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III rd Semester Fluid Mechanics Lab Manual
INTRODUCTION
1. Introduction to Fluid Mechanics:
Fluid Mechanics is that branch of science, which deals with the behaviour of
fluids (Liquids or gases) governed by the laws of conservation of mass, laws of
mechanics and of thermodynamics at rest as well as in motion. The fluid under
steady may be flowing in a pipe or in a channel, in a pump or in a compressor around
an aircraft or a missile, in the ocean or in the atmosphere thus making the subject of
fluid mechanics as the most vital of all engineering studies. The subject of fluid flow
with special emphasis to application in engineering is termed as Engineering Fluid
Mechanics. Thus this branch of science deals with static’s and dynamic aspect of
fluids. The study of fluids at rest is called fluid static’s. The study of fluids in motion
where pressure forces are not considered is called fluid kinematics and if the
pressure forces are also considered for the fluids in the motion that branch of science
is called fluid dynamics.
Introduction to fluids and non-fluids:
A matter exists in either solid state or the fluid state the fluid state refers to
liquid, vapour or gaseous phases and non-fluid state means only the solid phase. The
intermolecular attractive forces within a substance govern existence of matter in their
state. Very strong intermolecular attractive forces exist in solids which give them the
property of rigidity this forces are weaker in liquids and extremely weak in vapours
and gases, so that liquids may change shape easily and acquire the shape of the
container and that vapour and gases fill up the entire space of the container allotted to
them.
It is more appropriate to classify substances as fluids and solids on the basis of
behaviour under the application of external forces. In practical it is the effect of shear
forces, which distinguishes fluids from solids. A fluid is a substance, which deforms
continuously when subjected to shear force the tendency of continuous deformation
of a substance is called fluidity and the act of continuous deformation is called flow.
A fluid would therefore, flow when subjected to shear stress.
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Ideal fluids and Real fluids:
Ideal fluids are those fluids, which have no viscosity; surface tension and they are
incompressible. As such for ideal fluids no resistance is encountered as the fluid moves.
However in nature the ideal fluids do not exist and therefore these are only imaginary fluids.
The mathematicians conceived the existence of these imaginary fluids in order to simplify the
mathematical analysis of the fluids in motion. The fluids, which have no viscosity such as air
water etc., may however be treated as ideal fluids without much error.
Practical or real fluids are those fluids, which are actually available in nature. These fluids
possess the property such as viscosity; surface tension and compressibility and therefore these
fluids always offer a certain amount of resistance when they are set in motion.
2. Fluid properties:
1. Density or mass density (ρ)
Density is defined as the mass of a substance per unit volume it is also called
mass density.
It is denoted by the symbol ‘ρ’. In SI Units density is expressed in Kg/m3.
2. Specific weight
The weight of a substance per unit volume is called the specific weight. It is also
called as weight density. It is denoted by ‘w’. As it represents the force exerted by the
gravity on a unit volume of fluid it has a unit of force per unit volume. In SI units it is
expresses as N/m3.
w= (Weight of fluid)/Volume of fluid
= (mass of fluid x acceleration due to gravity)/volume of fluid
w= ρ X g
3. Specific Volume:
Specific volume of a fluid is defined as the volume of fluid occupied by a unit
mass.
Specific volume = Volume of fluid/ Mass of fluid
=1/(Mass of fluid/Volume of the fluid)=1/ρ
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This specific volume is the reciprocal of mass density it is commonly applied to
gas. In S I unit it is expressed an m3 /kg
4. Specific gravity
Specific gravity is the ratio of specific weight (mass density) of a fluid to the specific
weight of a standard fluid. For liquids the standard fluid chosen for comparison is pure
water at 4 0 C. For gases the standard fluid chosen is either hydrogen or air at some
specified temperature and pressure.. The specific gravity of water at standard temperature
is equal to 1. The specific gravity of mercury varies from 13.5 to 13.6. Knowing the
specific gravity of any liquid its specific weight may be readily calculated.
w= Specific gravity of liquid x Specific weight of water.
= Specific gravity of liquid x 9810 N/m3
5. Viscosity:
Viscosity is the property of the fluid by virtue of which it offers resistance to the
movement of one layer of fluid flow over an adjacent layer. It is primarily due to cohesion
and molecular momentum exchange between fluid layers, and as flow occur this effect
appears as shearing stress between the moving layers of fluid. In SI units it is expresses as
N-m/s2.
6. Surface Tension:
Surface Tension is the property of the fluid surface film to exert a tension is called the
surface tension. This is due to cohesion between liquid particles at the surface. It is
denoted by sigma and it is the force required to maintain unit length of the film in
equilibrium. In SI unit it is expressed in N/m.
7. Compressibility and elasticity
The fluids may be compressed by the application of external force, and the external
force is removed the compress volumes of fluids expands to their original volumes. The
fluids also posses elastic characteristics like elastic solids. Compressibility of a fluid is
quantitatively expressed as inverse of the Bulk modulus of elasticity K of the fluid, which
is defined as
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In S I units bulk modulus of elasticity is expressed in N/m2
8. Pressure or Intensity pressure:
Pressure or intensity of pressure may be defined as the force exerted by unit area. If
F represents the total force uniformly distributed over an area A, the pressure at any
point is P= F/A. However, if the force is not uniformly distributed, the expression will
give the average value only. When the pressure varies from point to point on an area, the
magnitude of pressure at any point can be obtained by the following expression:
P= dF/dA Where dF represents the force acting on an infinitesimal area dA. In S I units
pressure is expressed in N/m2
a. Atmospheric pressure
Atmospheric air exerts a normal pressure upon all surfaces with which it is in
contact, and is known as atmospheric pressure. The atmospheric pressure varies with
altitude and it can be measured by means of a barometer. At sea level under normal
conditions the equivalent values of atmospheric pressures are 10.1043 x 10 4 N/ m2 ; or
1.03 kg (f) / cm2 ; Or 10.3 m of water column; or 76 cm of mercury column.
b. Absolute pressure
When pressure is measured with reference to absolute Zero or complete vacuum
is called absolute pressure.
c. Gauge pressure
When pressure is measured either above or below the atmospheric pressure as a
datum, it is called as a gauge pressure. This is because practically all pressure gauges
reads zero when open to atmosphere and read only difference between pressure of the
fluid to which they are connected and the atmospheric pressure. However, gauge
pressures are positive if they are above that of the atmosphere and negative if they are
vacuum pressures.
Absolute pressure= Atmospheric pressure + Gauge pressure
Absolute pressure= Atmospheric pressure-Vacuum pressure
d. Vacuum pressure
If the pressure of the fluid is measured with reference to atmospheric pressure and the
measured pressure of the fluid is below the atmospheric pressure, it is known as
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vacuum pressure or suction pressure or negative gauge pressure. A gauge, which
measures the vacuum pressure, is known as vacuum gauge.
e. Vapour pressure:
The liquids posses a tendency to evaporate or vaporize i.e. to change from liquid
to the gaseous state. Such vaporization occurs because of continuous escaping of the
molecule through the free liquid surface. When the liquid is confined in a closed
vessel, the ejected vapour molecules get accumulate in the space between the free
liquid surface and the top of the vessel. These accumulated vapours of the liquid exert
a partial pressure on the liquid surface, which is known as vapour pressure of the
liquid.
