Fluid Mechanics-I Lab Manual

Civil Engineering Department Fluid Mechanics-I

EXPERIMENT NO: 01CALCULATION OF SURFACE TENSIONTheory and Scope:All liquids exhibit a free surface known as meniscus when in contact with vapour or gas. Liquid molecules exhibit cohesive forces binding them with each other. The molecules below the surface are generally free to move within the liquid and they move at random. When they reach the surface they reach a dead end in the sense that no molecules are present in great numbers above the surface to attract or pull them out of the surface. So they stop and return back into the liquid. A thin layer of little atomic thickness at the surface formed by the cohesive bond between atoms slows down and sends back the molecules reaching the surface. This cohesive bond exhibits a tensile strength for the surface layer and this is known as surface tension. Force is found necessary to stretch the surface.Surface tension may also be defined as the work in Nm/m2 or N/m required to create unit surface of the liquid. The work is actually required for pulling up the molecules with lower energy from below, to form the surface.Another definition for surface tension is the force required to keep unit length of the surface film in equilibrium (N/m). The formation of bubbles, droplets and free jets are due to the surface tension of the liquid.Surface tension is calculated as,

σ = Where, ρ = surface tensiond = diameter of capillary tubeh = rise of liquid in capillary tubeθ = contact angle between glass and liquidg = acceleration due to gravity

SBPCOE, Indapur Page 1


Aim: To determine the surface tension of water and mercury by capillary rise method.Apparatus:

Capillary tube A tipped pointer clamped in a stand Travelling microscope Clean water Mercury Beaker.

Procedure: Find the least count of the travelling microscope for the horizontal and the vertical scale and record it. Raise the microscope to a suitable height, keeping its axis horizontal and towards the capillary tube. Bring the microscope in front of first capillary tube. Make the horizontal cross wire just touch the central part of the concave meniscus. Note the reading of the position of the microscope on the vertical scale. Lower the stand so that pointer tip becomes visible. Move the microscope horizontally and bring it in front of the pointer. Lower the microscope and make the horizontal cross wire touch the tip of the pointer. Note the reading.

Observations:



DetailsReading of

meniscus, h1 (m)

Reading of pointer tip, h2

(m)

Height,h = h1-h2

(m)

Surface Tension, σ

in N/m

Average Surface Tension,

N/m

For

Wat

er

For 1st tube

For 2nd tube

For

Mer

cury

For 1st tube

For 2nd tube

Calculations:Surface tension = σ = N/m

A) For Water:Radius of the capillary tube:1. First Tube = …….m2. Second Tube = …….mHeight of water in the capillary tube:1. First Tube = …….m2. Second Tube = …….m

B) For Mercury:Radius of the capillary tube:3. First Tube = …….m4. Second Tube = …….mHeight of mercury in the capillary tube:3. First Tube = …….m4. Second Tube = …….m



Result:1. The surface tension of water =…………..N/m. 2. The surface tension of mercury =…………..N/m.

Conclusion:___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________EXPERIMENT NO: 02PRESSURE MEASURING DEVICESTheory and Scope:Pressure represents a contact force per unit area. It acts inwards and normal to the surface of any physical boundary that a fluid contacts. A basic understanding of the origin of a pressure involves the consideration of the forces acting between the fluid molecules and the solid boundaries containing the fluid. For example, consider the measurement of pressure at the wall of a vessel containing a perfect gas. As a molecule with some amount of momentum collides with the solid boundary, it will rebound off in a different direction. From Newton’s second law, we know that the change in linear momentum of the molecule produces an equal but opposite force on the boundary. It is net effect of these collisions that yields the pressure sensed at the boundary surface. Factors that affect the magnitude or frequency of the collisions, such as fluid temperature and fluid density, will affect the pressure.



Aim: To study different pressure measuring devices.Apparatus:

Piezometer tube simple U tube Differential U tube Inverted manometer Bourdon pressure gauge.

Details of Apparatus:A) Piezometer Tube: Piezometer is a simple transparent glass tube which is connected by flexible rubber tubing and pressure tapping to the pipe. Piezometric tubes are used for measurement of pressure at a point. A piezomeric tube is tapped into the wall of the container or conduit.

