Fluid Mechanics I - Jawaharlal Nehru Engineering College
MAHATMA GANDHI MISSION’SJAWAHARLAL NEHRU ENGINEERING COLLEGE,AURANGABAD. (M.S.)DEPARTMENT OF CIVIL ENGINEERINGFLUID MECHANICS LABORATORYMANUALPrepared ByApproved ByMr. L. K. KokateProf. B. M. PatilLab InchargeJNEC CIVIL/FM-I/AUG 2010H.O.D. CIVILPage 1
’FLUID MECHANICS -I’ EXPERIMENTSSUBJECT: - Fluid Mechanics-ICLASS: - Second Year Civil EngineeringLIST OF EXPERIMENTSSr. No.Name of ExperimentPage No.FromIStudy of pressure measuring devices.IIDetermination of meta centric height.IIICalibration of Bernoulli’s equation.IVCalibration of Venturimeter.VDetermination of Hydraulic coefficient for orifices.VIDetermination of coefficient of discharge for mouthpiece.VIICalibration of Rectangular notch.VIIICalibration of Triangular Notch.IXToStudy of electrical analogy method for plotting of flow nets.Time Allotted for each Practical Session 02 Hrs.JNEC CIVIL/FM-I/AUG 2010Page 2
EXPERIMENT NO: II - To Determine the Metacentric Height of a Cargo / War ShipAIM: - To Determine the Metacentric Height of a Cargo / War ShipINTRODUCTION:Metacenter is defined as, the point about which the body starts oscillating when it is tilted (inclined) by asmall angle.Metacenter may also be defined as, the point at which the line of action of force of buoyancy will meet thenormal axis of the body when the bodyody is given a small angular displacement.Metacentric Height is defined as, the distance between the Metacenter of a floating body & center of gravity.DESCRIPTION:The shipmodel isapproximately 37cm size square inplan and is about23 cm high. Themodel is floated onwater. The ship istilted by moving asmall weight at thelevel of the deckof the ship. Tonote down the tiltof the ship, aplumb is providedwhich records thetilt on a graduatedarc of a circle. Anarrangement ismade to load theJNEC CIVIL/FM-I/AUG 2010Page 3
ship as a War ship or Cargo ship.PROCEDURE:-Sr.For Cargo ShipNo.1Place suitable symmetrical weights at thePlace suitable symmetrical weights at the deckbottom of the ship and load it as a Cargo Ship.level of the ship and load it as a War Ship.23For War ShipFloat the ship on the water.Float the ship on the water.Adjust the balancing weights on both the sidesAdjust the balancing weights on both the sidesof the ship so that the Plumb indicates zeroof the ship so that the Plumb indicates zeroreading on the graduated arc.reading on the graduated arc.Keep the Moving (Hanging) Load/Weight at aKeep the Moving (Hanging) Load/Weight at adistance of 3.5 cm off the centre on left side.distance of 3.5 cm off the centre on left side.5Note down the tilt of the ship in degrees.Note down the tilt of the ship in degrees.6Go on shifting the Hanging Load towards left &Go on shifting the Hanging Load towards leftnote down the distance of the centre, & tilt of& note down the distance of the centre, & tiltthe ship.of the ship.47Repeat the procedure by shifting the load on theRepeat the procedure by shifting the load onright hand side of the centre.the right hand side of the centre.OBSERVATIONW1 Weight of the ship including balancing weight in grams.W2 Total weight added to make it as a Cargo / War Ship.W3 Weight of the Hanging Load in grams.JNEC CIVIL/FM-I/AUG 2010Page 4
OBSERVATION TABLE:-Distance offthe centre tothe left ‘X’ incmsSr.No.Tilt of theShip ‘θ’ indegreesMetacentricHeight MG1 incms.Distance offthe centre tothe left ‘X’in cmsTilt of theShip ‘θ’ indegreesMetacentricHeight MG2 incmsAverageMG incms1234SPECIMEN CALCULATIONS:W (w1 w2) in grams.MG1 or MG2 Metacentric Heights in centimeters. W1 x X / W x tan θ0Average MG MG1 MG2 / 2RESULTS: Metacentric Height of a Cargo Ship (MG c) .cms. Metacentric Height of a War Ship (MGw) .cms.CONCLUSION:-JNEC CIVIL/FM-I/AUG 2010Page 5
As the angle of tilt (θ0) increases, Metacentric Height (MG or GM) also increases / decreases.EXPERIMENT NO: III - to Verify Bernoulli’s TheoremAIM-: 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 anypoint 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,Pressure Energy P / ρgKinetic Energy V2 / 2g&Datum Energy ZThe applications of Bernoulli’s theorem are-:1) Venturi Meter2) Orifice Meter3) Pilot TubeJNEC CIVIL/FM-I/AUG 2010Page 6
