Department of Mechanical Engineering

FLUID MECHANICS

LAB MANUAL

Experiment No. Name of Experiment

1 To find out Reynolds Number

2 To verify Bernoulli’s Theorem

3 To measure the discharge through a venturimeter

4 Orifice Meter

5 Rectangular Notch

6 Friction in Pipe

7 Impact of Jet

8 Meta Centric Height

EXPERIMENT NO. 1

Aim To find out Reynolds Number. Apparatus Required Experimental set up which consists of Acrylic tube (transparent) of suitable length, Supply tank and die tank with die needle, flow control valve, measuring jar, stop watch for flow measurement. Theory The distribution of water from reservoir from a city is through closed conduits or pipes. Channels or used to convey water to agriculture fields. The flow in open channels is exposed to atmospheric pressure. The flow in pipe becomes atmospheric if it is running partially, full as in sewer pipes and pipe culverts. If the pipe is running full, the water is under pressure. The water rises against gravity and reaches the upper floors of building due to this pressure. Types of flow in pipe: Uniform flow Non - uniform flow Streamline or laminar flow Turbulent flow Steady flow Unsteady flow Steady uniform flow Fluid friction: Fluid friction depends upon the type of water. For turbulent flow the resistance is as follows. Proportional to the square of the velocity Independent of pressure. Proportional to the density of fluid. Varies slightly with temperature. Proportional to the area of the surface in contact. Depends upon the nature of the surface in contact.

The Reynolds’s number: Laminar flow is defined as flow in which the fluid moves in layers, one layer gliding smoothly over an adjacent layer with only a molecular interchange of momentum. Any tendencies towards instability and turbulence are damped out by viscous shear force that resists relative motion of adjacent fluid layers. While turbulent flow has very erratic motion of fluid particles with a violent transverse interchange of momentum. The nature of flow i.e., whether laminar or turbulent and its relative position along a scale indicating the relative importance of turbulent to laminar tendencies are indicated by the Reynolds number. Reynolds number (Re) is the ratio of the inertia force per unit volume to the viscous force per unit volume. The inertia force is due to the mass and velocity of the fluid particles trying to diffuse the fluid particles. The viscous force is the frictional force due to the viscosity of the fluid.

Re = = = = p = density of the lµ= Viscosity oQ = Dischard = Diametev = KinematV = mean velocity of flow Procedure First fill the supp Then fill Start the Start the flow o For getti

through the a The disch The moment wh

the Flow in t The disch

3-4 times and obta

pV Qd4Q

of the liquid ty of the liqui

rge in m3/sec ameter of circulanematic viscosity

mean velocity of flow

the supply tank with water ill the dye into thhe flow of wate

e flow of dye. ing the diffthe acrylic tu

scharge must bThe moment when d

the acrylic tube harge (Q) flow

4 times and obtain an avera

pVd/µ V d I v Qd/v.A 4Q I πdv

d in kg I m3

id in N -s/m2

c ar pipe in m

ity of the liquimean velocity of flow in a pipe

y tank with water nto the dye tank

er from supp. ferent pattern of dye in the ube. be varied graddye deviates f

c tube is no longeflowing in the n an average v

3 2

in m id in m2/sec

n a pipe in m/sec

y tank with water up to the didye tank.

pply tank.

ern of dye in the

adually. tes from its str

onger in laminar he acrylic tube at that

value of the

/sec

he die tank.

ern of dye in the acrylic tube

raight line pa

minar conditionsrylic tube at that mom

he lower critical Reynol

coz,(v = µI pwhere V = Q where A = π

crylic tube, cont

e pattern correspondence to the con

ions. oment is measu

tical Reynolds numb

p ) Q I A π d2 I 4

ontrol the flo

respondence to the con

easured. Repeat the s number.

ow of water f

respondence to the condi

Repeat the above procedure

ater flowing

itions, then

bove procedure

ing

Precautions and tips 1) Water should be filled more than half tank. 2) Don’t apply excess pressure on the tap. 3) Flow measuring pipe should be in horizontal position. 4) Reading should take 20 minutes after the start of the flow. Observations 1. Diameter of the acrylic tube (ID) = 25mm 2. Kinematic viscosity of water = 1 X 10-6 m2/sec Tabulation:

