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CIVIL ENGINEERING

LAB MANUAL

FLUID MECHANICS

DEPARTMENT OF CIVIL ENGINEERING

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LIST OF EXPERIMENTS

SL.

NO.

NAME OF EXPERIMENTS

1 DETERMINATION OF META-CENTRIC HEIGHT OF A

BOAT MODEL

2 VERIFICATION OF BERNOULLI’S THEOREM

3 VERIFICATION OF REYNOLD’S LAW

4 DETERMINATION OF CO-EFFICIENT OF DISCHARGE

FOR A VENTURIMETER

5 DETERMINATION OF CO-EFFICIENT OF DISCHARGE

FOR ORIFICE METER

6 VISCOSITY DETERMINATION OF A LIQUID BY

CAPILLARY TUBE METHOD

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Experiment 1

AIM:-To determine the Meta-centric height of a floating body or boat model

APPARATUS

Meta-centric Height Apparatus,

Water Tank

Water Supply

RELATED THEORY

Meta-Centre:

It is defined as the point about which a body starts oscillating when the body is tilted by a

small angle. The meta-centre may also be defined as the point at which the line of action of

the force of buoyancy will meet the normal axis of the body when the body is given a small

angular displacement. It is denoted by M.

Meta-Centric Height:

The meta-centric height (GM) is a measurement of the initial static stability of a floating

body. It is calculated as the distance between the centre of gravity of a ship and its meta-

centre.

Determination of Meta-centric Height:

Figure: Meta-centric Height apparatus

Consider a floating body which is partially immersed in the liquid, when such a body is tilted,

the center of buoyancy shifts from its original position ‘B’ to ‘B’ (The point of application of

buoyanant force or upward force is known as center of G which may be below or above the

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center of buoyancy remain same and couple acts on the body. Due to this couple the body

remains stable. At rest both the points G and B also Fb x Wc act through the same vertical line

but in opposite direction. For small change (θ) B shifted to B. The point of intersection M of

original vertical line through B and G with the new vertical, line passing through ‘B’ is known as

meta-centre. The distance between G and M is known as meta-centre height which is measure of

static stability.

Formula Used:-

GM = w X/W tanθ

G= Centre of gravity of the ship model

M= Meta-centric of the ship model

W= Applied weight

X= Distance moved by weight w

W= Weight of Ship model including weight w

ɵ= Angle of tilt

Observation & Calculation table

S.No. W(kg)

W(kg) X(cm) θ Meta-Centric Height

GM(CM)

Procedure: -

1. Note down the dimensions of the collecting tank, mass density of water.

2. Note down the water level when pontoon is outside the tank.

3. Note down the water level when pontoon is inside the tank and their difference.

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4. Fix the strips at equal distance from the center.

5. Put the weight on one of the hanger which gives the unbalanced mass.

6. Take the reading of the distance from center and angle made by pointer on arc.

7. The procedure can be repeated for other positioned and values of unbalanced mass

Precautions: -

1. The reading taking carefully without parallax error.

2. Put the weight on the hanger one by one.

3. Wait for pontoon to be stable before taking readings.

4. Strips should be placed at equal distance from the centre.

Result:- Meta centric height of the ship model is measured with different positions and weights

and value is………….

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Experiment No. 2

AIM-: To verify the Bernoulli’s theorem.

Apparatus-: Bernoulli’s Set – Up, Stop Watch, & Meter Scale.

Theory-: Bernoulli’s Theorem states that, in steady, ideal flow of an in compressible fluid the

total energy at any point of the fluid is constant. The total energy consists of Pressure

Energy, Kinetic Energy, & Potential Energy (Datum Energy). The energy per unit weight of

the fluid is Pressure Energy.

Therefore,

The applications of Bernoulli’s theorem are-:

1) Venturi Meter

2) Orifice Meter

3) Pilot Tube

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Description-: The equipment is designed as a self sufficient unit; it has a sump tank,

measuring tank, & 0.5 HP monoblock pump for water circulation. The apparatus consists of

Supply Tank & Delivery Tank, which are connected to a Perspex flow channel. The

channel tapers for a length of 25 cm & then piezo-meter tubes are fixed at a distance of 5 cm ,

centre – to – centre for measurement of pressure head.

Procedure-:

1. Keep the bypass valve open & start the pump & slowly start closing the valve.

2. The water shall start flowing through the flow channel. The level in the piezometer tubes shall

start rising.

3. Open the valve at the delivery tank side, & adjust the head in piezometer tubes to a steady

position.

