DARSHAN INSTITUTE OF ENGINEERING AND TECHNOLOGY

Transcription

1 DARSHAN INSTITUTE OF ENGINEERING AND TECHNOLOGY FLUID MECHANICS ( ) INDEX Sr. No Experiment Start Date End Date Sign Grade To validate Bernoulli s theorem as applied to the flow of water in a tapering circular duct. To study and measure velocity of flow using Pitot tube. To calibrate the given Rectangular, Triangular and Trapezoidal Notches. To determine the Metacentric height of a given floating body. 5. To calibrate and study Venturimeter. 6. To calibrate and study Orifice meter. 7. To calibrate and study Nozzle meter. 8 To calibrate and study Rota meter To determine Fluid friction factor for the given pipes. To determine loss coefficients for different pipe fittings. To study pressure and pressure measurement devices. To obtain surface profile of free and forced vortex flow. To study Laminar and Turbulent Flow and It s visualization on Reynolds s Apparatus. To determine Hydraulic Co-efficients using Orifice and Mouthpiece.

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3 1.1 Objective: EXPERIMENT NO. 1 Bernoulli s Theorem To validate Bernoulli s Theorem as applied to the flow of water in a tapering circular duct. 1.2 Introduction Bernoulli's principle is named after the Dutch-Swiss mathematician Daniel Bernoulli who published his principle in his book Hydrodynamica in Bernoulli s principle in its simplest form states that "the pressure of a fluid [liquid or gas] decreases as the speed of the fluid increases." The principle behind Bernoulli s theorem is the law of conservation of energy. It states that energy can be neither created nor destroyed, but merely changed from one form to another. The energy, in general, may be defined as the capacity to do work. Though the energy exists in many forms, yet the following are important from the subject point of view: 1. Potential Energy 2. Kinetic Energy and 3. Pressure Energy Potential Energy of a Liquid in Motion It is the energy possessed by a liquid particle, by virtue of its position. If a liquid particle is Z meter above the horizontal datum (arbitrary chosen), the potential energy of liquid particle will be gz per kg of liquid. Potential head of the liquid, at that point, will be Z meters of the liquid Kinetic Energy of a liquid Particle in Motion It is the energy, possessed by a liquid particle, by virtue of its motion or velocity. If a liquid particle is flowing with a mean velocity of V m/sec, then the kinetic energy of the particle will be V 2 2 per kg of the liquid. Velocity head of the liquid, at that velocity, will be V 2 2g meter of liquid Pressure Energy of a liquid Particle in Motion It is the energy, possessed by a liquid particle, by virtue of its existing pressure. If a liquid particle is under a pressure of p kg/m 2, then the pressure energy of the particle will be p/ρ per kg of liquid, where ρ is the density of the liquid. Pressure head of the liquid under that 1-1

4 Bernoulli s Theorem pressure will be p/w or p/ρg meter of the liquid. Where w is the specific weight of the liquid Total Energy of a liquid Particle in Motion The total energy of a liquid particle, in motion, is the sum of its potential energy, kinetic energy and pressure energy. Mathematically, 1.3 Bernoulli s Equation Total Energy, E = p ρg + V2 + Z, meter of liquid 2g It states, For a perfect incompressible liquid, flowing in a continuous stream, the total energy of a particle remains the same; while the particle moves from one point to another. This statement is based on the assumption that there are no losses due to friction in pipe. Mathematically, 1.4 Apparatus Description Total Energy, E = p ρg + V2 + Z = Constant 2g The apparatus is made from transparent acrylic and has both the convergent and divergent sections. Water is supplied from the constant head tank attached to the test section. Constant level is maintained in the supply tank. Piezometric tubes are attached at different distance on the test section. Water discharges to the discharge tank attached at the far end of the test section and from there it goes to the measuring tank through valve. The entire setup is mounted on a stand. 1.5 Experimental Procedure 1. Note down the area of cross-section of the conduit at sections where piezometers have been fixed. 2. Open the supply valve and adjust the flow in the conduit so that the water level in the inlet tank remains at a constant level (i.e., the flow becomes steady) 3. Measure the height of water level (above an arbitrarily selected suitable horizontal plane) in different piezometer tubes. 4. Measure the discharge by calculating time taken for L liters flow. 5. Repeat steps (2) to (4) for other discharges. 1-2