Description-:The equipment is designed as a self sufficient unit; it has a sump tank, measuring tank, & 0.5 HP monoblock pump forwater circulation. The apparatus consists of Supply Tank & Delivery Tank, which are connected to a Perspex flowchannel. The channel tapers for a length of 25 cm & then piezopiezo-metermeter 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 & slowlyslostart 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 headsads 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.JNEC CIVIL/FM-I/AUG 2010Page 7
Specifications-:Tube 63.8No.C/S3.6AreaObservation Table-:Result-:1) At discharge .liters / second,Total head is .centimeters.2) At discharge .liters / second,Total head is .centimeters.JNEC CIVIL/FM-I/AUG 2010Page 8
EXPERIMENT NO: IV - FLOW THROUGH VENTURIMETERAIM:To determine the co-efficient (K) of the Venturimeter.DESCRIPTION:Venturimeter is a device, used to measure the discharge of any liquid flowing through a pipe line. Thepressure difference between the inlet and the throat of the Venturimeter is recorded using a mercury differentialmanometer, and the time is recorded for a measured discharge. Venturimeters are used to measure the flow rate offluid in a pipe. It consists of a short length of pipe tapering to a narrow throat in the middle and then diverginggradually due to the reduced area and hence there is a pressure drop. By measuring the pressure drop with amanometer, 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 differentialmanometer. Each pipe line is provided with a flow control water is collected in an M.S. collecting tank of crosssectional are 0.4 m x 0.4 m provided with gauge scale fitting and drain valve.PROCEDURE:1. The diameters of the inlet and throat are recorded and the internal plandimensions of the collecting tank are measured.2. Keeping the outlet valve closed, the inlet valve is opened fully.3. The outlet vale is opened slightly and the manometric heads in both the limbs (h1 and h2) are noted.4. The outlet valve of the collecting tank is closed tightly and the time‘t’ required for ‘H’ rise of waterin the collecting tank is observed using a stop watch.5. The above procedure is repeated by gradually increasing the flow and observing the requiredreadings.6. The observations are tabulated and the co-efficient of the Venturimeter is computed.JNEC CIVIL/FM-I/AUG 2010Page 9
FORMULAE USED:Constant of Venturimeter, K Where, a1 area of inleta2 area of throath Venturi head in terms of flowing liquid h1 Manometric head in one limb of the manometerh2 Manometric head in other limb of the manometerSm Specific gravity of following liquidS1 Specific gravity of following liquidg Acceleration due to gravityActual Discharge (Qa) JNEC CIVIL/FM-I/AUG 2010Page 10
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OBSERVATIONS AND RESULT:Diameter of inlet,d1 .mmDiameter of inlet,d2 .mmInternal plan dimensions of collecting tankSr.No.Manometric Readings (mm)of Waterh2Length,l .mmBreadth,b .mmVenturihead interms offlowingfluidDifferenceTime for‘H’ 100mm rise ‘t’Sec. ℎTrialsActualDischarge(mm3/sec)Coefficient ofVenturimeterAvg.(h) mmHX (h1-h2)12010203Mean Value of Cd .JNEC CIVIL/FM-I/AUG 2010Page 12
MODEL CALCULATIONS : (Reading No. )Area of inlet of Venturimetera1 πd12 /4 (mm2)Area of throat of Venturimetera2 πd22 /4 (mm2)Internal plan area of collecting tank lxbActual discharge,Qa Coefficient of Meter,(K) (mm2) (mm3/s)Qa / C. ℎGRAPH:Qa vs. ℎ----- ℎ on X-axisRESULT:Average Co-efficient of the Venturimeter, Cd ----------------------------------JNEC CIVIL/FM-I/AUG 2010Page 13
EXPERIMENT NO: VII CALIBRATION OF RECTANGULARNOTCHESObjectivesTo Determine the coefficient of discharge of the given Rectangular notch for different rates of flow.Equipment requiredThe given notch fitted on an open channel of the experiment setup, hookgauge to measure the water level over the notch and measuring tank with stopwatch to measure the actual flow rate.PrincipleIn open channel flows, weirs are commonly used to either regulate or to measure the volumetric flow rate.They are of particular use in large scale situations such as irrigation schemes, canals and rivers. For smallscale applications, weirs are often referred to as notches and are sharp edged and manufactured fromthin plate material. The basic principle is that discharge is directly related to the water depth above thecrotch (bottom) of the notch. This distance is called head over the notch. Due to the minimal installationcosts flow rate measurement with a notch is very less expensive. The rectangular notch is the mostcommonly used thin plate weir. The flow pattern over a notch or weir is complex and there is no analyticalSolution to the relationship between discharge and head so that a semi-empirical Approach has to be used.The expression for discharge over a rectangular notch is given by,where,L width of the notch, (m)h head of water over the notch, (m)g acceleration due to gravity (m/s2)Water is allowed to pass through the given notch at different flow rates. Actual discharge through the channel can be determined using the collecting tankand stopwatch setup.JNEC CIVIL/FM-I/AUG 2010Page 14
