MAHATMA GANDHI MISSION S JAWAHARLAL NEHRU ENGINEERING COLLEGE, FLUID MECHANICS LABORATORY MANUAL


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1 MAHATMA GANDHI MISSION S JAWAHARLAL NEHRU ENGINEERING COLLEGE, AURANGABAD. (M.S.) DEPARTMENT OF CIVIL ENGINEERING FLUID MECHANICS LABORATORY MANUAL Prepared By Mr. L. K. Kokate Lab Incharge Approved By Prof. B. M. Patil H.O.D. CIVIL JNEC CIVIL/FMI/AUG 2010 Page 1
2 FLUID MECHANICS I EXPERIMENTS SUBJECT:  Fluid MechanicsI CLASS:  Second Year Civil Engineering LIST OF EXPERIMENTS Sr. No. Name of Experiment Page No. From To I II III IV V VI VII VIII IX Study of pressure measuring devices. Determination of meta centric height. Calibration of Bernoulli s equation. Calibration of Venturimeter. Determination of Hydraulic coefficient for orifices. Determination of coefficient of discharge for mouthpiece. Calibration of Rectangular notch. Calibration of Triangular Notch. Study of electrical analogy method for plotting of flow nets. Time Allotted for each Practical Session = 02 Hrs. JNEC CIVIL/FMI/AUG 2010 Page 2
3 EXPERIMENT NO: II  To Determine the Metacentric Height of a Cargo / War Ship AIM:  To Determine the Metacentric Height of a Cargo / War Ship INTRODUCTION: Metacenter is defined as, the point about which the body starts oscillating when it is tilted (inclined) by a small angle. Metacenter may also be defined as, the point at which the line of action of force of buoyancy will meet the normal axis of the body when the body 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 ship model is approximately 37 cm size square in plan and is about 23 cm high. The model is floated on water. The ship is tilted by moving a small weight at the level of the deck of the ship. To note down the tilt of the ship, a plumb is provided which records the tilt on a graduated arc of a circle. An arrangement is made to load the JNEC CIVIL/FMI/AUG 2010 Page 3
4 ship as a War ship or Cargo ship. PROCEDURE: Sr. No. For Cargo Ship For War Ship 1 Place suitable symmetrical weights at the bottom of the ship and load it as a Cargo Ship. Place suitable symmetrical weights at the deck level of the ship and load it as a War Ship. 2 Float the ship on the water. Float the ship on the water. 3 Adjust the balancing weights on both the sides of the ship so that the Plumb indicates zero reading on the graduated arc. 4 Keep the Moving (Hanging) Load/Weight at a distance of 3.5 cm off the centre on left side. Adjust the balancing weights on both the sides of the ship so that the Plumb indicates zero reading on the graduated arc. Keep the Moving (Hanging) Load/Weight at a distance of 3.5 cm off the centre on left side. 5 Note down the tilt of the ship in degrees. Note down the tilt of the ship in degrees. 6 Go on shifting the Hanging Load towards left & note down the distance of the centre, & tilt of the ship. 7 Repeat the procedure by shifting the load on the right hand side of the centre. Go on shifting the Hanging Load towards left & note down the distance of the centre, & tilt of the ship. Repeat the procedure by shifting the load on the right hand side of the centre. OBSERVATION W 1 = Weight of the ship including balancing weight in grams. W 2 = Total weight added to make it as a Cargo / War Ship. W 3 = Weight of the Hanging Load in grams. JNEC CIVIL/FMI/AUG 2010 Page 4
5 OBSERVATION TABLE: Sr. No. Distance off the centre to the left X in cms Tilt of the Ship θ in degrees Metacentric Height=MG 1 in cms. Distance off the centre to the left X in cms Tilt of the Ship θ in degrees Metacentric Height=MG 2 in cms Average MG in cms SPECIMEN CALCULATIONS: W = (w 1 + w 2 ) in grams. MG 1 or MG 2 = Metacentric Heights in centimeters. = W1 x X / W x tan θ 0 Average MG = MG 1 + MG 2 / 2 RESULTS: Metacentric Height of a Cargo Ship (MG c ) =..cms. Metacentric Height of a War Ship (MGw) =..cms. CONCLUSION: JNEC CIVIL/FMI/AUG 2010 Page 5
6 As the angle of tilt (θ 0 ) increases, Metacentric Height (MG or GM) also increases / decreases. EXPERIMENT NO: III  to Verify Bernoulli s Theorem 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, Pressure Energy = P / ρg Kinetic Energy = V 2 / 2g & Datum Energy = Z The applications of Bernoulli s theorem are: 1) Venturi Meter 2) Orifice Meter 3) Pilot Tube JNEC CIVIL/FMI/AUG 2010 Page 6
7 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 piezometer 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. JNEC CIVIL/FMI/AUG 2010 Page 7
8 Specifications: Tube No. C/S Area Observation Table: Result: 1) At discharge..liters / second, Total head is..centimeters. 2) At discharge..liters / second, Total head is..centimeters. JNEC CIVIL/FMI/AUG 2010 Page 8