5 Bernoulli s Theorem 1.6 Observation & Calculation Table Piezometer Tube Number Diameter of Cross- Section (m) Area of Cross-Section, A,( m 2 ) Piezometer Tube Distance, (m) E E E E E E E Potential Head, Z Run No. 1 L = 10 lit, t = Sec Run No. 2 L = 10 lit, t = Sec Run No. 3 L = 10 lit, t = Sec Q 1 = L t, m3 /s V = Q 1 A, m/s p ρg, m V 2 2g, m E = p ρg + V2 2g + Z Q 2 = L t, m3 /s V = Q 2 A, m/s p ρg, m V 2 2g, m E = p ρg + V2 2g + Z Q 3 = L t, m3 /s V = Q 3 A, m/s p ρg, m V 2 2g, m E = p ρg + V2 2g + Z 1-3

6 Bernoulli s Theorem Plot the following on an ordinary graph paper for all the runs taken. 1. {( P ) + z} V/s distance (x) of piezometer tubes from some reference point. Draw a ρg smooth curve passing through the plotted points. This is known as the Hydraulic Gradient Line. 2. E = {( P ρg ) + z + V2 2g } V/s distance (x) of piezometer tubes on the graph ( P ρg ) + z v/s distance. Draw a smooth curve passing through the plotted points. This is the Total Energy Line. 1.7 Conclusion

7 Pitot Tube EXPERIMENT NO Objective To study and measure velocity of flow using Pitot tube 2.2 Introduction A Pitot tube is a pressure measurement instrument used to measure fluid flow velocity. The Pitot tube was invented by the French engineer Henri Pitot in the early 1700s and was modified to its modern form in the mid 1800s by French scientist Henry Darcy. It is widely used to determine the airspeed of an aircraft and to measure air and gas velocities in industrial applications. The basic Pitot tube consists of a tube pointing directly into the fluid flow. As this tube contains fluid, a pressure can be measured; the moving fluid is brought to rest (stagnates) as there is no outlet to allow flow to continue. This pressure is the stagnation pressure of the fluid, also known as the total pressure or (particularly in aviation) the Pitot pressure. The measured stagnation pressure cannot of itself be used to determine the fluid velocity (airspeed in aviation). However, Bernoulli's equation states: Stagnation or Total pressure = Static pressure + Dynamic pressure Mathematically this can also be written: Solving that for velocity we get: Where, V is fluid velocity, P t is stagnation or total pressure; P s is static pressure; Figure 2.1 Pitot tube P t = P S + ( V2 2g ) V = 2g (P t P s ) 2-1

8 Pitot Tube The dynamic pressure, then, is the difference between the stagnation pressure and the static pressure. 2.3 Apparatus Description The setup consist of simple clear Perspex channel with two tube each to measure static and stagnation pressure of the fluid in the channel. Channel is supplied water with the help of tank and the flow is controlled by a gate valve. Scale is imprinted next to the tube to measure the pressure heads. 2.4 Experimental Procedure 1. Switch on the pump and feel the tank that supplies water to the Pitot apparatus. 2. Now slowly open the Pitot outlet valve so that channel is filled completely with water 3. Observe and note down the pressure heads reading in m of water 4. Calculate time for discharge for known quantity of water 5. Calculate and compare theoretical and actual velocities 2.5 Observation Table Diameter of flow pipe, D = 0.03 m Run No Total Pressure Head P t, (m) Static Pressure Head P s, (m) Dynamic Pressure Head (P t P s ), (m) Time for L=5 lit, t, (sec) 2.6 Calculations 1. Actual Discharge, 2. Actual Velocity, Q act = L t = t V act = Q act A = m 3 /sec = m sec 2-2

9 Pitot Tube 3. Theoretical Velocity V th = 2g (P t P s ) = m sec 4. Co-efficient of Pitot Tube C v = V act V th = 2.7 Result Table Run No. Theoretical Velocity, V th, (m/sec) Actual Discharge, Q act, (m 3 /sec) Actual Velocity, V act, (m/sec) Co-efficient of Velocity, C v Conclusion.. 2-3

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11 Notches EXPERIMENT NO Objective To calibrate the given Rectangular, Triangular and Trapezoidal Notches 3.2 Introduction Measurement of flow in open channel is essential for better management of supplies of water. Notches and Weirs are used to measure the rate of flow of liquid (discharge) indirectly from measurements of the flow depth. Notch is a device used for measuring the rate of flow of liquid through a small channel or a tank. It is an opening in the side of a measuring tank or reservoir extending above the free surface. Weir is a concrete or masonry structure, placed in open channel over which the flow occurs like a river. A notch is small in size whereas weir is a notch on a large scale. A weir/notch is an orifice placed at the water surface so that the head on its upper edge is zero. Hence, the upper edge can be eliminated, leaving only the lower edge named as weir crest. A weir/notch can be of different shapes - rectangular, triangular, trapezoidal etc. A triangular weir is particularly suited for measurement of small discharges. Equation of discharge for notch and weir will remain same Rectangular Notch The discharge over an un-submerged rectangular sharp-crested notch is defined as: H = Head of water over the crest L = Length of notch or weir Figure 3.1 Rectangular notch 3-1