4. Basic principles of fluid flow
In fluid mechanics there are three basic principles used in the analysis of fluid problems are
motioned below:
Principle of conservation of mass
It states that mass can be neither created nor destroyed. On the basis of this
principle continuity equation is derived.
Principle of conservation of energy
It states that energy can neither created nor destroyed on the basis of this principle
the energy equation is derived.
Principle of conservation of momentum or Impulse momentum principle
It states that Impulse of resultant force, or the product of the force and time
increment during which it acts, is equal to the change in the momentum of the body. On
the basis of this principle the momentum equation is derived.
In applying these principles usually control volume approach is applied, in
which a definite volume with fixed boundary shape is chosen in space along the fluid
flow passage. This definite volume is called control volume and the boundary of this
volume is known as the control surface.
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Pascal’s law: The pressure at any point in a fluid at rest has the same magnitude in all
directions. In other words when certain pressure is applied at any point in a fluid at rest, the
pressure is equally transmitted in all the directions and to every other point in the fluid this
fact was established by B. Pascal, a French mathematician in 1653.
Archimedes principle: It states that when a body is immersed in a fluid either wholly or
partially, it is buoyed or lifted up by a force, which is equal to weight of the fluid displaced by
the body.
Newton’s second law of motion: It states that the resultant force of any fluid element
must equal to the product of the mass and acceleration of the element. The acceleration and the
resultant external force must be along the same line of action. In the mathematical form this
Law may be expressed as:
∑F = M x a Where ∑F represents resultant external force acting on the fluid element
of mass ‘M’ & ‘a’ is the total acceleration.
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EXPERIMENT NO. 1 BERNOULLI’S THEOREM
1.1 Objective. 1.2 Apparatus Required. 1.3 Theory. 1.4 Procedure. 1.5 Observations.
1.6 Observation table & Result Table. 1.7 Sample Calculations. 1.8 Results & Discussions.
1.1 Objective: Verification of Bernoulli’s theorem.
1.2 Apparatus Required: Bernoulli’s apparatus and stopwatch.
1.3 Theory:
Bernoulli’s equation relates velocity, pressure and elevation changes of a fluid in
motion. The equation is obtained when the Euler’s equation is integrated along the
streamline for a constant density (incompressible) fluid. The constant of integration
(called the Bernoulli’s constant) varies from one streamline to another but remains
constant along a streamline in steady, frictionless, incompressible flow.
Bernoulli’s equation states that the “sum of the kinetic energy (velocity head), the
pressure energy (static head) and Potential energy (elevation head) per unit weight of the
fluid at any point remains constant” provided the flow is steady, irrotational, and
frictionless and the fluid used is incompressible. This is however, on the assumption that
energy is neither added to nor taken away by some external agency. It is given by,
P1/w+V12/2g+Z1= P2/w+V2
2/2g+Z2= constant
Where P/w is the pressure head
V/2g is the velocity head
Z is the potential head.
The Bernoulli’s equation forms the basis for solving a wide variety of fluid flow
problems such as jets issuing from an orifice, jet trajectory, flow under a gate and over a
weir, flow metering by obstruction meters, flow around submerged objects, flows
associated with pumps and turbines etc.
The equipment is designed as a self-sufficient unit it has a sump tank, measuring
tank and a pump for water circulation as shown in figure1. The apparatus consists of a
supply tank, which is connected to flow channel. The channel gradually contracts for a
length and then gradually enlarges for the remaining length.
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In this equipment the Z is constant and is not taken for calculation.
1.4 Procedure:
1. Keep the bypass valve open and start the pump and slowly start closing valve.
2. The water shall start flowing through the flow channel. The level in the Piezometer
tubes shall start rising.
3. Open the valve on the delivery tank side and adjust the head in the Piezometer tubes
to steady position.
4. Measure the heads at all the points and also discharge with help of diversion pan in
the measuring tank.
5. Varying the discharge and repeat the procedure.
1.5 Observations:
Distance between each piezometer = 7.5 cm
Density of water = 0.001 kg/cm3
1. Note down the Sl. No’s of Pitot tubes and their cross sectional areas.
2. Volume of water collected q = ……………. cm3
3. Time taken for collection of water t = …………….sec
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1.6 Observation & Result Table:
Tube
No
Area of the flow
‘A’ in (cm2)
Discharge
‘Q’ in
(cm3/sec)
Velocity
‘V’ in
(cm/sec)
Velocity
head in
(cm)
Pressure
head in
(cm)
Total head
‘H’ (cm)
1
2
3
4
5
6
7
8
9
10
11
1.7 Sample Calculations:
1. Discharge Q = q / t =………….. cm3/sec
2. Velocity V= Q/ A= ................... = ………. cm/sec
Where A is the cross sectional area of the fluid flow
3. Velocity head V2/2g = ………….. cm
4. Pressure head (actual measurement or piezometer tube reading)
P/w= ……………… cm
5. Total Head
H = Pressure head + Velocity Head = = ………...........…….. cm
1.8 Result & Discussion:
Plot the graph between P/w and x.
Plot the graph between V2/2g and x.
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EXPERIMENT NO. 2 LOSSES IN PIPES DUE TO SUDDEN
CONTRACTION, SUDDEN ENLARGEMENT, BEND AND ELBOW
2.1 Objective 2.2 Apparatus Required 2.3 Experimental setup 2.4 Theory. 2.5 Procedure 2.6
Observations 2.7 Observation table 2.8 Sample Calculations 2.9 Result Table 2.10 Results &
Discussions.
2.1 Objective: Determination of loss of head due to
i) Large bend made up of G.I.(Galvanized Iron) of 90o
ii) Gate valve made of gunmetal ISO marked
iii) Sudden enlargement from25 mm diameter to 50 mm diameter.
iv) Globe valve made of gunmetal.
v) Sudden contraction from 50 mm diameter to 25 mm diameter.
vi) Elbow bend.
2.2 Apparatus required: Minor losses in pipes apparatus and stopwatch.
2.3 Experimental Setup:
The model consists of the hydraulic pipe circuit which consisting of Sudden Contraction,
Sudden enlargement, Gate valve, bend and elbow. The outlet of the pump is connected
to the hydraulic pipe circuit through the bypass valve. At the downstream end of the pipe
a valve is provided to regulate the flow. The restrictions to the flow like Sudden
Contraction, Sudden enlargement, bend and elbow is provided in the pipe one after one.
The pressure tapping across the each restriction is connected to a differential manometer
through the cocks.
Water is drawn from the sump tank delivered to a pipeline circuit of 25 m diameter fitted
with following fittings.
i. Large bend made up of G.I. of 90o
ii. Gate valve made of gunmetal ISO marked
iii. Sudden enlargement from25 mm diameter to 50 mm diameter.
iv. Globe valve made of gunmetal.
v. Sudden contraction from 50 mm diameter to 25 mm diameter.
vi. Elbow bend.
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Pressure tapings are provided on upstream and downstream end of each of these
fittings and the same may be connected to tubes of the same U-tube differential
manometer of 50 cm. Length, one by one with the help of a common manifold. Valve is
provided in the downstream side of the circuit to regulate the flow. A supporting stand to
support the pipe circuit is provided.
The help of collecting tank 40 cm × 40 cm × 30 cm fabricated with 3 mm thick M.S.
sheet can measure discharge of water. Tank is provided with gauge glass tube. Drain
valve of 25 mm size and provided with flow diverging arrangement.