4. Measure the heads at all the points and also discharge with the help of Diversion Pan in the

measuring tank.

5. Change the discharge & repeat the procedure.

6. Do the necessary calculations using the readings noted down before.

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Result-:

1) At discharge ………..liters / second,

Total head is ………..centimeters.

2) At discharge ………..liters / second,

Total head is ………..centimeters

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EXPERIMENT NO: 3

AIM:-VERIFICATION OF REYNOLDS LAW

REYNOLD’S NUMBER:

Reynolds number ‘Re’ is the ratio of inertia force to the viscous force where viscous force Is the

product of shear stress and area inertia force is the product of mass and acceleration.

APPARATUS:

1. Reynolds’s apparatus which consists glass tube, water tank and a small dye container at the

top of tank.

2. Potassium permanganate (dye).

3. Thermometer.

4. Measuring tank.

5. Stop watch.

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DIAGRAM:

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Experiment No. 4

Aim:- To determine the coefficient of discharge of Orifice meter.

Apparatus Used:- Orifice meter, installed on different pipes, arrangement of varying flow rate,

U- tube manometer, collecting tube tank, vernier calliper tube etc.

Where

A = Cross section area of inlet

a = Cross section area of outlet

Δh = Head difference in manometer

Q = Discharge

Cd = Coefficient of discharge

g = Acceleration due to gravity

Theory:- Orifice meter are depending on Bernoulli’s equation. Orificemeter is a device used for

measuring the rate of fluid flowing through a pipe. It is a cheaper device than Venturimeter.

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Procedure:-

1. Set the manometer pressure to the atmospheric pressure by opening the upper valve.

2. Now start the supply at water controlled by the stop valve.

3. One of the valves of any one of the pipe open and close all other of three.

4. Take the discharge reading for the particular flow.

5. Take the reading for the pressure head on from the u-tube manometer for corresponding

reading of discharge.

6. Now take three readings for this pipe and calculate the Cd for that instrument using formula.

7. Now close the valve and open valve of other diameter pipe and take the three reading for this.

8. Similarly take the reading for all other diameter pipe and calculate Cd for each.

Observations:-

Diameter of Orifice meter =

Area of cross section =

Area of collecting tank =

Result:-

Precautions:-

1. Keep the other valve closed while taking reading through one pipe.

2. The initial error in the manometer should be subtracted final reading.

3. The parallax error should be avoided.

4. Maintain a constant discharge for each reading.

5. The parallax error should be avoided while taking reading the manometer

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EXPERIMENT NO.- 5

Aim:- To determine the coefficient of discharge of Venturimeter.

Apparatus Used:- Venturimeter, installed on different diameter pipes, arrangement of varying

flow rate, U- tube manometer, collecting tube tank, vernier calliper tube etc.

Formula Used:-

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Procedure:-

1. Set the manometer pressure to the atmospheric pressure by opening the upper valve.

2. Now start the supply at water controlled by the stop valve.

3. One of the valves of any one of the pipe open and close all other of three.

4. Take the discharge reading for the particular flow.

5. Take the reading for the pressure head on from the u-tube manometer for corresponding

reading of discharge.

6. Now take three readings for this pipe and calculate the Cd for that instrument using formula.

7. Now close the valve and open valve of other diameter pipe and take the three reading for this.

8. Similarly take the reading for all other diameter pipe and calculate Cd for each.

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Experiment No-6

AIM: - To determine Viscosity of a liquid by Capillary Tube method

Apparatus

Poiseuille’s apparatus

Travelling microscope

Measuring cylinder

Stop watch.

Thermometer

Theory:

Some liquids like petrol, alcohol, water etc. flow more freely than honey, glycerin, oil etc. This is

due to the property of the liquid called viscosity by virtue of which the liquid opposes the

relative motion between its different layers. It is analogous to friction between solid surfaces,

except that it comes into play only when the fluid flows. Viscosity is estimated in terms of

coefficient of viscosity which is a constant for a liquid and depends on the nature of the liquid,

being greater for thick liquids like wax and glycerin than for thin liquids like water. Poiseuille’s

method is used to determine the coefficient of viscosity where liquid flows through the capillary

tube at different pressures.

Poiseuille’s apparatus shown in Figure 1 consists of a capillary tube AB placed horizontally on a

bench. The capillary tube must be placed horizontally to avoid flow of water under the effect of

gravity. The capillary must be clean and free from dustor grease. The bore of the capillary should

be narrow and uniformly spherical. M is the manometer. T is the constant level water tank.