12 Notches Triangular Notch (V-Notch) The rate of flow over a triangular weir mainly depends on the head H, relative to the crest of the notch; measured upstream at a distance about 3 to 4 times H from the crest. For triangular notch with apex angle, the rate of flow Q is obtained from the equation, Figure 3.2 Triangular notch Trapezoidal Notch Also known as Cipolletti weirs are trapezoidal with 1:4 slopes to compensate for end contraction losses. The equation generally accepted for computing the discharge through an unsubmerged sharp-crested Cipolletti weir with complete contraction is: Where, Q = Discharge over notch (m 3 /sec) L = Bottom of notch width H = Head above bottom of opening in meter Figure 3.3 Trapezoidal notch 3-2

13 Notches 3.3 Apparatus Description The pump sucks the water from the sump tank, and discharges it to a small flow channel. The notch is fitted at the end of channel. All the notches and weirs are interchangeable. The water flowing over the notch falls in the collector. Water coming from the collector is directed to the measuring tank for the measurement of flow. The following notches are provided with the apparatus: 1. Rectangular notch (Crest length L = 0.050m) 2. Triangular notch (Notch Angle 60 0 ) 3. Trapezoidal notch (Crest length L = 0.075m; Slope = 4V:1H) (1) Rectangular not (2) V- notch (3) Trapezoidal notch Figure 3.4 Different types of notches used in apparatus 3.4 Experimental Procedure 1. Fit the required notch in the flow channel. 2. Fill up the water in the sump tank. 3. Open the water supply gate valve to the channel and fill up the water in the channel up to sill level. 4. Take down the initial reading of the crest level (sill level). 5. Now start the pump and open the gate valve slowly so that water starts flowing over the notch. 6. Let the water level become stable and note down the height of water surface at the upstream side by the sliding depth gauge. 7. Close the drain valve of measuring tank, and measure the discharge. 8. Take the reading for different flow rates. 9. Repeat the same procedure for other notch also. 3-3

14 Notches 3.5 Observations Notch Type: Rectangular Sr. No Still level reading, s, (m) Water height on upstream side, h, (m) Discharge time for 10 liters, t, (sec) Notch Type: Triangular Sr. No Still level reading, s, (m) Water height on upstream side, h, (m) Discharge time for 10 liters, t, (sec) Notch Type: Trapezoidal Sr. No Still level reading, s, (m) Water height on upstream side, h, (m) Discharge time for 10 liters, t, (sec) 3.6 Calculations Rectangular Notch 1. Head over the notch, ( ) 2. Actual Discharge, 3. Crest length of notch = 0.05 m

15 Notches Triangular notch 1. Head over the notch, ( ) 2. Actual Discharge, 3. Crest length of notch = m Trapezoidal Notch (or Cipolletti Weir) 1. Head over the notch, ( ) 2. Actual Discharge, 3. Crest length of notch = m Result Tables Notch Type: Rectangular Sr. No Theoretical discharge, Q th,. (m 3 /sec) Actual discharge, Q act,. (m 3 /sec) C d Notch Type: Triangular Sr. No Theoretical discharge, Q th,. (m 3 /sec) Actual discharge, Q act, (m 3 /sec) C d 3-5

16 Notches Notch Type: Trapezoidal Sr. No. Theoretical discharge, Q th,. (m 3 /sec) Actual discharge, Q act,. (m 3 /sec) C d Conclusion