2.4 Theory:
When a fluid flows through a pipe, certain resistance is offered to the flowing fluid,
which results in causing loss of energy. The various energy losses in pipes may be
classified as:
1. Major losses
2. Minor losses
The major loss of energy, as a fluid flows through the pipe, is caused due to friction.
It may be computed by Darcy-Weisbach equation as indicated in the last experiment. The
loss of energy due to friction is classified as a major loss because in case of long pipes it
is usually much more than the loss of energy incurred by other causes.
The minor losses of energy are those, which are caused an account of the change in
the velocity of flowing fluid (either in direction or magnitude). In case of long pipes these
losses are usually quite small as compared to loss of energy due to friction and hence
termed as minor losses, which may even be neglected without serious error. However, in
short pipe these losses causes may some time outweigh the frictional loss. Some of the
losses of energy that may be caused due to the change of velocity are indicated below.
1. Loss of energy due to sudden enlargement.
2. Loss of energy due to sudden Contraction
3. Loss of energy at the entrance to the pipe
4. Loss of energy at the exit from the pipe
5. Loss of energy due to gradual contraction or enlargement
6. Loss of energy in bends
7. Loss of energy in various pipes fittings.
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The loss coefficient K is defined as
Any fitting except for expansion
K=he/(V2/2g)
For expansion
H=(V12-V2
2)/2g where V= velocity of flow
2.5 Procedure:
a. Initially keep all the pressure tapings closed position.
b. Allow the water to (steady flow) through the circuit by removing the trapped air by
using air vent valve.
c. Using the bypass valve and the outlet valve can regulate flow.
d. For the particular discharge passing through the system open sequentially pressure-
tapping connections going to manometer note down the loss of head separately due
to each fitting in terms of mercury or convenient measuring liquid in the
manometer.
e. Measure the discharge and time taken for particular volume of discharge.
f. Vary the discharge and repeat the above procedure.
2.6 Observations:
1. Diameter of the smaller pipe d1=25 cm
2. Diameter of the larger pipe d2=50 cm
2.7 Observation Table:
Type of
Head loss
Manometer reading in terms
of mercury column ‘Hg’in
(cm of Hg)
Discharge
‘q’ in (cm3)
Time taken for
discharge ‘t’ in (sec)
h1 h2 Hg=h1-h2
Contraction
Enlargement
Globe valve
Gate valve
Elbow Bend
Large bend
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2.8 Sample Calculations:
1. Area of the small pipe A1=…………. cm2
2. Area of the larger pipe A2 =…………. cm2
3. Actual discharge Q = q / t =………….cm3/sec
Where t= time taken for discharge ‘q’in seconds
Manometer reading ‘hg’ in terms of water
hw = hg (13.6-1) =…………..cm of water
Where hg=Manometer reading in terms of cm of Hg
Specific gravity of Hg= 13.6
Velocity of water V= Q/A =…………cm/sec
Head loss due to sudden contraction:
Hc= (K.V2)/2g =…………..cm
Where K= ((1/Cc)-1) 2 =…………….
V= Velocity in the smaller pipe.
The value of Cc=0.62
Head loss due to sudden Enlargement:
He = (V2-V1) 2/2g=………….cm
Where V1= Velocity of the smaller pipe and V2=Velocity of the larger pipe
Head loss due Bend and Elbow
Hb=V2/2g=…………cm
Where V= Velocity of the smaller pipe.
2.9 Result table:
Type of Head lossManometer reading
‘hw’ in (cm of water)
Actual Discharge
‘Q’ in cc/sec
Loss of head in
(cm of water)
Contraction
Enlargement
Globe valve
Gate valve
Elbow Bend
Large bend
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2.10 Results and discussion:
1. For head loss due to sudden contraction =……………………..
2. For head loss due to sudden Enlargement =……………………..
3. For head loss due to Elbow Bend =…………………….
4. For Head loss due to Globe valve =…………………….
5. For Head loss due to Gate valve =…………………….
6. For Head loss due to Large bend =……………………
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EXPERIMENT NO. 3 IMPACT OF JET
3.1 Objective 3.2 Apparatus Required 3.3 Theory 3.4 Experimental setup 3.5 Procedures 3.6
Observation & Result Table 3.7 Results & Discussions. 3.8 Precaution.
3.1 Objective:
To verify the momentum equation experimentally through impact of jet experiment.
3.2 Apparatus Required: Impact of jet apparatus, weights, stop watch.
3.3 Theory:
The momentum equation based on Newton’s 2nd law of motion states that the algebraic
sum of external forces applied to control volume of fluid in any direction equal to the
rate of change of momentum in that direction.
The external forces include the component of the weight of the fluid and of the forces
exerted externally upon the boundary surface of control volume.
If a vertical water jet moving with velocity ‘V’ made to strike a target (Vane) which is
free, to move in vertical direction, force will be exerted on the target by the impact of jet.
Applying momentum equation in z- direction, force exerted by the jet on the vane, Fz is
given by
F = ρQ (Vzout- VZ in)
For flat plate, Vz out= 0
Fz = ρQ(0-v)
FZ= ρQv
For hemispherical curved plate , vz out= -v, vz in= v
Fz = ρQ[v+(-v)]
FZ = 2 ρQv
Where Q= Discharge from the nozzle (Calculated by volumetric method)
V= Velocity of jet = (Q/A)
3.4 Experimental setup:
The set up primarily consists of a nozzle through which jet emerges vertically in
such a way that it may be conveniently observed through the transparent cylinder. It
strikes the target plate or disc positioned above it. An arrangement is made for the
movement of the plate under the action of the jet and also because of the weight placed
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on the loading pan. A scale is provided to carry the plate to its original position i.e. as
before the jet strikes the plate. A collecting tank is utilized to find the actual discharge
and velocity through nozzle.
Fig No. 2 Impact of Jet.
3.5 Procedure:
i. Note down the relevant dimensions as area of collecting tank and diameter of
nozzle.
ii. When jet is not running, note down the position of upper disc or plate.
iii. Admit water supply to the nozzle.
iv. As the jet strikes the disc, the disc moves upward, now place the weights to bring
back the upper disc to its original position.
v. At this position find out the discharge and note down the weights placed above the
disc.
vi. The procedure is repeated for different values of flow rate by reducing the water
supply in steps.
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3.6 Observation:
Diameter of nozzle (d) = 10 mm
Area of the nozzle (A) = πd2/4
Mass density of water = 1gm/cm3
Area of collecting tank = 1200cm2
When jet is not running, position of upper disc = ......................... cm
Observation Table:
Sl.
No.
Discharge/ Velocity measurementBalancing
Fz =
ρQv
(Dyne)
Error (%)Initial
(cm)
Final
(cm)
Time
(sec)
Discharge
(Q)
(cm3/s)
Jet
velocity
(v)
(cm/s)
Mass
(m)
Force
F= mg
(dyne)
1.
2.
3.
4.
3.7 Results & Discussion
1. Find the theoretical force & error in balancing.
3.8 Precaution:
1. Apparatus should be in levelled condition.
2. Reading must be taken in steady conditions.
3. Discharge must be varied very gradually from a higher to smaller value.
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EXPERIMENT NO. 4 LOSSES IN PIPES DUE TO FRICTION
4.1 Objective 4.2 Apparatus required 4.3 Theory 4.4 Procedure 4.5 Observations 4.6 Observation
Table 4.7 Sample Calculations 4.8 Result Table 4.9 Result and discussion.
4.1 Objective:
Determination of coefficient of friction for different pipes.