S. No. Discharge Time Discharge, Reynolds’s Type of flow

(Liters) (sec) Q (m3/sec) number ( Re)

1

2

3

4

5 If Reynolds' number < 2000, then flow is laminar If Reynolds' number> 2000, then the flow is turbulent. Result/ Conclusions The value of the Reynolds no. is…………. And it shows that the flow is ………………. Viva Questions 1) What is Reynolds number? 2) Define laminar flow. 3) Define turbulent flow. 4) Can we use dye other than KMnO4 in Reynolds experiment. 5) Why Water tank should be kept clean? 6) What is transition flow?

EXPERIMENT NO. 2

Aim To verify Bernoulli’s Theorem Apparatus Bernoulli’s Apparatus Experimental setup which consists of flow channel 700 mm long, transparent acrylic, Supply with control valve, Manometric tubes (11 no)fixed over flow channel with separate scale, Sump tank, Measuring tank and inlet and outlet pipe (150mm diameter) with stop watch and accessories .

Theory Kinetic Energy:- The kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. Potential Energy:- The potential energy is the energy of an object or a system due to the position of the body or the arrangement of the particles of the system. The SI unit for measuring work and energy is the joule (symbol J). If the work of forces of this type acting on a body that moves from a start to an end position is defined only by these two positions and does not depend on the trajectory of the body between the two, then there is a function known as a potential that can be evaluated at the two positions to determine this work. Furthermore, the force field is defined by this potential function, also called potential energy. Pressure Energy:- Pressure in a fluid may be considered to be a measure of energy per unit volume or energy density. For a force exerted on a fluid, this can be seen from the definition of pressure. Pressure in a fluid can be seen to be a measure of energy per unit volume by means of the definition of work. This energy is related to other forms of fluid energy by the Bernoulli equation. Bernoulli’s theorem:- Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy, and a decrease in its static pressure and potential energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ρ g h) is the same everywhere.

Experimental procedure (1) Start the motor. (2) Open the bypass valve fully. (3) Control the gate valve for steady flow. (4) Allow some time to raise the water level in manometer tubes. (5) Take the height level in manometer tubes. (6) Take the time required for 100 mm rise in water level of measuring tank. Precautions & Tips 1) Carefully kept some level of fluid in inlet and outlet supply tank. 2) When fluid is flowing there is fluctuation in the height of piezometer tubes, note the mean position

carefully.

Observations Size of the sump tank = 1 x 0.5 x 0.4(height) m3 Size of the measuring tank = 0.5 x 0.4 x 0.4(height) m3 Width of channel = 0.05 m Tabulation:

Working Sheet 1. Discharge, Q = Area of measuring tank x rise in water level of measuring tank / Time required

= ------------------m3/sec. 2. Velocity, V = Q/A = ----------------m/sec 3. Pressure, P = ρ. g. h = ---------------- N/m2

Where, ρ=Density of the liquid, kg/m3 g = Acceleration due to gravity, 9.81 m2/sec h = Head in meters.

4. Pressure head = P/w =-----------------meters.of water. Where, w = Specific weight of water, 9810N/m3

Results & conclusions On the basis of above results it concludes that the sum of kinetic, potential and pressure energy of fluid is same at any point in the tube. Hence Bernoulli’s theorem is verified. Viva questions 1) Briefly Explain the various term involve in Bernoulli’s Equation. 2) What is Piezometer tube? 3) What Assumptions made to get Bernoulli’s equation from Euler equation?