17 Metacentre EXPERIMENT NO Objective To determine the Metacentric height of a given floating body. 4.2 Buoyancy When a body is completely submerged in a fluid, or it is floating or partially submerged, the resultant fluid force acting on the body is called the buoyant force. It is also known as the net upward vertical force acting on the body. A net upward vertical force results because pressure increases with depth and the pressure forces acting from below are larger than the pressure forces acting above. The Center of buoyancy is the center of gravity of the displaced water. It lies at the geometric center of volume of the displaced water. 4.3 Metacentre For the investigation of stability of floating body, it is necessary to determine the position of its metacentre with respect to its centre of gravity. Consider a floating ship model, the weight of the ship acts through its centre of gravity and is balanced by an equal and opposite buoyant force acting upwards through the centre of buoyancy i.e. the centre of gravity of liquid displaced by the floating body. Figure 4.1 Metacentric height A small angular displacement shifts the centre of buoyancy and the intersection of the line of action of the buoyant force passing through the new centre of buoyancy and the extended line would give the metacentre. The distance between centre of gravity (G) and metacentre (M) is known as Metacentric height (GM). 4-1

18 Metacentre There are three conditions of equilibrium of a floating body 1. Stable Equilibrium - Metacentre lies above the centre of gravity 2. Unstable Equilibrium- Metacentre lies below the centre of gravity 3. Neutral Equilibrium - Metacentre coincides with centre of gravity The Metacentric height (GM) is given by GM = (m x X) (W x tan θ) Where, W = weight of the floating body, (N) m = movable weight, (N) X = distance through which the movable load is shifted, (m) = Angle of Heel 4.4 Apparatus Description The apparatus consist of a SS tank and is provided with a drain cock. The floating body is made from Clear Transparent Acrylic. It is provided with movable weights, protractor to measure the angle of Heel and pointer. Weights are also provided to increase the weight of floating body by known amount. 4.5 Experimental Procedure 1. Fill the SS tank to about 2/3 levels 2. Place the floating body in the tank. 3. Apply momentum to the floating body by moving one of the adjustable weights (m) through a known distance. 4. Note down the angle of heel corresponding to this shifts of weight with the help of protractor and pointer. 5. Take about 4-5 such readings by changing the position of the adjustable weight and find out centre of gravity in each case 4.6 Observation & Result Table Weight of the ship model = 1.5 X 9.81 = N Given Movable Weights = 50 gm = N 4-2

19 Metacentre Sr. No. Movable Weight, m, (N) Distance of Weight from Center, X (m) Angle of Tilt, Tan Metacentric Height, GM, (m) Calculations Metacentric height GM = (m x X) (W x tanθ) Metacentric height, GM =, m 4.8 Conclusion.. 4-3

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21 Venturimeter 5.1 Objective To calibrate and study Venturimeter EXPERIMENT NO Introduction Venturimeter is used for the measurement of discharge in a pipeline. Since head loss caused due to installation of Venturimeter in a pipeline is less than that caused due to installation of Orifice meter, the former is usually preferred particularly for higher flow rates. A Venturimeter consists of a converging tube, which is followed by a diverging tube. The junction of the two is termed as 'throat' which is the section of minimum cross-section. Figure 5.1 Venturimeter 5.3 Apparatus Description Venturimeter is mounted along a pipeline with sufficient distance to stabilize flow between two meters. The pressure taps are provided at sections as given in the fig. Pressure head difference between sections can be read on manometer having mercury as the manometer fluid. A valve, fitted at the end of the pipeline, is used for regulating the discharge in the pipeline. 5-1

22 Venturimeter 5.4 Experimental Procedure 1. Fill the storage tank/sump with the water. 2. Switch on the pump and keep the control valve fully open and close the bypass valve to have maximum flow rate through the meter. 3. Open control valve of the Venturimeter. 4. Open the vent cocks provided at the top of the manometer to drive out the air from the manometer limbs and close both of them as soon as water start coming out. 5. Note down the difference of level of mercury in the manometer limbs. 6. Keep the drain valve of the collection tank closed till its time to start collecting the water. 7. Close the drain valve of the collection tank and note down the initial level of the water in the collection tank. 8. Collect known quantity of water in the collection tank and note down the time required for the same. 9. Change the flow rate of water through the meter with the help of control valve and repeat the above procedure. 10. Take about 2-3 readings for different flow rates. 5.5 Observations For Venturimeter, Diameter at inlet d 1 = 26 mm; Area a 1 = 5.31 x 10-4 m 2 Diameter at throat d 2 = 16 mm; Area a 2 = 2.01 x 10-4 m 2 Sr. No 1 h 1 (cm of Hg) Manometric Reading h 2 (cm of Hg) Manometer Difference (m of Hg) x = h 2 h Time for 10 lit, t, (sec)