B) Simple U tube Manometer: A manometer transparent tube of 10mmor more, bent in a U shape is called U-tube or simple manometer. U tube manometer can measure both positive and negative pressures.The manometric liquid used should fulfill the following requirements:-1. It should not mix with the flowing fluid.2. It should not chemically react with the flowing fluid or the pipe wall material.3. It should have higher density than the flowing fluid.4. It should not stick (adhere) to the tube.5. Its boiling point should be much higher than the atmospheric temperature.6. It should be clearly visible.SBPCOE, Indapur Page 5


One of the limbs of U-tube manometer is longer than the other and is kept open to the atmosphere. This is called open limb. The other limb is connected to the pressure tapping. The mercury level (bottom of the concave meniscus of the mercury) in each limb is read, difference is calculated; called deflection.

C) Differential manometer: A U tube manometer having equal limbs, connected to two pressure tappings (none open to atmosphere) is called differential manometer. The two pressure tappings may be on two different pipes or on one pipe, at two places.

D) Inverted U-tube manometer: A tube manometer having two equal limbs connected to be inverted position. Whenever the manometric liquid is lighter in density than the liquid in the pipe, the differential manometer (U-tube) is required to be held inverted. Use of lighter manometric liquid increases sensitivity of the manometer.



E) Bourdon Pressure Gauge: It consists of an elastic metal tube, having elliptical cross-section. The tube is bent in circular shape one end of the tube is called tip which is sealed and connected by a link to a geared sector. A pointer is fixed to the pinion and the movement of the tip is communicated to the pointer. The pointer moves on scale and indicates pressure in kPa or KN/m²

Procedure:a) Piezometer (Refer fig 2.1)SBPCOE, Indapur Page 7


1) When the pressure is to be measured, the tap is put on.2) The liquid in the pipe rises into the Piezometer till the time when the pressure inside the pipe is equal to the pressure exerted by ‘h’ m of the liquid plus the atmospheric pressure.3) When the liquid stop rising, the piezometer head ‘h’ is measured by a scale or graduations on the tube, with its zero at the centre of the pipe.4) Under the equilibrium condition,PA = SLγh in terms of gauge pressure.Where γ - specific weight of liquidSL – specific gravity of liquid.b) U-tube manometer1. Pressure at A is positive (Refer fig. 2.2 a). The manometric equation can be written as PB = PCPA+ SLγ y1 = SmγhPA = Smγh – SLγy1Where, Sm – specific gravity of manometric liquid2. Pressure at A is negative (Refer fig 2.2 b). The Manometric equation for this condition is, PB = PC --------------- (Pascal’s law) PA + SLγy1 + Smγh = 0 ---------------- (gauge pressure) PA = - [ SLγy1 + Smγh]c) Differential manometer (Refer fig. 2.3)1. The point C and D are on the horizontal line, in continuos liquid; Even though points E and F are on horizontal line, the liquid is not continuous and hence pressure at E is not to equal pressure at F2. PC= PA + SLγy1PD = PB + SLγy2+ Smγh (∴ PC = PD)PA – PB = SL γ (y2 – y1) + Sm γhFrom geometry of the fig, y1 + z = y2 + hy2 – y1 = z - hPA – PB = SL γz – SL γh [Sm/SL – 1]3. If points A and B are at the same level, z = o hence;PA – PB =– SL γh [Sm/SL – 1]SBPCOE, Indapur Page 8


d) Inverted manometer (Fig. 2.4)1. Applying Pascal law, PA = PBP1 – SL γy1 = P2 – SLγ y2 – SmγhP1 – P2 = SLγ ( y1 – y2) – Smγh2. By geometry, y1 = y2 + h i.e. y1 – y2 = h3. Substituting P1 – P2 = SLγ (y1 – y2) – Smγh, in step (1)P1 – P2 = SLγh (1 –Sm/SL)e) Bourdon’s pressure gauge1. The fluid under pressure enters the curved tube at the fixed end and tends to straighten out this tube.2. The movement of the free end of the tube is transferred to the needle by means of levers, rack and pinion arrangements, and the needle moves to indicate the pressure on a properly calibrated scale.Oberservations: Sr No Type of Device Manometric Readings Formula Pressure/ Pressure differencey1 y2 y = y1 – y21 Piezometer PA = SLγh2 Single U-tube manometer PA = Smγh – SLγy13 Differential manometer PA – PB =– SL γh [Sm/SL – 1]4 Inverted U-tube manometer