S. no. Tubes No.

Head h in meters

Height of the channel in

mts

C/s area of channel. A in m2

P/w V2/2g P/w+ V2/2g

1

2

3

4

EXPERIMENT NO .3 Aim To measure the discharge through a venturimeter. Apparatus Venturimeter, U-tube manometer, Stop watch, water tank Theory Principle on which venturimeter works:- The fluid whose flow rate is to be measured enters the entry section of the venturimeter with a pressure P1.As the fluid from the entry section of venturimeter flows into the converging section, its pressure keeps on reducing and attains a minimum value P2 when it enters the throat. That is, in the throat, the fluid pressure P2 will be minimum. The differential pressure sensor attached between the entry and throat section of the venturimeter records the pressure difference (P1-P2) which becomes an indication of the flow rate of the fluid through the pipe when calibrated. The diverging section has been provided to enable the fluid to regain its pressure and hence its kinetic energy Procedure 1. Start the Centrifugal pump which supplies water to the Venturimeter. 2. Regulate the supply of water to the Venturimeter by adjusting the valve to a particular Discharge

Position. 3. Note down the time (t) taken for a given amount to rise (y meters) in the level of water in the

Measuring tank. 4. Note down the manometer reading. 5. Repeat the procedure Nos. (1) to (4) for different discharge through the venturimeter. 6. Tabulate the result: and determine the average value of the coefficient of discharge. Precautions & Tips 1. Keep the other valve closed while taking reading through one pipe. 2. The intial error in 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 while taking reading the manometer.

Observations Diameter of Venturimeter at inlet, d1 = meters Diameter of Venturimeter at throat, d2 = meters Specific gravity of manometer liquid, Sm = 13.6 (Hg) Specific gravity of water, Sw = Area of the measuring tank, A = meters Rise in level of water in measuring tank, y = meters Tabulations:

S. no. Manometer reading

Mts. of Hg X=X1-X2 mts of Hg

Head,(h) mts of H2O

Time taken for 2 cm rise,

sec

Qthe m3/sec

Qact m3/sec Cd Avg. Cd

X1 X2

1

2

3

4

5

6

7 Specimen Calculations: 1. C/ S area of venturimeter at inlet A1 = π. (d1 )2/4 = ----------m2

2. C/ S area of venturimeter at throat A 2 = π. (d2 )2/4 = ----------m2

3. Reading differential manometer, X = X1 - X2 = -----------------------mts of Hg. 4. Head in mts of water, h = X[(Sm/ Sw)-1] = ----------mts of water. 5. Theoretical Discharge, Q theo. = {A1A2(2gh)1/2] / [ A1

2 – A22]1/2

6. Actual discharge, Q act = Ay/t 7. Coefficient of discharge, Cd = Q act /Q theo. Results & Conclusion From the experiments it concludes that the mass flow rate of fluid is constant. By using the venturimeter we calculate the difference of manometer reading & coefficient of discharge for different sets of reading. Viva questions 1. Venturimeter are used for flow measuring. How? 2. Define coefficient of discharge? 3. Define parallax error? 4. Define Throat? 5. Define diverging part?

EXPERIMENT NO .4 AIM To measure discharge through orifice meter. Apparatus Experimental setup. Theory 1. Explain the principle on which orifice meter works. 2. Derive an expression for the theoretical discharge through the orifice meter starting

from Bernoulli’s equation Experimental procedure 1. Start the Centrifugal pump which supplies water to the orifice meter. 2. Regulate the supply of water to the orifice meter by adjusting the valve to a particular Discharge

position. 3. Note down the time (t) taken for a given amount to rise (y mts) in the level of water in the measuring

tank. 4. Note down the manometer reading. 5. Repeat the procedure Nos. (1) to (4) for different discharge through the orifice meter. 6. Tabulate the result and determine the average value of the coefficient of discharge. Precaution & Tips 1. Take the reading of discharge accurately. 2. Take value of h without any parallax error 3. Set the orifice and mouthpiece. 4. Take reading from hook gauge carefully. Observation Diameter of Orifice at inlet , d1 = Diameter of Orifice at throat, d2 = Specific gravity of manometer liquid, Sm = Specific gravity of water, Sw = 1 Area of the measuring tank, A = Rise in level of water in measuring tank, y =

Tabulation:

S. no. Manometer

reading Mts. of Hg X=X1-X2 mts of Hg

Head, h mts of H2O

Time taken for 2 cm rise, t sec

Qthe m3/sec

Qact m3/sec Cd Avg. Cd

X1 X2

1

2 3 4 5 6 7

Specification Calculations: 1. C/ S area of orifice meter at inlet A1 = π. (d1)2/4 = ----------m2