9 EXPERIMENT NO: IV  FLOW THROUGH VENTURIMETER AIM: To determine the coefficient (K) of the Venturimeter. DESCRIPTION: 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 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. PROCEDURE: 1. The diameters of the inlet and throat are recorded and the internal plan dimensions 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 (h 1 and h 2 ) are noted. 4. 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. 5. The above procedure is repeated by gradually increasing the flow and observing the required readings. 6. The observations are tabulated and the coefficient of the Venturimeter is computed. JNEC CIVIL/FMI/AUG 2010 Page 9
10 FORMULAE USED: Constant of Venturimeter, K = Where, a 1 = area of inlet a 2 = area of throat h = Venturi head in terms of flowing liquid = h 1 = Manometric head in one limb of the manometer h 2 = Manometric head in other limb of the manometer S m = Specific gravity of following liquid S 1 = Specific gravity of following liquid g = Acceleration due to gravity Actual Discharge (Q a ) = JNEC CIVIL/FMI/AUG 2010 Page 10
11 JNEC CIVIL/FMI/AUG 2010 Page 11
12 OBSERVATIONS AND RESULT: Diameter of inlet, Diameter of inlet, d 1 =.mm d 2 =.mm Internal plan dimensions of collecting tank Length, l =.mm Breadth, b =.mm Sr. No. Manometric Readings (mm) of Water H h 2 Difference X=(h 1 h 2 ) Venturi head in terms of flowing fluid (h) mm h Time for H =100mm rise t Sec. Trials Avg. Actual Discharge (mm 3 /sec) Coefficient of Venturimeter Mean Value of C d =. JNEC CIVIL/FMI/AUG 2010 Page 12
13 MODEL CALCULATIONS : (Reading No. ) Area of inlet of Venturimeter a 1 = 2 πd 1 /4 ( mm 2 ) Area of throat of Venturimeter a 2 = 2 πd 2 /4 ( mm 2 ) Internal plan area of collecting tank = l x b (mm 2 ) Actual discharge, Q a = (mm 3 /s) Coefficient of Meter, (K) = Q a / C. h GRAPH: Q a vs. h h on Xaxis RESULT: Average Coefficient of the Venturimeter, C d = JNEC CIVIL/FMI/AUG 2010 Page 13
14 EXPERIMENT NO: VII CALIBRATION OF RECTANGULAR NOTCHES Objectives To Determine the coefficient of discharge of the given Rectangular notch for different rates of flow. Equipment required The given notch fitted on an open channel of the experiment setup, hook gauge to measure the water level over the notch and measuring tank with stop watch to measure the actual flow rate. Principle In 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 small scale applications, weirs are often referred to as notches and are sharp edged and manufactured from thin plate material. The basic principle is that discharge is directly related to the water depth above the crotch (bottom) of the notch. This distance is called head over the notch. Due to the minimal installation costs flow rate measurement with a notch is very less expensive. The rectangular notch is the most commonly used thin plate weir. The flow pattern over a notch or weir is complex and there is no analytical Solution to the relationship between discharge and head so that a semiempirical 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/s 2 ) Water is allowed to pass through the given notch at different flow rates. Actual discharge through the channel can be determined using the collecting tank and stopwatch setup. JNEC CIVIL/FMI/AUG 2010 Page 14
15 Where, a = area of the collecting tank. (m 2 ) 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 discharge obtained 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 made with one device and another measurement made in as similar way as possible with a second device. In order to use any device for measurement it is necessary to empirically calibrate them. That is, here in this case pass a known discharge through the notch and note the reading in order to provide a standard for measuring other quantities in a different location. Provided the standard mechanics of construction are followed no further calibration is required for a similar second device with same geometry. The calibration equation is stated as, where, Qac = K h n K and n are constants depending on the geometry of the notch. Taking logarithm on both sides we get, logqac = log k+n log h which 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/FMI/AUG 2010 Page 15
16 Procedure 1. Check the experimental setup for leaks. Measure the dimensions of collecting tank and the notch. 2. Observe the initial reading of the hook gauge and make sure there is no discharge. 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 the reading. Difference of this hook gauge reading with initial still level reading is the head over the notch (h). 5. Collect the water in the collecting tank and observe the time t to collect H height of water. 6. Repeat the above procedure for different flow rates by adjusting the inlet valve 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 calculations Length of the rectangular notch = m Angle of the triangular notch = deg Collecting tank area = m 2 JNEC CIVIL/FMI/AUG 2010 Page 16