P1 – P2 = SLγh (1 –Sm/SL)5 Bourdon pressure gauge --

Result: The pressure by various pressure measuring devices is measured.SBPCOE, Indapur Page 9


EXPERIMENT NO: 03VISCOCITY TESTTheory and Scope:Viscosity is the property of fluid. It is defined as “The internal resistance offered by the fluid to the movement of one layer of fluid over an adjacent layer”. It is due to the Cohesion between the molecules of the fluid. The fluid which obeys the Newton law of Viscosity is called as Newtonian fluid.The dynamic viscosity of fluid is defined as the shear required to produce unit rate of angular deformation.The redwood viscometer consists of vertical cylindrical oil cup with an orifice in the centre of its base. The orifice can be closed by a ball. A hook pointing upward serves as a guide mark for filling the oil. The cylindrical cup is surrounded by the water bath. The water bath maintains the temperature of the oil to be tested at constant temperature. The oil is heated by heating the water bath by means of an immersed electric heater in the water bath, the provision is made for stirring the water, to maintain the uniform temperature in the water bath and to place the thermometer ti record the temperature of oil and water bath. The cylinder is 47.625mm in diameter and 88.90mm deep. The orifice is 1.70mm in diameter and 12mm in length, this viscometer is used to determine the kinematic viscosity of the oil. From the kinematic viscosity the dynamic viscosity is determined.Kinematic Viscosity = ν = At - B in Stokes tDynamic viscocity = μ = νρ in Poise Where, A = 0.0026 & B = 1.72 are constants of instruments.t = time in seconds



Aim: To determine the kinematic viscosity and absolute viscosity of the given lubricating oil at different temperatures using Redwood Viscometer.Apparatus:

Redwood Viscometer Thermometer 0-100°C Stop watch 50 ml standard narrow necked flask Given Sample of oil

Procedure: Clean the cylindrical oil cup and ensure the orifice tube is free from dirt. Close the orifice with ball valve. Place the 50 ml flask below the opening of the Orifice. Fill the oil in the cylindrical oil cup upto the mark in the cup. Fill the water in the water bath. Insert the thermometers in their respective places to measure the oil and water bath temperatures. Heat the by heating the water bath, Stirred the water bath and maintain the uniform temperature. At particular temperature lift the ball valve and collect the oil in the 50 ml flask and note the time taken in seconds for the collecting 50 ml of oil. A stop watch is used measure the time taken. This time is called Redwood seconds. Increase the temperature and repeat the procedure ‘8’ and note down the Redwood seconds for different temperatures.



Observations:

Sr No Temperature of oil 0C Time required to fill 50 ml flask in secKinematic viscocity in Strokes

Density in kg/m3Absolute or Dynamic viscocity in Poise12345678

Result: The kinematic and dynamic viscosity of given oil at different temperatures were determined.Graphs:

(1)Temperature Vs Redwood seconds(2)Temperature Vs Kinematic Viscosity(3)Temperature Vs Dynamic ViscosityConclusion:___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________



EXPERIMENT NO: 04DETERMINATION OF METACENTRIC HEIGHTTheory and Scope:Metacentre is the point at which the vertical through the centre of buoyancy intersects the vertical centre line of the section of body after a small angle of heal as shown in the figure below.



The distance between the centre of gravity G of the body and metacentre M (GM) is called as ‘Metacentric height’. Metacentric height is important in deciding the stability of floating body.Consider a ship floating in water. Let m be the movable wt. of a jockey placed centrally on the ship or body. Let W be weight of ship as well as jockey. Assume that the ship is initially horizontal and in equilibrium. Now move the jockey towards the right by a distance x, so that the body or vessel tilts by equilibrium position. The angle can be noted by hanging a pendulum from initial position of jockey. In the new equilibrium position the C.G. & center of buoyancy B are in a straight line again.