4.2 Apparatus required: Losses in pipes due to friction apparatus and stopwatch.
4.3 Theory:
A pipe is a closed conduit, which is used for carrying fluids under pressure. Pipes
are commonly circular in section. As the pipes carries fluids under pressure, the pipes
always run full. The fluid flowing in a pipe is always subjected to resistance due to shear
forces between fluid particles and the boundary walls of the pipe and between the fluid
particles themselves resulting from the viscosity of the fluid. The resistance to the flow
of fluid is in general known as frictional resistance. Since certain amount of energy
possessed by the flowing fluid will be consumed in overcoming this resistance to the
flow, there will be always loss of energy in the direction of flow, which however
depends on the type of flow. The flow of fluid in a pipe may be either laminar or
turbulent. As such the frictional resistance in the laminar and turbulent flows obeys
different laws. On the basis of experimental observations the loss of fluid friction for the
two types of flows may be narrated as follows.
1. Laws of fluid friction for laminar flow.
2. Laws of fluid friction for turbulent flow.
Since mostly the flow of fluids in pipes is turbulent, in the various pipe flow problems
turbulent flow is considered.
The apparatus consists of four pipes of different material for which common inlet
connections are provided with control valves to regulate the flow, near the down stream
end of the pipe. Pressure tapings are taken at suitable distance apart, between which
common manometer board is connected.
4.4 Procedure:
a) Allow the water to flow (steady flow) through a particular pipe and remove air in the
equipment.
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b) During a particular observation the valve position regulating the flow should be
maintained constant.
c) Note down the manometer readings, which give the loss of head due to friction for
the length of pipe under consideration.
d) Allow the outlet to flow into the measuring tank of the hydraulic bench and measure
discharge.
e) Change the discharge through the pipe by operating flow regulating the valve and
repeat the above procedure.
f) Then the manometer is to be connected to other pipes by opening and closing of
relevant valves provided on the pipes and similar observations are to be taken which
are taken for the first pipe.
4.5 Observations:
Corresponding length of two tapings L=…………..cm
4.6 Observation Table:
S.No Pipe No.
Diameter
of pipe
‘d’ in (cm)
Manometer reading ‘hg’
in (cm of Hg) Discharge
‘q’ in (cm3)
Time taken for
discharge ‘t’
in (sec)h1 h2 hg=h1-h2
4.7 Sample Calculations:
a) Area of the pipe A =…………..cm2
b) Discharge Q = q / t =………… cm3/sec
where t= time taken for discharge ‘q’ in seconds
c) Manometer reading hw in terms of water
hf = hg (13.6-1) =…………….cm of water
where hg =Manometer reading in terms of cm of Hg
Specific gravity of Hg =13.6
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d) Velocity of water =……… = …….......cm/sec
e) Coefficient of friction …….............
4.8 Result Table:
Sl.No Pipe No.Manometer reading ‘hw’ in
(cm of water)
Discharge
‘Q’ in
(cm3/sec)
Velocity
‘V’
(cm/sec)
Coefficient of
friction ‘f’
1
2
3
4
4.9 Result and discussion:
i) The Co-efficient of friction of pipe 1 f =……………
ii) The Co-efficient of friction of pipe 2 f =……………
iii) The Co-efficient of friction of pipe 3 f =…………...
iv) The Co-efficient of friction of pipe 4 f =…………...
EXPERIMENT NO. 5 Hele-shaw Apparatus
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5.1 Objective 5.2 Apparatus Required 5.3 Experimental Setup 5.4 Theory 5.5
Observation
2.1 Objective:
Study and visualization of streamlines with the help of Hele-shaw Apparatus.
2.2 Apparatus Required: Hele-shaw Apparatus.
2.3 Experimental Setup:
The test channel consists of two parallel sheets of 60cm x30cm which are kept 1 mm
apart with the help of spacer and clamps copper strips of 1mm thickness separates them.
The model is sandwiched between these sheets. Water flows along the channel at a
sufficiently low Reynold number. Two tanks are placed in position one as a discharge
tank and another for supplying water.
2.4 Theory:
When the apparatus is switched on, the water from the supply tank flows through the
channel at very low Reynold number and discharges to the collecting tank. Just before the
channel there are number of small holes (openings) along the width of the channel. These
holes are connected to a separate tank (beside the supply tank) with the help of a number
of tubes.
When steady condition is reached the separate tank is filled with coloured water and
it mixes with the main flow at the inlet of the channel. The resulting pattern of the dye
gives the streamline pattern of the flow between two parallel sheets. The streamline
pattern can be drawn on a tracing paper by spreading it over the apparatus. Later on one
can get flow net by drawing equipotent lines (perpendicular to streamlines) over the
tracing paper.
5.5 Observation: Draw the streamlines on butter paper.
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Fig No. 3 Hele-shaw Apparatus
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EXPERIMENT NO. 6 Discharge of Triangular Notch
6.1 Objective 6.2 Apparatus Required 6.3 Theory 6.4 Procedure 6.5 Observation table
6.6 Results & Discussions.
6.1 Objective:
To study the flow over a triangular notch or weir and to find the value of coefficient of
discharge (Cd) and value of constant ‘K’ in Q = K H5/2 .
6.2 Apparatus Required: Triangular notch apparatus, stop watch.
6.3 Theory:
A weir is an obstruction placed in an open channel (free surface flow ) over which the
flow occurs. Weir is generally in the form of vertical wall with a sharp edge at the top
running all the way across the channel. When the liquid flows over the weir, the height
of the liquid above the tip of sharp edge bears a relationship with the discharge across it.
A Weir with a sharp edge is commonly referred to as a notch. The only difference
between weir and notch is that a weir runs all the ways across the channel where as a
rectangular notch may be as wide as a channel.
Installation of a notch is exclusively for the purpose of measuring the discharge in the
stream other type of weir shaped like dam whose primary purpose is to harness the flow
are also quite common in irrigation system.
Fig No. 4 Discharge through Triangular Notch.
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6.4 Procedure:
a. Measure the level of crest ‘H’ of the notch relative to the bed of the channel.
b. Start the water supply and allow the flow to take place over the notch.
c. After steady state condition has been attained, measure the level ‘H2’ of the free
liquid surface relative to bed or flume at a point sufficiently upstream of the notch.
d. Measure discharge by volumetric method .
e. Repeat step 4 for different flow rates.
f. Qualitatively observed the mechanism of nappe formation the side contraction effect
and other features of the flow for various flow rates.
For triangular notch
Or Q = K H5/2
K = Q/H5/2
Cd = 15 K/8 √2g
6.5 Observation table
S.No. Static
head
(H) cm
Water rise
in the Tank
(X) cm
Volume
of Water
in the
Tank
(v) cm3
Collecting
Time (t)
sec
Discharge
Q = V/t
cm3/s
K=Q/H5/2 Cd
1
2
3
Mean
6.6 Results & Discussions:
a. Plot log Q Vs log H
b. Mean value of coefficient of discharge = -------------
c. Mean value of ‘K’ = -----------
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Discussions:
Generally a triangular notch preferred over a rectangular weir or notch for
measuring the flow discharge. This is so because for measuring low discharge a
triangular notch gives more accurate results than a rectangular notch and the
expression for discharge for a right angled V-notch or weir is very simple. In case of
triangular notch only one reading i.e. ‘H’ is required for the computation of discharge.