Water enters the tank from a water tap through inlet tube I and flows into the capillary tube

Constantly through outlet tube O. There is an excess flow tube F which helps in maintaining the

water level constant. By lowering or raising the

Constant level tank, the pressure in the manometer can be altered. By opening the pinch cock Q,

the level of water in the manometer on the B side of capillary goes down to level D. The pinch

cock Q is used to maintain a pressure difference at the two ends of the capillary tube AB. By

opening Q, water starts flowing through the capillary and comes out of the tube and collected in

the measuring cylinder. The volume collected depends on the pressure difference at the two ends

of the Capillary tube.

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Poiseuille’s apparatus shown in Figure 1 consists of a capillary tube AB placed horizontally on a

bench. The capillary tube must be placed horizontally to avoid flow of water under the effect of

gravity. The capillary must be clean and free from dustor grease. The bore of the capillary should

be narrow and uniformly spherical. M is the manometer. T is the constant level water tank.

Water enters the tank from a water tap through inlet tube I and flows into the capillary tube

constantly through outlet tube O. There is an excess flow tube F which helps in maintaining the

water level constant. By lowering or raising the

constant level tank the pressure in the manometer can be altered. By opening the pinch cock Q,

the level of water in the manometer on the B side of capillary goes down to level D. The pinch

cock Q is used to maintain a pressure difference at the two ends of the capillary tube AB. By

opening Q, water starts flowing through the capillary and comes out of the tube and collected in

the measuring cylinder. The volume collected depends on the pressure difference at the two ends

of the capillary tube.

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In this section we will use the Poiseuille’s apparatus to study the linear and nonlinear flow of

water through the capillary tube and use the data to determine the coefficient of viscosity of

water at room temperature.

Theory Consider a liquid flowing over a fixed horizontal surface. Each layer of the liquid moves

steadily, parallel to the fixed surface, as long as the motion is slow. The velocity of different

layers of the liquid is different and increases with distance from the fixed surface .

This kind of flow is called laminar or streamline. In case of a liquid flowing in a tube / capillary,

the axial stream is moving with a definite velocity and the layer in contact with the wall of the

tube is at rest (provided the pressure difference causing the flow is not too great)

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Procedure

1. Set up the viscosity apparatus as shown in Figure 1.

2. Open the pinchcock Q and regulate the pressure difference, so that water flows out slowly,

drop by drop.

3. Note the steady position of water level in manometer tubes. The difference in levels gives h

which should be kept small (1-2 cm) in the beginning.

4. Place a clean dry graduated cylinder below the flowing water. Start the stop watch

simultaneously and collect the water for at least two minutes. The accuracy of the result can be

improved by collecting sufficient quantity of water over a larger period of time.

5. Pressure difference between the ends of the capillary may change during the course of the

experiment. Therefore, again note the position of water level in the manometer tubes and take the

mean of both the measurements.

6. Change the rate of flow slightly by opening the pinch–cock a little further steps 3 -5 for

another difference in levels, h.

7. Repeat step 6 seven to ten times and make a record of the measurements in Table 1. These

measurements should be spread uniformly corresponding to a range of about 2 cm to 20 cm for

h.

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8. Measure the length of the capillary tube AB using a ruler.

9. Note down the temperature of water using thermometer and corresponding density of water

from standard tables.

10. Take a sample of the capillary tube which has been used in the apparatus (this is provided

with the apparatus) and measure its inner diameter (i.e., bore) in two perpendicular directions

(Figure 5) with the help of a traveling microscope. Take4-5 such readings and record the

observations in Table 2 and 3.

Observations

Length of the capillary tube, l = .......cm

Temperature of water, T =......

Density of water at T , ρ =..... gm/cc

Least count of measuring cylinder =......cc

Least count of scale of manometer =....... cm

Least count of stop watch =....... s

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Calculations

1.Using Table 1, draw a graph (Figure 4) between rate of flow, V

in cc/sec and the difference of levels, h in cm (which represents pressure difference).

2. The straight line portion of the graph indicates the streamline flow at low pressures (linear

flow). The curved portion of the graph depicts turbulent flow (nonlinear flow).

3. Calculate the slope of the straight line portion of the graph.

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4. Substitute the values of r, ρ, g land slope in the Equation.(4) and calculate the coefficient of

viscosity, i.e.,

Result

The value of η is found to be =........ Poise

Standard value = .......poise