23 Venturimeter 5.6 Calculations 1. Actual Discharge, Volume of Water in m3 Q act = Time in Sec 2. Difference in Pressure Head, 3. Theoretical Discharge, = 0.01 t =, m 3 sec h = x [ S h 1] = x [ ] =, m of water S o 1 4. Co-efficient of Discharge, Q th = a 1a 2 2gh a 2 1 a =, 2 m3 sec 2 C d = Q act Q th = 5.7 Result Table Sr. No. Theoretical Discharge, Qth, (m 3 /s) Actual Discharge, Qact, (m 3 /s) Cd Conclusion.. 5-3

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25 6.1 Objective To calibrate and study Orifice meter EXPERIMENT NO. 6 Orifice Meter 6.2 Introduction A circular opening in a plate which is fitted suitably in a pipeline is a simple device to measure the discharge flowing in the pipeline. Such a device is known as orifice meter. The opening is normally at the centre of the plate as shown in Fig.6.1. Major advantages of orifice meter are that it is low cost device, simple in construction & easy to install in pipe lines. The major disadvantage of using orifice plate is the permanent pressure drop that is normally experienced in the orifice plate as shown in Fig The pressure drops significantly after the orifice and can be recovered only partially. The magnitude of the permanent pressure drop is around 40%, which is sometimes objectionable. It requires more pressure to pump the liquid. This problem can be overcome by improving the design of the restrictions. Venturimeter and flow nozzle are two such devices. Figure 6.1 Simple orifice meter & permanent pressure drop 6-1

26 Orifice Meter 6.3 Apparatus Description Orifice meter is mounted along a pipeline with sufficient distance to stabilize flow between two meters. The pressure taps are provided at sections as given in the fig.6.1. Pressure head difference between sections can be read on manometer having mercury as the manometer fluid. A valve, fitted at the end of the pipeline, is used for regulating the discharge in the pipeline. 6.4 Experimental Procedure 1. Fill the storage tank/sump with the water. 2. Switch on the pump and keep the control valve fully open and close the bypass valve to have maximum flow rate through the meter. 3. Open control valve of the orifice meter. 4. Open the vent cocks provided at the top of the manometer to drive out the air from the manometer limbs and close both of them as soon as water start coming out. 5. Note down the difference of level of mercury in the manometer limbs. 6. Keep the drain valve of the collection tank closed till it s time to start collecting the water. 7. Close the drain valve of the collection tank and note down the initial level of the water in the collection tank. 8. Collect known quantity of water in the collection tank and note down the time required for the same. 9. Change the flow rate of water through the meter with the help of control valve and repeat the above procedure. 10. Take about 2-3 readings for different flow rates. 6-2

27 6.5 Observations Orifice Meter For Orifice meter: Diameter of pipe inlet d1= 26 mm; Area a 1 = 5.31 x 10-4 m 2 Diameter of orifice do = 16 mm; Area a o = 2.01 x 10-4 m 2 Sr. No h 1 (cm of Hg) Manometric Reading h 2 (cm of Hg) Manometer Difference (m of Hg) x = h 2 h Time for 10 lit, t, (sec) Calculations 1. Actual Discharge, Volume of Water in m3 Q act = Time in Sec 2. Difference in Pressure Head, 3. Theoretical Discharge, = 0.01 t =, m 3 sec h = x [ S h 1] = x [ ] =, m of water S o 1 Where, Q th = a oa 1 2gh a 2 1 a =, 2 m3 sec o a o = Area of cross section of the orifice a 1 = Area of cross section of the pipe h = Difference in the Piezometric heads at manometer tappings 4. Co-efficient of Discharge C d = Q act Q th = 6-3

28 Orifice Meter 6.7 Result Table Sr. No Theoretical discharge, Qth, (m 3 /s) Actual Discharge, Qact, (m 3 /s) Cd Conclusion.. 6-4

29 7.1 Objective To calibrate and study Nozzle Meter EXPERIMENT NO. 7 Nozzle Meter 7.2 Introduction The Flow nozzle or Nozzle meter is a compromise between Venturimeter and orifice meter as shown in Fig. 7.1 The streamlined entrance of the nozzle causes a straight jet without contraction, so its effective discharge coefficient is nearly the same as the venturi meter. Flow nozzles allow the jet to expand of its own accord. The flow nozzle costs less than venturimeter. It has the disadvantage that the overall losses are much higher because of the lack of guidance of the jet downstream from the nozzle opening. Figure 7.1 Simple nozzle meter 7.3 Apparatus Description Nozzle meter is mounted along a pipeline with sufficient distance to stabilize flow between two meters. The pressure taps are provided at sections as given in the fig.7.1. Pressure head difference between sections can be read on manometer having mercury as the manometer fluid. A valve, fitted at the end of the pipeline, is used for regulating the discharge in the pipeline. 7-1