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EXPERIMENT NO. 7 Discharge of Rectangular Notch
7.1 Objective 7.2 Apparatus Required 7.3 Theory 7.4 Procedure 7.5 Observation table 7.6
Results & Discussions.
7.1 Objective:
To study the flow over a rectangular notch or weir and to find the value of coefficient of
discharge (Cd) and value of constant ‘K’ in Q = K H3/2.
7.2 Apparatus Required: Rectangular notch apparatus, stop watch.
7.3 Theory:
A weir is an obstruction placed in an open channel (free surface flow) over which
the flow occurs. Weir is generally in the form of vertical wall with a sharp edge at the
top. Running all the way across the channel, when the liquid flows over the weir, the
height of the liquid above the tip of sharp edge bears a relationship with the discharge
across it.
A Weir with a sharp edge is commonly referred to as a notch . The only difference
between weir and notch is that a weir runs all the ways across the channel where as a
rectangular notch may be as wide as a channel.
Installation of a notch is exclusively for the purpose of measuring the discharge in
the stream other type of weir shaped like dam whose primary purpose is to harness the
flow are also quite common in irrigation system.
Fig No. 5 Discharge through Rectangular Notch.
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7.4 Procedure:
a. Measure the level of crest ‘H’ of the notch relative to the bed of the channel.
b. Start the water supply and allow the flow to take place over the notch.
c. After steady state condition has been attained, measure the level ‘H2’ of the
free liquid surface relative to bed or flume at a point sufficiently upstream of
the notch.
d. Measure discharge by volumetric method.
e. Repeat step 4 for different flow rates.
f. Qualitatively observed the mechanism of nappe formation the side contraction
effect and other features of the flow for various flow rates.
For rectangular notch
Or Q = K H3/2
K = Q/H3/2
Cd = 3k/2 b √2g
7.5 Observation table:
S.N. Static
head
(H) cm
Water rise
in the
tank
(x) cm
Volume
of water
in the
tank (V)
cm3
Collecting
time (t)
sec
Discharge
Q= V/t
cm3/s
K=Q/H3/2 Cd
1
2
Mean
7.6 Results & Discussions:
a. Plot log Q Vs log H
b. Mean value of coefficient of discharge = ---------------
c. Mean value of ‘K’ = --------------
EXPERIMENT NO. 8 METACENTRIC HEIGHT
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8.1 Objective. 8.2 Apparatus Required. 8.3 Theory. 8.4 Procedure. 8.5 Observations.
8.6 Observation table & Result Table. 8.7 Sample Calculations. 8.8 Results & Discussions.
8.1 Objective: To determine experimentally the Metacentric height of a flat-bottomed
pontoon.
8.2 Apparatus Required: Metacentric height apparatus and Different weights.
8.3 Theory:
A body floating in a fluid is subjected to the following system of forces:
Weight of the body Wc acting downward at the centre of the gravity G of the body.
The buoyant force Fb acting upward at the centre of the buoyancy B.
The forces Wc & Fb are equal and opposite and as shown in fig 2. The points G and B
lie along the same vertical line, which is the vertical axis of the body. When the body
is tilted though an angle . The centre of gravity G of the body & the centre of buoyancy
B will change its position from G to G1, B to B1 respectively. The line of action of Fb in
the new position cuts the axis of the body at M, which is called Metacentre and the
distance between Centre of Gravity G and Metacentre M is called the Metacentric
height.
Stability of floating body: The position of the Metacentre relative to the position of the
centre of gravity of a floating body determines the stability of the floating body.
1. Stable equilibrium: If the point M is above G, the floating body will be in
stable equilibrium.
2. Unstable equilibrium: If the point M is below G, the floating body will be in
unstable equilibrium.
3. Neutral equilibrium: If the point M is at the centre of the gravity of the body,
the floating body will be in neutral equilibrium.
Under equilibrium the moment caused by the movement of the unbalanced mass ‘w’
through a distance ‘x1’ must be equal to moment caused by the shift of the centre of
gravity from G to G1.
Metacentric Height
where Wc is the weight of the ship model.
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‘w’ is the weight of unbalanced mass causing the moment on the body
x1 is the distance of the unbalanced mass from the centre of the body
is the angle of tilt.
8.4 Procedure:
a. Note down the relevant dimensions as area of the tank and mass density of water etc.
b. Note down the water level when the pontoon is not in the tank.
c. Pontoon is allowed to float in the tank. Note down the reading of water level in the
tank. Mass of the pontoon can be calculated by using Archmidie’s principle.
d. Position of the unbalanced mass, weight of unbalanced mass and the angle of heel can
be noted down. Calculate the Metacentric height of the pontoon.
e. The procedure is repeated for other positions and different value of unbalanced mass.
f. Also the procedure is repeated while changing the weight of the pontoon by changing
the number of strips in the pontoon.
8.5 Observations:
a) Area of the tank A = ……………..cm2
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b) Water level reading without pontoon Y1 =………………cm
c) Specific weight of water =……………….N/m3
8.6 Observation & Result Table:
S.No
Water level
Reading with
pontoon ‘Y2’
(cm)
Unbalance
d mass
‘Wc’ (gm)
Angle of
heel ‘’
(degree)
Distance of
unbalanced
mass ‘x1’ (cm)
Mass of
pontoon
‘Wc’ (kg)
Metacentric
height ‘GM’
(cm)
8.7 Sample Calculations:
1. Mass of the pontoon Wp = Volume X Density of water
=(Y2-Y1) X Area of the tank X Density of water
2. Metacentric Height =........................cm
8.8 Result and Discussion:
The Avg. Metacentric Height of a given ship model GM =.................cm
EXPERIMENT NO. 9 FLOW MEASUREMENTS BY VENTURI METER, ORFICE METER AND NOZZLE METER
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9.1 Objective 9.2 Apparatus Required 9.3 Theory 9.4 Procedure 9.5 Observations
9.6 Observation table 9.7 Sample Calculations 9.8 Result Table 9.9 Results & Discussions.
9.1 Objective:
Determine the coefficient of discharge using Venturimeter, Orifice meter and
Nozzle meter.
9.2 Apparatus Required:
Venturimeter test rig, Orifice meter test rig, Nozzle meter test rig and stop watch.
9.3 Theory:
Venturimeter:
A Venturimeter is a device, which is used for measuring the rate of flow of
fluid through a pipe. The basic principle on which a venturimeter works is that by
reducing the cross sectional area of the flow of passage, a pressure difference is
created and the measurement of the pressure difference enables the determination of
the discharge through a pipe.
The Venturimeter consists of three main parts as shown in fig 5.
1. Convergent cone
2. A Cylindrical throat
3. Divergent cone
The inlet section of the venturimeter is of the same diameter as that of the pipe,
which is followed by a convergent cone. The convergent cone is a short pipe, which
tapers from the original size of the pipe to that of the throat of the venturimeter. The
throat of the venturimeter is a short parallel-sided tube having uniform cross
sectional area smaller than that of the pipe. The divergent cone of the venturimeter
is a gradually diverging pipe with its cross sectional area increasing from that of the
throat to the original size of the pipe. At the inlet section and at the throat, (i.e.,
section 1 and 2) pressure taps are provided to measure the pressure difference. By
applying the Bernoulli equation to the inlet section and at the throat, (i.e., section 1
and 2) an expression for the discharge is obtained.