17 For a rectangular notch Q = K H (3/2) K = C d.(2/3). (2g) B = m Sr. No. Hook Guage Reading H Measuring Tank Reading R Vol. Q act. Q th Cd. log H log Q act C.B W. S Diff. H' (cm). (m) I.R. F.R. Diff. R' (cm) (m) V=AXR (m 3 ) V/T (m3/s ec) (2/3). (2g).L.H (3/2) (m3/sec) Q act/q th For first reading: Q act = m 3 /sec Q theo = m 3 /sec C d = Q/ Q theo K = 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 = C d =. Results and Inference The given notches are calibrated with the calibration equation where k=, n= for rectangular notch. The average coefficient of discharge of the given notches are, Rectangular notch, CDR = The required characteristics are plotted. JNEC CIVIL/FMI/AUG 2010 Page 17
18 EXPERIMENT NO: VIII CALIBRATION OF TRIANGULAR NOTCHES Objectives To Determine the coefficient of discharge of the given Triangular notch for different rates of flow. Equipment required The given notch fitted on an open channel of the experiment setup, hook gauge to measure the water level over the notch and measuring tank with stop watch to measure the actual flow rate. Principle In 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 small scale applications, weirs are often referred to as notches and are sharp edged and manufactured from thin plate material. The basic principle is that discharge is directly related to the water depth above the crotch (bottom) of the notch. This distance is called head over the notch. Due to the minimal installation costs flow rate measurement with a notch is very less expensive. The V notch or triangular notch design causes small changes in discharge to have a large change in depth allowing more accurate head measurement than with a rectangular notch. The flow pattern over a notch or weir is complex and there is no analytical solution to the relationship between discharge and head so that a semiempirical approach 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/s 2 ) JNEC CIVIL/FMI/AUG 2010 Page 18
19 Water is allowed to pass through the given notch at different flow rates. Actual discharge through the channel can be determined using the collecting tank and stopwatch setup. Where, a = area of the collecting tank. (m 2 ) 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 discharge obtained 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 made with one device and another measurement made in as similar way as possible with a second device. In order to use any device for measurement it is necessary to empirically calibrate them. That is, here in this case pass a known discharge through the notch and note the reading in order to provide a standard for measuring other quantities in a different location. Provided the standard mechanics of construction are followed no further calibration is required for a similar second device with same geometry. The calibration equation is stated as, where, Qac = K h n K and n are constants depending on the geometry of the notch. Taking logarithm on both sides we get, logqac = log k+n log h which 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/FMI/AUG 2010 Page 19
20 Procedure 1. Check the experimental setup for leaks. Measure the dimensions of collecting tank and the notch. 2. Observe the initial reading of the hook gauge and make sure there is no discharge. 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 the reading. Difference of this hook gauge reading with initial still level reading is the head over the notch (h). 5. Collect the water in the collecting tank and observe the time t to collect H height of water. 6. Repeat the above procedure for different flow rates by adjusting the inlet valve 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 calculations Length of the rectangular notch = m Angle of the triangular notch = deg Collecting tank area = m 2 JNEC CIVIL/FMI/AUG 2010 Page 20
21 For a triangular notch Q = K H (3/2) K = C d.(8/15). (2g) B = m Sr. No. Hook Guage Reading H Measuring Tank Reading R Vol. Q act. Q th Cd. log H log Q act C.B W.S Diff. H' (cm). (m ) I.R. F. R. Diff. R' (cm) (m) V=AXR (m 3 ) V/T (m3/sec) (8/15). (2g) (1/2).tan(Ѳ/2) H (5/2) (m3/sec) Q act /Q th For first reading: Q act = m 3 /sec Q theo = m 3 /sec C d = Q/ Q theo K = 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 = C d =. JNEC CIVIL/FMI/AUG 2010 Page 21
22 Results and Inference The given notches are calibrated with the calibration equation where k=, n= for triangular notch. The average coefficient of discharge of the given notches are, Triangular notch, CdR = The required characteristics are plotted. JNEC CIVIL/FMI/AUG 2010 Page 22
MAHATMA GANDHI MISSION S JAWAHARLAL NEHRU ENGINEERING COLLEGE, AURANGABAD. (M.S.)
MAHATMA GANDHI MISSION S JAWAHARLAL NEHRU ENGINEERING COLLEGE, AURANGABAD. (M.S.) DEPARTMENT OF CIVIL ENGINEERING FLUID MECHANICS I LAB MANUAL Prepared By Prof. L. K. Kokate Lab Incharge Approved By Dr.
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