2. C/ S area orifice meter at throat A 2 = π. (d2)2/4 = ----------m2

3. Reading differential manometer, X = X1 - X2 = -----------------------mts of Hg. 4. Head in mts of water, h = X [(Sm/ Sw)-1] = ----------mts of water. 5. Theoretical Discharge, Q theo. = {A1A2 (2gh) 1/2] / [A1

2 – A22]1/2

6. Actual discharge, Q act = A y/t 7. Coefficient of discharge, Cd = Q act /Q theo Result and conclusion Orifice meter is used to measure the discharge through pipe flow system by using following formula Q theo. = {A1A2 (2gh)1/2] / [ A1

2 – A22]1/2

Viva questions 1. Define orifice 2. Define mouthpiece 3. Define vena contracta 4. Define coefficient of velocity

EXPERIMENT NO.5 AIM: To find Metacentric Height The metacentric height 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 metacenter. A larger metacentric height implies greater initial stability against overturning. Metacentric height also has implication on the natural period of rolling of a hull, with very large metacentric heights being associated with shorter periods of roll which are uncomfortable for passengers. Hence, a sufficiently high but not excessively high metacentric height is considered ideal for passenger ships. OBJECTIVE: This activity aims to find the metacentric height of the body under various conditions of loading. APPARATUS AND SUPPLIES The unit shown in Fig. 1 consists of a pontoon and a water tank as float vessel. The rectangular pontoon is fitted with a vertical sliding weight which permits adjustment of the height of the center of gravity and a horizontal sliding weight that generates a defined tilting moment. The sliding weights can be fixed in any position using knurled screws. The position of the sliding weights and the draught of the pontoon can be measured using the scales. A heel indicator is also available for measuring the heel angle. PROCEDURE 1. Set the horizontal sliding weight to position x from the center. 2. Move the vertical sliding weight to bottom position. 3. Fill the tank with water and insert the floating body. 4. Gradually raise the vertical sliding weight and read off angle on heel indicator. Read off height of

sliding weight at top edge of weight and enter in table together with angle. 5. Raise the vertical sliding weight until the floating apparatus reach instability point and record this

data point. Compare it with the previous results. DISCUSSION: Floating bodies are a special case; only a portion of the body is submerged with the remainder poking of the free surface. The buoyant force, FA, which is the weight of the displaced water, i.e., submerged body portion, is equal to its dead weight, FG. The center of gravity of the displaced water mass is referred to as the center of buoyancy, A and the center of gravity of the body is known as the center of mass, S. In equilibrium position buoyant force, FA, and dead weight, FG, have the same line of action and are equal and opposite (see Fig. 2). A submerged body is stable if its center of mass locates below the center of buoyancy. However, this is not the essential condition for stability in floating bodies. A floating body is stable as far as a resetting moment exists in the event of deflection or tilting from the equilibrium position. As shown in Fig. 3, dead weight FG and buoyant force FA

form a couple force with the lever arm of b, which provides a righting moment. The distance between the center of gravity and the point of intersection of line of action of buoyant force and symmetry axis, is a measure of stability. The point of intersection is referred to as the metacentre, M, and the distance between the center of gravity and the metacentre is called the metacentric height, zm. The floating object is stable when the metacentric height zm is positive, i.e., the metacentre is located above the center of gravity; else it is unstable. The position of the metacentre is not governed by the position of the center of gravity. It merely depends on the shape of the portion of the body under water. There are two methods of determining the metacentre position. In the first method, the center of gravity is laterally shifted by a certain constant distance, xs , using an additional weight, causing the body to tilt. Further vertical shifting of the center of gravity alters the heel angle, ɑ. A stability gradient formed from the derivation dxs/dɑ is then defined which decreases as the vertical center of gravity position approaches the metacentre. If the center of gravity and metacentre coincide, the stability gradient is equal to zero and the system is stable. This problem is easily solved graphically (see Fig. 4). The vertical center of gravity position is plotted versus the stability gradient. A curve is drawn through the measured points and extrapolated as far as it contacts the vertical axis. The point of intersection with the vertical axis .

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