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Orifice Meter:
An orifice meter is a simple device used for measuring the discharge through
pipe. The basic principle on which a orifice meter works is that by reducing the
cross sectional area of the flow of passage, a pressure difference between the two
sections is developed and the measurement of the pressure difference enables the
determination of the discharge through pipe. However, an orifice meter is a cheaper
arrangement for discharge measurement through pipes and its installation requires a
smaller length as compared to venturimeter.
An orifice meter consists of a flat circular plate with a circular hole called
orifice as shown in fig 6. The diameter of the hole generally kept as 0.5 times the
pipe diameter. The thickness of the plate is less than or equal to 0.05 times the
diameter of the pipe. From the upstream face of the plate the edge of the orifice is
made flat for a thickness less than or equal to 0.02 times the diameter of the pipe
and for the remaining thickness of the plate it is beveled with the bevel angle lying
between 300 to 450. The plate is inserted in a pipe for the measurement of the
discharge. The beveled edge of the orifice is kept on the downstream side. Two
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pressure taps are provided one is upstream side of the orifice plate and another is
downstream side of the orifice plate. (i.e., section 1 and 2) to measure the pressure
difference.
By applying the Bernoulli equation to the upstream section and downstream
section an expression for the discharge is obtained.
Theoretical discharge for venturimeter/orifice meter
9.4 Procedure:
1. Adjust flow of water (Steady flow) through venturimeter/orifice meter/nozzle meter
by using the bypass valve at inlet and flow control valve at outlet.
2. Remove the air bubbles inside the venturimeter/orifice meter/nozzle meter and also in
the manometer tube.
3. During a particular observation the valve position regulating the flow should be
maintained constant.
4. Note down the reading of differential U tube manometer reading ‘hg’ in cm of Hg.
5. Collect actual discharge of water in the measuring tank by using diversion pan.
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6. By changing discharge through the venturimeter/orifice meter/nozzle meter by
operating flow-control valve at outlet repeat the procedure.
9.5 Observations:
1. Diameter at inlet of the venturimeter d1 = …………………..cm
2. Diameter at throat of the venturimeter d2 =…………………..cm
9.6 Observation Table:
Sl.
No
Name of
device
Manometer reading in terms
of mercury column ‘hg’ in (cm
of Hg)
Discharge
‘q’ in (cm3)
Time taken for
discharge ‘t’ in (sec)
h1 h2 hg=h1-h2
1 Venturimeter
2 Orifice meter
3 Nozzle meter
9.7 Specimen Calculations:
1. Cross sectional area at inlet of the Venturimeter a1=……………….cm2
2. Cross sectional area at outlet of the Venturimeter a2= ……………... cm2
3. Manometer reading ‘hw’ in terms of water
hw = hg (13.6-1) =………….cm of water
Where hg=Manometer reading in terms of cm of Hg
13.6=Specific gravity of Hg
4. Actual discharge Qa = q /t =………..…cm3/sec
Where t= time taken for discharge of water in seconds
5. Theoretical discharge =…………………….=……….cm3/s
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6. Co-efficient of Discharge Cd= Qa/Qt =………….
9.8 Result Table:
Sl.
No
Name
of
device
Manometer
reading ‘hw’ in
(cm of water)
Actual
discharge ‘Qa’
in (cm3/sec)
Theoretical
discharge ‘Qt’
in (cm3/sec)
Coefficient
of Discharge
‘Cd’
Averag
e ‘Cd’
1Venturi
meter
2Orifice
meter
3Nozzle
meter
9.9 Result and discussion:
The Average Co-efficient of discharge of the Venturimeter Cd=……………..
The Average Co-efficient of discharge of the Orifice meter Cd=……………..
The Average Co-efficient of discharge of the Nozzle meter Cd=……………..
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EXPERIMENT NO. 10 REYNOLD’S APPARATUS
10.1 Objective 10.2 Apparatus Required 10.3 Theory 10.4 Procedure 10.5 Observations
10.6 Observation table & Result Table 10.7 Sample Calculations 10.8 Results & Discussions.
10.1 Objective: Determine the Reynold’s Number and hence the Type of Flow
10.2 Apparatus Required: Reynolds Apparatus test rig and stop watch
10.3 Theory:
The fluid flow is classified based on the flow pattern as: Laminar and Turbulent
flows. In laminar flow the fluid particles move along well-defined paths or streamlines,
such that the paths of the individual fluid particles do not cross those of neighbouring
particles. Laminar flow is possible only low velocities and when the fluid is highly
viscous. But when the velocity is increased or fluid is less viscous, the fluid particles do
not move in straight paths. The fluid particles move in a random manner resulting
mixing of the particles. This type of flow is called as Turbulent flow.
A laminar flow changes to turbulent flow when:
1. Velocity is increased or
2. Diameter of the pipe is increased or
3. Viscosity of fluid is decreased
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Reynold was first to demonstrate that the transition from laminar to turbulent
depends not only on the mean velocity but also on the quantity (V d)/. This quantity is
a dimensionless and is called Reynolds Number (Re). In case of circular pipe if Re 2000
the flow is said to be laminar. If Re2000 the flow is said to be turbulent. If Re lies in
between 2000 to 4000 the flow changes from laminar to turbulent.
The apparatus consists of a glass tube with one end having bell mouth entrance
connected to a water tank. The tank is of sufficient capacity to store water. At the other
end of the glass tube a ball valve is provided to vary the rate of flow. A capillary tube is
introduced centrally in the bell mouth. To this tube dye is fed from small container
placed at the top of tank through polythene tubing.
10.4 Procedure:
a. Open the ball valve so that flow will start. Then adjust flow of dye through
capillary tube so that a fine colour thread is observed indicating laminar flow.
b. Increase the flow through glass tube and observe the colour thread. If it is still
straight the flow still remains to be in laminar region and if waviness starts, it is
the indication that the flow is not laminar.
c. Note down the discharge at which colour thread starts moving in wavy from
which corresponds to ‘Higher critical Reynolds Number’ and higher critical
velocity.
d. Increase the discharge still further. The filament starts breaking on indicating
creating turbulence.
e. Further increase in the discharge will cause the flow to be turbulent which is
apparent from the diffusion of the dye with the flowing water.
f. Now start decreasing the discharge, first diffusion will continue, further reduced,
a stage will be reached when the dye filament becomes straight. This corresponds
to ‘lower critical Reynolds number’ and lower critical velocity.
g. If the experiment is repeated again it may be seen that the higher critical
Reynold’s Number (and the higher critical velocity) is different for each run
whereas the lower critical Reynolds number (and hence, the lower critical
velocity) is constant for each run. As such it can be concluded that “ Lower
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Critical Reynolds Number ”and hence the lower critical velocity) is the criteria for
distinguish weather the flow is laminar or not.
10.5 Observations:
1. Diameter of the pipe d = ………………cm
2. Kinematic viscosity of water ‘’ =…………………cm2/sec
10.6 Observation and Result Table:
S.No
Discharge
‘q’ in
(liters)
Time taken for
discharge
‘t’ in (sec)
Discharge
‘Q’ in
(cm3/sec)
Velocity
‘V’
(cm/sec)
Reynold’s
Number
‘Re’
Type of
flow
1
2
3
4
10.7 Sample Calculations:
1. Actual Discharge Q = q / t cm3/sec
2. Area of the Pipe a=…………….. cm2
3. Velocity of the water v=Q/a =………………..cm/sec
4. Reynolds Number Re= (v d)/ υ =……………..
Where υ = Kinematic viscosity of fluid.