Now m*x = W *(GG1)GG1= GM tan

m*x = W*(GM*tan )

Now if L is the length of pendulum & d the distance moved by it on the horizontal Scale

The true metacentric height is the limiting value of GM as

Aim: To determine metacentric height of given ship model.Apparatus:

Ship model Plumb bob Weights Water tank

Procedure:SBPCOE, Indapur Page 14


1. Weigh the weight of ship model and note down its value, say W.2. Put the ship model in the tank filled with water and displace the movable mass so as to tilt the model through a small angle θ.3. Note down the distances x1 and x2 from the crossbar and find x.4. Note down the angle of deflection on the graduated scale.5. Repeat the procedure for various distances of jockey weight on left and right to the center of ship model. Obeservations:

Sr. No.Weight on Ship, jockey weight (m)Kg

x1, cm x2, cm x, cm Angle of deflection θMetacentric Height Average Metacentric Height, cm12345678910Calculations:

Experimentally the GM (Metacentric height) is given by,GM= W = Weight of Ship model in kg = ……….kg m = Load attached (jockey weight). = Angle through which the ship is deflected.Result:The metacentric height for the given ship model is found to be ……………cmConclusion:SBPCOE, Indapur Page 15


As the angle of tilt (θ) increases, Metacentric Height (MG or GM) also ……………increases / decreases.

EXPERIMENT NO: 05HELESHAW APPARUTUSTheory and Scope:The flow of real fluids can take place in laminar, transition or turbulent states. The laminar flow can be distinguished by a non-dimensional number called Reynolds number which should be less than 2000 for normal conditions. Then flow becomes transitional after 2000 and beyond 4000 it is turbulent. The flow patterns can be visualized by immersing bodies of various shapes and maintaining the flow in the laminar region. For water to flow in streamlines i.e. laminar flow the space between transparent sheets is kept very small. Water and colored lines are introduced in alternate flow paths to differentiate them from each other. As the water and color lines flow pass around the immersed bodies a flow SBPCOE, Indapur Page 16


pattern is developed. These flow patterns are different for different bodies and their orientation.Aim: Study of flow around immersed bodies by Heleshaw apparatus.Apparatus:

Heleshaw apparatus Objects of different shapes Colour dye Measuring cylinder, etc.

Procedure: Heleshaw apparatus is filled with water till, air is driven out. The outlet tap is partially opened and a drop by drop flow through it is maintained. The water and color dye is simultaneously filled in respective compartments keeping water level more than that of color dye to avoid diffusion of color in to water compartment. The flow lines developed around the object and salient features like stagnation point, formation of wake, etc are observed. Fix a tracing paper over glass plate, between inlet and outlet reservoir and trace the pattern of streamlines and geometry of the object. This flow is measured by collecting it in a measuring cylinder and noting the time by a stop watch. Flow rate is varied and flow pattern is studied as mentioned earlier. The orientation of object is changed and again the flow pattern is studied. The procedure is repeated for another model.

Observations:Length of flow passage, L =Width of flow passage, W =Kinematic viscosity ν of liquid at temperature °C = Sr.No. Shape of object

Volume of water collected (m3)Time ‘ t ‘( sec) Discharge m3/s Reynolds number Type of flow

12



345678910

Calculations:C/s area of flow passage, A =Discharge, Q = Volume / time = m3/sVelocity, V = Q / A = m/sReynolds number Re = VW/ν = Conclusion: The various flow patterns around the bodies are observed. The points of stagnation and wake formation are clearly noted. For laminar flow streak lines remain parallel to each other. Hence clear flow pattern can be observed. For turbulent flow streak lines mix with each other hence clear flow patterns cannot be observed.

EXPERIMENT NO: 06BERNOULLI’S THEOREMTheory and Scope:The principal of conservation of energy gives Bernoulli’s theorem, which states that for an incompressible fluid flowing through passage the SBPCOE, Indapur Page 18


total energy (total head ) remains constant for all points. The total head possessed by the fluid motion at a point is sum of datum head, z, pressure head and velocity head .For ideal fluid, mathematically it can be written as,

2

222

1

211

22z

g

vpz

g

vp

,

zg

vp

2

2

Constant

Where, P / + Z = piezometric head

For real fluids, loss of energy due to friction and minor losses has to be considered in the direction of flow and account separately .Thus mathematically modified Bernoulli’s theorem is

Lhzg

vpz

g

vp 2

222

1

211

22

Where, hL=Losses

Aim: To verify modified Bernoulli’s theorem.Apparatus:

Bernoulli’s apparatus with flow table of self-circulating system. Measuring tank. Stopwatch.

