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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: Department of Mechanical Engineering IIT GHAZIABAD 1
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Page 1: Fm Manual New 2

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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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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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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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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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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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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