Where,a area of the collecting tank. (m2)H height difference of the water column in the piezometer, (m)t time taken to rise H meters, (sec)The coefficient of discharge CD is defined as the ratio of actual dischargeobtained experimentally to the theoretical discharge. i.e.Calibration is the validation of specific measurement techniques and equipment.It is the comparison between measurements of known magnitude madewith one device and another measurement made in as similar way as possiblewith a second device. In order to use any device for measurement it is necessaryto empirically calibrate them. That is, here in this case pass a known dischargethrough the notch and note the reading in order to provide a standard for measuringother quantities in a different location. Provided the standard mechanicsof construction are followed no further calibration is required for a similar seconddevice with same geometry.The calibration equation is stated as,Qac K hnwhere ,K and n are constants depending on the geometry of the notch. Takinglogarithm on both sides we get,logQac log k n log hwhich is the equation of a straight line,where ,log k is the y intercept and n is its slope.The graph logQac Vs. logh is to be plotted to find k and n.JNEC CIVIL/FM-I/AUG 2010Page 15
Procedure1. Check the experimental setup for leaks. Measure the dimensions of collectingtank and the notch.2. Observe the initial reading of the hook gauge and make sure there is nodischarge. Note down the sill level position of the hook gauge.3. Open the inlet valve of the supply pipe for a slightly increased discharge.Wait for sometime till the flow become steady.4. Adjust the hook gauge to touch the new water level and note down thereading. Difference of this hook gauge reading with initial still level readingis the head over the notch (h).5. Collect the water in the collecting tank and observe the time t to collect Hheight of water.6. Repeat the above procedure for different flow rates by adjusting the inletvalve opening and tabulate the readings.7. Complete the tabulation and find the mean value of CD.8. Draw the necessary graphs and calibrate the the notch.Observations and calculationsLength of the rectangular notch —mAngle of the triangular notch —degCollecting tank area — m2JNEC CIVIL/FM-I/AUG 2010Page 16
For a rectangular notch Q K H(3/2)K Cd .(2/3). (2g)(1/2).LSr.No.Hook GuageReadingC.BW.SDiff.H'(cm).H(m)Measuring TankReadingI.R.F.R.Diff.R'(cm)R(m)@ B mVol.Qact.QthCd.V AXR (m )V/T(m3/sec)(2/3). (2g).L.H(3/2)(m3/sec)Qact/Qth3log HlogQact1234567For first reading:Qact m3/secQtheo m3/secCd Q/ QtheoK Should be n (3/2 ) if we take the log for the two sides of equation :log Q log K n log H ,where n : the power of H ( the slope.) from table .log k from graph k Cd .Results and InferenceThe given notches are calibrated with the calibration equationwherek ,n for rectangular notch.The average coefficient of discharge of the given notches are,Rectangular notch, CDR The required characteristics are plotted.JNEC CIVIL/FM-I/AUG 2010Page 17
EXPERIMENT NO: VIII CALIBRATION OF TRIANGULARNOTCHESObjectivesTo Determine the coefficient of discharge of the given Triangular notch for different rates of flow.Equipment requiredThe given notch fitted on an open channel of the experiment setup, hookgauge to measure the water level over the notch and measuring tank with stopwatch to measure the actual flow rate.PrincipleIn open channel flows, weirs are commonly used to either regulate or to measurethe volumetric flow rate. They are of particular use in large scale situationssuch as irrigation schemes, canals and rivers. For small scale applications, weirsare often referred to as notches and are sharp edged and manufactured fromthin plate material. The basic principle is that discharge is directly related to thewater depth above the crotch (bottom) of the notch. This distance is called headover the notch. Due to the minimal installation costs flow rate measurementwith a notch is very less expensive.The V notch or triangular notch design causes small changes in discharge to have alarge change in depth allowing more accurate head measurement than with arectangular notch. The flow pattern over a notch or weir is complex and there is no analyticalsolution to the relationship between discharge and head so that a semi-empiricalapproach has to be used.The expression for discharge over a triangular notch is given by,where,L width of the notch, (m)θ angle of the notch, (deg)h head of water over the notch, (m)g acceleration due to gravity (m/s2)JNEC CIVIL/FM-I/AUG 2010Page 18