Procedure: The Bernoulli’s apparatus is set up and connected to inlet pipe. Make sure that no air bubble is entrapped in the piezometers.



The flow of water is then started and allowed to stabilize following which the pressure head readings in ‘m’ of water column are noted at all the pressure tappings provided. (11 in this case) The flow of water is collected in measuring tank for known capacity and time required to collect the water is measured. The procedure is repeated for different values of the discharge.

Observations:Piezometer

No.

Height mm.

Width mm

Area m2

Pressure head

‘m’ of water

column

‘m’ of water

column

Velocity

V m/sec

velocity head

Total energy

1 24.46 25 1a =0.000612

2 23.17 25 2a =0.000579

3 21.88 25 3a =0.000547

4 20.58 25 4a =0.000515

5 19.29 25 5a =0.000482

6 18 25 6a =0.00045

7 18.64 25 7a =0.000466

8 19.27 25 8a =0.000482

9 19.91 25 9a =0.000498

10 20.25 25 10a =0.000506

11 21.18 2511a =0.00053

Calculations: 1. Pressure head = =_______ ‘m’ of water columnSBPCOE, Indapur Page 20


2. Discharge = Q = volume of collected water / Time for collection of 1 lit of water. = =_________ m3/sec.3. Velocity at First Piezometer location :

11 a

Qv = =______m/s

g

v

2

21 = ______

4. As channel is horizontal 16321 ........... zzzz = constant and therefore the value is not substituted in the equation.5. Total Energy head: =__________

Graph:

A graph is to be plotted by plotting the number of piezometers on X-axis and pressure head, and total head on Y axis to show the total energy line and hydraulic gradient line.

Conclusion:1. In real flow, there is loss of energy in the direction of flow hence the total energy gradient is falling.2. The hydraulic gradient is observed to rise or fall.3. For a real fluid to account for losses, adding the losses modifies the Bernoulli’s theorem.



Bernoulli’s Apparatus



EXPERIMENT NO: 07DETERMINATION OF PIPE FRICTION FACTORTheory:The flow of liquid through a pipe is resisted by viscous shear stresses within the liquid and the turbulence that occurs along the internal walls of the pipe, created by the roughness of the pipe material. This resistance is usually known as pipe friction and is measured is meters head of the fluid, thus the term head loss is also used to express the resistance to flow.Many factors affect the head loss in pipes, the viscosity of the fluid being handled, the size of the pipes, the roughness of the internal surface of the pipes, the changes in elevations within the system and the length of travel of the fluid. The resistance through various valves and fittings will also contribute to the overall head loss. In a well designed system the resistance through valves and fittings will be of minor significance to the overall head loss and thus are called Major losses in fluid flow.The Darcy-Weisbach equation

Weisbach first proposed the equation we now know as the Darcy-Weisbach formula or Darcy-Weisbach equation:gD2

vfh

2

f

Hence, 2

f

v

gD2hf

Where, f = Darcy’s Friction factorl = length between pressure tappingV= velocity in pipeD = Diameter of pipehf = Head lossAim: To determine friction factor for the given pipes.Apparatus:

A set of pipes fitted with control valves for varying the flow and provided with pressure tapping manometer stopwatch measuring tank



Procedure: Fill the storage tank/sump with the water. Switch on the pump and keep the control valve fully open and close the bypass valve to have maximum flow rate through the meter. To find friction factor of pipe 1 open control valve of the same and close other to valves Open the vent cocks provided for the particular pipe 1 of the manometer. Note down the difference of level of mercury in the manometer limbs. Keep the drain valve of the measuring tank open till its time to start collecting the water. Close the drain valve of the measuring tank and collect known quantity of water Note down the time required for the same. Change the flow rate of water through the meter with the help of control valve and repeat the above procedure. Similarly for pipe 2 and 3 . Repeat the same procedure indicated in step 4-9 Take about 2-3 readings for different flow rates.