10.8 Result and discussion:
i. For Laminar flow Reynold’s Number Re=……………..
ii. For Turbulent flow Reynold’s Number Re=……………..
iii. For Laminar to Turbulent Reynold’s Number Re=……………..
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EXPERIMENT NO. 11 PITOT STATIC TUBE
11.1 Objective 11.2 Apparatus Required 11.3 Theory 11.4 Experimental Setup 11.5 Procedure
11.6 Observations 11.7 Observation table 11.8 Sample Calculations 11.9 Result Table 11.10
Results & Discussions.
11.1 Objective: To determine the velocity coefficient of closed circuit pitot tube apparatus.
11.2 Apparatus Required: Pitot static tube apparatus and stopwatch.
11.3 Theory:
A pitot tube is a simple device used for measuring the velocity of flow. The basic
principle used in this device is that if the velocity of flow at a particular point is reduced
to zero, which is known as stagnation point, the pressure is increased due to conversion
of the kinetic energy into pressure energy, and by measuring the increase in the pressure
energy at this point the velocity of flow can be determined.
The simple Pitot tube consists of a glass tube, large enough for capillary effects to
be negligible and bent at right angles. A single tube of this type may be used for
measuring the velocity of flow in an open channel. If the Pitot tube is used for measuring
the velocity of flow in a pipe or any other closed conduit then the Pitot tube may be
inserted in the pipe as shown in fig 7. Since the pitot tube measures the stagnation
pressure head (or the total head) at its dipped end, the static pressure head is also
required to be measured at the same section where the tip of the pitot tube is held, in
order to determine the dynamic pressure head ‘h’. For measuring the static pressure head
a pressure tap is provided at this section to which a Piezometer may be connected.
Alternatively the dynamic pressure head may also be determined directly by connecting
a suitable differential manometer between the Pitot tube and the pressure tap meant for
measuring the static pressure.
The equipment is designed as a self-sufficient system, which includes a sump tank,
measuring tank and a pump with piping circuit. A acrylic duct is fitted in the line with a
provision of a traversing type pitot tube. Flow through the duct can be varied with the
bypass valve provided at the outlet of the pump. A inclined tube manometer is fitted
across the pitot tube to measure the dynamic pressure head.
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Fig No. 9 Prandle Type Pitot Tube
11.4 Experimental Setup:
Prandle type pitot tubes are provided at both inlet & outlet, so that the velocity had can
be determined separately. This prandle pitot tube consisting of two co- axial tubes and
one coming within the other and both bend in the L shape so, that when interred inside
the pipe. The tubes are parallel to the axis of the pipes at the place of measurements. The
inner tube has a facing upstream and hence measure the total head including both
pressure and velocity. The outlet tube has holes at he sides so, that it measure only the
pressure head , thus the difference between the two given the velocity a head separately
hence , the inner and outer tubes are connected to a differential manometer to indicate
the velocity head .
11.5 Procedure:
1. Start the pump and the water shall start flowing through the duct.
2. Allow some time for the flow to get uniform flow.
3. Note down the reading of U-tube manometer.
4. Measure the actual discharge.
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5. Change the discharge and repeat the above procedure.
11.6 Observations:
1. Diameter of pipe d = 25 mm
2. Area of measuring tank = 400mm X 300 mm.
11.7 Observation Table:
Sl.
No
Manometer reading in terms of
mercury column ‘hg’ in
(cm of Hg)
manometer reading
‘hw’ in (cm of water)
Discharge ‘q’
in (liters)
Time taken
for
discharge ‘t’
in (sec)h1 h2 hg=h1-h2
1
2
3
11.8 Sample Calculations:
1. Manometer reading in cm of water hw=hg (13.6-1)=……………..cm of water
2. Theoretical Velocity cm/sec = …………cm/sec
3. Area of the duct A=……………..cm2
4. Actual discharge Qa = q /t =…………. Cm3/sec
5. Actual Velocity Va= Qa / A =………….cm/sec
6. Coefficient of Velocity Cv = Va / Vt =………………
11.9 Result Table:
Sl.
No
Manometer reading
‘hw’ in (cm of
water)
Theoretical
Velocity
‘Vt’ in (cm/sec)
Actual Velocity
‘Va’ (cm/sec)
Coefficient of
velocity
‘Cv’
1
2
3
Average velocity of co-efficient of velocity (Cv)
11.10 Result and discussion:
The average Co-efficient of velocity of the Pitot tube Cv =………………
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EXPERIMENT NO. 12 SURFACE TENSION
12.1 Objective 12.2 Apparatus Required 12.3 Introduction 12.4 Procedure 12.5 Observations
12.6 Observation & Result Table 12.7 Sample Calculations 12.8 Results & Discussions.
12.1 Objective: To measure surface tension of a given liquid
12.2 Apparatus Required: Capillary tubes & Beaker with Stand to place the Capillary tubes
12.3 Introduction:
Due to molecular attraction, liquids possess certain properties such as cohesion and
adhesion. Cohesion means inter-molecular attraction between molecules of the same
liquid. That means it is a tendency of the liquid to remain as one assemblage of particles.
Adhesion means attraction between the molecules of a liquid and the molecules of a
solid boundary surface in contact with the liquid. The property of cohesion enables a
liquid to resist tensile stress, while adhesion enables it to stick to another body.
The cohesion between liquid particles at the surface of the liquid exhibits the property of
surface tension. It is defined as property of the liquid surface film to exert a tension is
called surface tension. It is denoted by ‘σ’ expressed as force per unit length and has a
unit N/m. Similarly because of adhesive properties, a liquid wets the solid surface and if
a known (small) diameter tube is immersed in a liquid there will be a rise or fall of liquid
takes place and it is termed as capillary rise or fall as shown in fig 1. In equilibrium
state, the weight of the liquid column ‘h’ must be balanced by the opponent of the
surface tension force at the surface of the liquid in the capillary tube. Thus
∏ d σ Cos = (∏d2/4) g h
The value of between water and clean glass tube is approximately equal to zero and
hence cos is equal to unity. For mercury and glass tube is 1280. Hence for water
surface tension is equal to
σ = ( g h d)/ 4
The experimental set up consists of a small beaker which is partly filled with the liquid,
whose surface tension is to be determined. Besides there are few glass capillary tubes of
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different diameters viz. 1.0, 2.0, 2.5, 3.5 & 4.0 mm. Suitable arrangement is made so
that any one of these tubes can be placed up-right in the beaker containing the liquid at a
time.
12.4 Procedure:
a. Partly fill the beaker with the liquid whose specific weight is known.
b. Dip one of the capillary tubes at a time.
c. Note down the capillary rise or fall of the tube.
d. Repeat above steps for the other capillary tubes.
e. Fill up the Observation Table.
f. Calculate the value of surface tension for different type of liquid for different types of
capillary tubes.
12.5 Observations:
Density of the given liquid =……………………… kg/m3
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12.6 Observation & Result Table:
S.No Liquid
Diameter of
capillary tube ‘d’
in (m)
Capillary rise ‘h’
in (m)
Surface Tension
‘σ’ (N/m)Average
12.7 Sample Calculations:
Surface tension of a given liquid
Where d=Diameter of the Capillarity tube in meters
h=Capillary rise or fall in meters
= Density of liquid Kg/m3
g= Acceleration due to gravity m/sec2
= Angle of contact between the liquid and & the tube.