Water is allowed to pass through the given notch at different flow rates.Actual discharge through the channel can be determined using the collecting tankand stopwatch setup.Where,a area of the collecting tank. (m2)H height difference of the water column in the piezometer, (m)t time taken to rise H meters, (sec)The coefficient of discharge CD is defined as the ratio of actual dischargeobtained experimentally to the theoretical discharge. i.e.Calibration is the validation of specific measurement techniques and equipment.It is the comparison between measurements of known magnitude madewith one device and another measurement made in as similar way as possiblewith a second device. In order to use any device for measurement it is necessaryto empirically calibrate them. That is, here in this case pass a known dischargethrough the notch and note the reading in order to provide a standard for measuringother quantities in a different location. Provided the standard mechanicsof construction are followed no further calibration is required for a similar seconddevice with same geometry.The calibration equation is stated as,Qac K hnwhere ,K and n are constants depending on the geometry of the notch. Takinglogarithm on both sides we get,logQac log k n log hwhich is the equation of a straight line,where ,log k is the y intercept and n is its slope.The graph logQac Vs. logh is to be plotted to find k and n.JNEC CIVIL/FM-I/AUG 2010Page 19
Procedure1. Check the experimental setup for leaks. Measure the dimensions of collectingtank and the notch.2. Observe the initial reading of the hook gauge and make sure there is nodischarge. Note down the sill level position of the hook gauge.3. Open the inlet valve of the supply pipe for a slightly increased discharge.Wait for sometime till the flow become steady.4. Adjust the hook gauge to touch the new water level and note down thereading. Difference of this hook gauge reading with initial still level readingis the head over the notch (h).5. Collect the water in the collecting tank and observe the time t to collect Hheight of water.6. Repeat the above procedure for different flow rates by adjusting the inletvalve opening and tabulate the readings.7. Complete the tabulation and find the mean value of CD.8. Draw the necessary graphs and calibrate the the notch.Observations and calculationsLength of the rectangular notch —mAngle of the triangular notch —degCollecting tank area — m2JNEC CIVIL/FM-I/AUG 2010Page 20
For a triangular notch Q K H(3/2)K Cd .(8/15). (2g)(1/2).tan(Ѳ/2)Sr. No.Hook GuageReadingC.BW.SDiff.H'(cm).H(m)Measuring TankReadingI.R.F.R.Diff. R'(cm)R(m)Vol.V AXR(m3)@ B mQact.V/T(m3/sec)Qth(8/15). t/Qth1234567For first reading:Qact m3/secQtheo m3/secCd Q/ QtheoK Should be n (3/2 ) if we take the log for the two sides of equation :log Q log K n log H ,where n : the power of H ( the slope.) from table .log k from graph k Cd .JNEC CIVIL/FM-I/AUG 2010Page 21
Results and InferenceThe given notches are calibrated with the calibration equationwherek ,n for triangular notch.The average coefficient of discharge of the given notches are,Triangular notch, CdR The required characteristics are plotted.JNEC CIVIL/FM-I/AUG 2010Page 22
FLUID MECHANICS LABORATORY MANUAL . 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, . Solution to the relationship between discharge and head so that a semi-empirical Approach has to be used.
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Jawaharlal Nehru Engineering College, Aurangabad Department of Computer Science and Engineering Vision of CSE Department: To develop computer engineers with necessary analytical ability and human values who can creatively design, implement a wide spectrum of computer systems for welfare of the society.
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