Observations:A) For Pipe No.1:Diameter of pipe =0.015 mLength of pipe = 2.5 mArea of measuring tank = 0.5 x 0.35 m 2

Sr.NoVolume of water collectedV m3

Time ‘t’ required for collection of water in secActual Discharge Qact m3/s

Velocity of flow in pipe v m/s

Head difference in manometer (Head Loss)hf in m

Friction factorfAverageValue of f

123456SBPCOE, Indapur Page 24


A) For Pipe No.2:Diameter of pipe =0.025 mLength of pipe = 2.5 mArea of measuring tank = 0.5 x 0.35 m2






123456A) For Pipe No.3:Diameter of pipe =0.040 mLength of pipe = 2.5 mArea of measuring tank = 0.5 x 0.35 m2






123456Calculations:1. Discharge (Q) = A x h tSBPCOE, Indapur Page 25


2. Velocity (v) = Q A3. Head loss (hf) = 4. Friction factor

Result: The friction factor for given pipes is found as-A) For Pipe-1= ______________B) For Pipe-2 = ______________C) For Pipe-3 = ______________



EXPERIMENT NO: 08CALIBERATION OF VENTUREMETERTheory and Scope:

Venturimeter is a device, used to measure the discharge of any liquid flowing through a pipe line. The pressure difference between the inlet and the throat of the Venturimeter is recorded using a mercury differential SBPCOE, Indapur Page 27


manometer, and the time is recorded for a measured discharge. Venturimeters are used to measure the flow rate of fluid in a pipe. It consists of a short length of pipe tapering to a narrow throat in the middle and then diverging gradually due to the reduced area and hence there is a pressure drop. By measuring the pressure drop with a manometer, the flow rate can be calculated by applying Bernoulli’s equation.The meters are fitted in the piping system with sufficiently long pipe lengths (greater than 10 mm diameter) upstream of the meters. Each pipe has the respective Venturimeter with quick action cocks for pressure tappings. These pressure tappings are connected to a common middle chamber, which in turn is connected to a differential manometer. Each pipe line is provided with a flow control water is collected in an M.S. collecting tank of cross sectional are 0.4 m x 0.4 m provided with gauge scale fitting and drain valve.Aim: To determine the Coefficient Cd of Venturimeter.Apparatus:

Ventrurimeter, Manometer Measuring tank Stopwatch

Procedure: The diameters of the inlet and throat are recorded and the internal plan dimensions of the collecting tank are measured. Keeping the outlet valve closed, the inlet valve is opened fully. The outlet vale is opened slightly and the manometric heads in both the limbs (h1 and h2) are noted. The outlet valve of the collecting tank is closed tightly and the time‘t’ required for ‘H’ rise of water in the collecting tank is observed using a stop watch. The above procedure is repeated by gradually increasing the flow and observing the required readings. The observations are tabulated and the co-efficient of the Venturimeter is computed.

Observations:1. Diameter of pipe = 26 mm2. Diameter of throat = 16 mmSBPCOE, Indapur Page 28


3. Area of pipe a1 = 5.22 x 10-4 m24. Area of throat a2 = 2.01 x 10-4 m25. Area of tank = 0.5 x 0.35 = 0.175 m2

Sr NoManometer Readings Volume of water collected V m3

Time ‘t’ required for collection of water in sec

Actual Discharge Qact m3/sHeight of water (H) in m of water

Therotical DischargeQthe m3/sCoefficient of Discharge Cd

Average Coefficient of Discharge, Cdh1 h2 h=h1-h2

12345678Calculations:1) Manometric Head H= 2) Theoretical Discharge:Qthe =

3) Actual Discharge:Qact = 4) Coefficient of discharge of venturimeter:Cd =



Graphs:Draw a graph of Actual Discharge Vs Theoretical Discharge and Find the Slop of the resultant straight line.

Result:1. The average co-efficient of discharge was calculated and found out to be _______.2. The Slope of the Straight line in the curve is found to be __________.


Documents

Fluid Mechanics-I Lab Manual