12.8 Result and Discussion:
The average value of the Surface tension of a given liquid
σ = .........................N/m
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Appendix A
TABLE NO: 1 Physical Properties of Water
Temper
ature0C
Density’’
kg/m3
Sp. Weight
’’ KN/m3
Dynamic
Viscosity ’’
N-s/m2
Kinematic
Viscosity ‘’
m2/s
Surface
Tension
‘’ N/m
0
5
10
15
20
25
30
40
50
60
999.8
1000
999.7
999.1
998.2
997.0
995.7
992.2
988.0
983.2
9.805
9.807
9.804
9.798
9.789
9.777
9.764
9.730
9.689
9.642
1.785x10-3
1.518x10-3
1.307x10-3
1.139x10-3
1.002x10-3
0.890x10-3
0.798x10-3
0.653x10-3
0.547x10-3
0.446x10-3
1.785x10-6
1.519x10-6
1.306x10-6
1.139x10-6
1.003x10-6
0.893x10-6
0.800x10-6
0.658x10-6
0.553x10-6
0.474x10-6
0.0756
0.0749
0.0742
0.0735
0.0728
0.0720
0.0712
0.0696
0.0679
0.0662
TABLE NO: 2 Physical Properties of air at atmospheric pressure
Temper
ature0C
Density’’
Kg/m3
Sp. Weight
’’ N/m3
Dynamic
Viscosity’’
N-s/m2
Kinematic
Viscosity ‘’ m2/s
-20
0
10
20
30
40
60
1.395
1.293
1.248
1.205
1.165
1.128
1.060
13.68
12.68
12.24
11.82
11.43
11.06
10.40
1.61x10-5
1.71x10-5
1.76x10-5
1.81x10-5
1.86x10-5
1.90x10-5
2.00x10-5
1.15x10-5
1.32x10-5
1.41x10-5
1.50x10-5
1.60x10-5
1.68x10-5
1.87x10-5
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III rd Semester Fluid Mechanics Lab Manual
TABLE NO: 3 Physical Properties of Common Liquids at 20 o C
FluidDensity’’
Kg/m3
Specific
Weight
KN/m3
Specific
Gravity
Dynamic
Viscosity N-
s/m2 x 10-3
Kinematics
Viscosity
m2/s x 10-6
Tension
N/m x
10-3
Kerosene 804.0 7.89 0.804 1.914 2.381 27.73
Mercury 13555.0 132.97 13.555 1.555 0.11471 513.7
SAE-10 Oil 917.4 9.00 0.917 81.34 88.664 36.49
SAE-30 Oil 917.4 9.00 0.917 440.2 479.834 35.03
Benzene 881.3 8.65 0.881 0.651 0.739 28.90
Gasoline 680.3 6.67 0.680 0.292 0.429 ---
Conversion Factors
1 kgf =9.81 N
1 Atmospheric Pressure = 1.01325 bar =1.01325 x 105 Pascal
760 mm of Hg = 10.33 meters of Water
1 kgf/cm2 = 10 meters of water
1 Poise = 0.1 N-s/m2
1 Stoke = 10-4 m2/s
1 Metric HP = 75 kgf-m/s =746 W
1 bar =105 Pascal
1 m3 =1000 L.
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III rd Semester Fluid Mechanics Lab Manual
Viva Voce Questions
SURFACE TENSION
1. Define the following terms:
fluids and non-fluids, Ideal fluids and real fluid Density or mass density, Specific
weight Specific volume Specific gravity Viscosity, Pressure or intensity of pressure
and Atmospheric pressure.
2. What is surface tension?
3. What is capillary effect and capillary rise.
4. What are factors affects the surface tension of the liquid.
5. What is adhesive and cohesiveness
6. Define viscosity and explain variation of viscosity with reference to temperature
variations.
METACENTRIC HEIGHT
1. Define the term’s buoyancy and centre of buoyancy?
2. Define total pressure and centre of pressure.
3. Explain the terms Meta centre and Meta centric height?
4. What would happen if the metacentre is a) below the centre of gravity b) at centre of
gravity?
5. Can you determine the metacentric height analytically? If so how?
6. How the metacentric height of the ship can be increased?
7. What is Archimedes principle?
8. Define stable unstable and neutral equilibrium.
BERNOULLIS THEOREM
a. State Bernoulli’s theorem.
b. What are the assumptions made while deriving the Bernoulli’s equation?
c. What are the limitations of Bernoulli’s theorem?
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III rd Semester Fluid Mechanics Lab Manual
d. What do you understand by
a. An ideal fluid b) An incompressible fluid c) A study flow and unsteady flow ?
e. What is the piezometric head? How is it measured?
f. What is a hydraulic gradient line?
g. What is the total energy line?
VENTURIMETER
1. What is flow rate or discharge?
2. What is the basic principle of venturimeter.
3. What is the effect of the ratio D2 / D1 on the value of Cd
4. Why the angle of diverging cone kept small?
5. What are the advantages & disadvantages of a venturimeter over an orifice meter?
6. What are the Application of venturimeter?
7. Why venturimeter is preferred to an orifice meter?
8. Name some of the flow measurement apparatus?
ORIFICEMETER
1. What are the advantages and disadvantages of an orifice meter over a venturimeter?
2. What is the basic principle of orifice meter?
3. Why the value of Cd for an orifice meter is less than that of venturimreter?
4. What is venacontracta?
5. Why the orifice is fitted at an adequate distance from the inlet of the pipe?
PITOT STATIC TUBE
1. What is pitot static tube
2. What is the basic principle of pitot meter
3. Explain the basic principle of construction of pitot static tube
4. Determine the coefficient of velocity of a pitot tube?
5. What are the limitations and applications of pitot static tube?
6. Define static, total and dynamic pressure?
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III rd Semester Fluid Mechanics Lab Manual
REYNOLDS APPERATUS
1. Define viscosity, dynamic viscosity and the kinematics viscosity, specific weight.
2. What is laminar and turbulent flow and hence transition stage?
3. What is Reynolds number?
4. What is the significance of Reynolds number
5. What are the factors which effect the type of flow
6. How will you classify the type of flow based on Reynolds number
7. What are Upper critical Reynolds number and the lower critical Reynolds number?
LOSS IN PIPES DUE TO FRICTION
1. What are major and minor energy losses in pipes?
2. Define friction, coefficient of friction, viscosity, frictional resistance, and Shear force
3. What are the factors that the pipe friction depends?
4. What is Darcy s coefficient of friction?
5. What are the types of manometers?
6. Define chezy s formula?
LOSS IN PIPES DUE TO SUDDEN CONTRACTION, SUDDEN ENLARGEMENT,
BEND AND ELBOW
1. What are the different minor losses in pipes?
2. Why these losses are called minor losses?
3. Why the losses in a converging pipe are less than those in a diverging pipe?
NOTCH AND WEIR
1. What is the difference between a weir and notch?
2. List the various methods of finding the discharge in open channel flow.
3. Define the nappe in case of free surface flow.
4. What is the effect of end contraction on the measurement of coefficient of discharge
by a triangular notch?
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III rd Semester Fluid Mechanics Lab Manual
HELE-SHAW APPERATUS
1. Define steady flow, unsteady flow, uniform flow, non-uniform flow, Laminar flow
and turbulent flow.
2. Define streamline, path line and streak line? When these lines will coincide?
3. What is a flow net?
1. What are the streamlines and equi-potential lines? How they are useful in
drawing flow nets?
2. Define stream function and velocity potential function.
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