OF VOLUMETRIC FLOW RATE

I. OBJECTIVES OF EXPERIMENT

Comparison of flow measurement devices in a duct: − Orifice plat. − Venturi nozzle.

II. EQUIPMENT SET - UP

The fan inlet is a duct 149 mm diameter (1) provided with pressure tapings whereby the static pressure may be measured simultaneously at each of 4 sections. All four pressure tapings are connected to a bank of pressurized manometer tubes (4). Two flow measurement devices are:

- 65mm orifice plate (2) - 65mm – 149mm diameter ventury nozzle (3).

Figure 1: Experimental equipment

12

ρπεβ

/241

2

4pdCQ Δ⎟⎟

⎠

⎞⎜⎜⎝

⎛

−=

≈

( ) )3(0158.0100390.0Re

100029.01840.00312.05959.0C 314473.06

5.221.2 β−β−β+⎟⎟⎠

⎞⎜⎜⎝

⎛β+β−β+=

−

DQUD

πμρ

μρ

4Re ==

III. SUMMARY OF THEORY The volume flow rate at the orifice plate and venturi nozzle in the pipe is determined by

formula as follows (1)

Where: Q: volumetric flow rate. C: discharge coefficient. Δp: pressure difference from inlet to throat. The manometer containing liquid of density ρ1 is used to indicate Δp, the pressure difference may be expressed in terms of the manometric head differential Δh by: Δp = (ρ1 –ρ)gΔh (2) ρ: flow density. ρ = 1.226 kg/m+3 ρ1: water density ρ1 = 1000kg/m3

β : diameter ratio = d/D. ε: expandability factor. The expandability factory is also detailed in the code and allows for the effects of density change in gas flows where a high pressure reduction occurs. For liquid flows and gas flows with moderate variation in pressure at the meter, ε 1.00. The discharge coefficients of the orifice plate and the venturi nozzle can be determined by empirical formula

For the orifice plate. Where: Re: Reynolds number (4)

U: upstream pipe velocity. Q: discharge in pipe D: diameter of pipe μ: dynamic viscosity (μ=1.002x10-3 Pa.s at 20o C)

When determining Q from Δp, it is necessary to estimate a value C initially as Re cannot be calculated until Q is known. From an initial estimate of C (example C = 1), Q can be

13

5.4196.09858.0 β−=C

calculated and thus Re found. The value of C can then be corrected and new values of Q and Re are recalculated. For the Venturi nozzle. (5)

IV. PROCEDURE

Check water level in the tank, it should be at the level of half of tank. Open the valve at the outlet of fan and turn on the motor. Take the readings of 4 manometer level. In order to decrease or increase the volume flow rate, the valve is closed or opened partly. Repeat for three valve settings and write the readings of manometer level into the Table 1

Table 1

Tube N0

Cross Section

Manometer Levels (mm) Exp.1 Exp.2 Exp.3

1 2 3 4

V. REPORT

1. Derive the formula(1) in case of C = 1 and Ɛ=1 2. Derive the formula(2) 3. Determine the volumetric flow rater in three experiments by using orifice flat. 4. Determine the volumetric flow rater in three experiments by using Venturi nozzle. 5. Compare the computed results between the using of orifice plate and Venturi nozzle,

give the conclusions.

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Experiment 5 MEASUREMENT OF DENSITIES AND SPECIFIC GRAVITIES

I. THE OBJECTIVES OF EXPERIMENT

To determine densities and specific gravities of liquids.

II. APPARATUS

Universal Hydrometer Using four Hydrometer Jars containing water, engine oil, glycerol and castor oil.

III. ANALYSIS

The specific gravity is read directly from scale. See Figure 2 for the principle on which the instrument works.

IV. METHOD

(a) Fill one hydrometer jar with sufficient water to float the hydrometer and check that the scale marking corresponding to depth of immersion reads 1.00.

(b) Fill three hydrometer jars with the liquids to be tested with sufficient of the liquids to float the hydrometer and note for each liquid the scale reading.

NOTE: It is suggested that the liquids should be those to be used in Experiment 5 for determining the viscosity of liquids: an engine oil, glycerol and castor oil.

V. RESULTS

Barometric pressure..............................................mm of Hg,

THE HYDROMETER

15

Temperature.............................................oC

The weight of hydrometer : ............................................. gf

Liquid Scale Reading = Specific Gravity, s

Water Engine Oil Glycerol Castor oil

since wwaterofdensity

liquidofdensitys

ρρ1

____

== (Eqn. 1.2)

ρ1 = sρw

and 3

310m

kgW =ρ

Density ρ Liquid g/ml kg/m3 Water Engine Oil Glycerol Castor oil

VI. REPORT

1. Determine density and specific gravity of fluids. 2. Depend upon Archimedes’ principle, explain why we can read the specific gravity

directly from scale of the hydrometer? 3. For each case, determine the volume of the hydrometer which immersed in liquids.

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APPENDIX

HYDRAULIC BENCH I. INTRODUCTION Hydraulic bench is a system providing the source of water to the experiments. The function of hydraulic bench include:

− To supply the source of water with various discharges − To determine the discharges supplied.

II. EQUIPMENT SET – UP

A self – priming centrifugal pump (9), draws water from sump tank (6), and delivers the water into a vertical transparent pipe (8). A panel mounted control valve(2), is used to regulate the flow in the pipe which terminate in a quick release pipe connector (11), situated in the bed of channel (13). The male connector(11) allows for rapid substitution of accessories, which are supplied with a flexible supply tube terminating in a mating connector. Special purpose termination may be connected to the pump supply by unscrewing connector (11). No hand tools are required for either of these operations. A drain valve (5) is incorporated in the wall of the sump to facilitate emptying. The mounded bench top incorporates an open channel, (13) with side channels (10), to support the accessory on test. In addition to the inlet connector (11), the channel incorporates a pair of wall slots (12) and a weir carrier (14), for use with accessory F1-13. Water discharging from the accessory on test is collected in a volumetric measuring tank (16). This tank is stepped to accommodate low or high flow rates and incorporates a stilling baffle (15), to reduce turbulence. A remote sight tube and scale (1) is connected to a tapping (17), in the base of the volumetric tank and gives an instantaneous indication of water level. A dump valve, (18) in the base of the volumetric tank is operated by a remote actuator (4) lifting the actuator opens the dump valve allowing the entrained water to return to the sump (6), for recycling. When lifted, a twist of 900 at the actuator will retain the dump valve in the open position. An overflow, (19) adjacent to the sump (6) returns water to the sump in the event of incorrect use. A measuring cylinder (7) is provided for measurement of very small flow rates. The cylinder is stored in the compartment housing the pump. Electrical supply to the pump motor(9) is via a starter (3).

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