30 Nozzle Meter 7.4 Technical Specifications of Nozzle meter Size = 26 mm Nozzle Size = 16 mm 7.5 Experimental Procedure 1. Fill the storage tank/sump with the water. 2. Switch on the pump and keep the control valve fully open and close the bypass valve to have maximum flow rate through the meter. 3. Open control valve of the nozzle meter. 4. Open the vent cocks provided at the top of the manometer to drive out the air from the manometer limbs and close both of them as soon as water start coming out. 5. Note down the difference of level of mercury in the manometer limbs. 6. Keep the drain valve of the collection tank closed till it s time to start collecting the water. 7. Close the drain valve of the collection tank and note down the initial level of the water in the collection tank. 8. Collect known quantity of water in the collection tank and note down the time required for the same. 9. Change the flow rate of water through the meter with the help of control valve and repeat the above procedure. 10. Take about 2-3 readings for different flow rates. Sr. No Observations For Nozzle meter: Diameter at inlet d 1 = 26 mm; Area a 1 = 5.31 x 10-4 m 2 h 1 (cm of Hg) Diameter at orifice d 2 = 16 mm; Area a 2 = 2.01 x 10-4 m 2 Manometric Reading h 2 (cm of Hg) Manometer Difference (m of Hg) x = h 2 h Time for 10 lit, t, (sec) 7-2

31 Nozzle Meter 7.7 Calculations 1. Actual Discharge, Volume of Water in m3 Q act = Time in Sec 2. Difference in Pressure Head, = 0.01 t =, m 3 sec h = x [ S h 1] = x [ ] =, m of water S o 1 3. Theoretical Discharge, 4. Co-efficient of Discharge, Q th = a 1a 2 2gh a 2 1 a =, 2 m3 sec 2 C d = Q act Q th = 7.8 Result Table Sr. No. Theoretical Discharge, Qth, (m 3 /s) Actual Discharge, Qact, (m 3 /s) Cd Conclusion.. 7-3

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33 8.1 Objective To calibrate and study Rotameter EXPERIMENT NO. 8 Rota meter 8.2 Introduction The rotameter is an industrial flow meter used to measure the flow rate of liquids and gases. The rotameter consists of a tube and float. The float response to flow rate changes is linear. The rotameter is popular because it has a linear scale, a relatively long measurement range, and low pressure drop. It is simple to install and maintain. The rotameter's operation is based on the variable area principle: fluid flow raises a float in a tapered tube, increasing the area for passage of the fluid. The greater the flow, the higher the float is raised. The height of the float is directly proportional to the flow rate. With liquids, the float is raised by a combination of the buoyancy of the liquid and the velocity head of the fluid. With gases, buoyancy is negligible, and the float responds to the velocity head alone. S= Flow Force A = Buoyancy G= Gravity 8.3 Apparatus Description Figure 8.1 Rotameter Rota meter is mounted along a pipeline with sufficient distance to stabilize flow between two meters. A valve, fitted at the end of the pipeline, is used for regulating the discharge in the pipeline. 8.4 Technical Specifications of Rotameter Size = LPH Type = Thread Ends 8-1

34 Rota meter 8.5 Experimental Procedure 1. Fill the storage tank/sump with the water. 2. Switch on the pump and keep the control valve fully open and close the bypass valve to have maximum flow rate through the meter. 3. Verify the rotameter readings flow marking provided by manufacturer. 4. Take about 2-3 readings for different flow rates. 8.6 Observation & Calculation Table Sr. No Time for 10 lit., t, (sec) Rota meter Scale, (LPH) Actual discharge, Q act, (LPH) Calculations 1. Actual discharge, Volume of Water in m3 Q act = Time in Sec = 0.01 t =, m 3 sec Discharge in LPH = Q act =, LPH 8.8 Conclusion.. 8-2

35 9.1 Objective EXPERIMENT NO. 9 To determine fluid friction factor for the given pipes. Pipe Friction Losses 9.2 Introduction 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 Minor losses in fluid flow. Figure 9.1 head loss due to friction 9.3 The Darcy-Weisbach equation Weisbach first proposed the equation we now know as the Darcy-Weisbach formula or Darcy-Weisbach equation. Where, hf = Head loss in meter h f = 4fLV2 2gD 9-1

36 Pipe Friction Losses f = Darcy friction factor L = length of pipe work, (m) V = Velocity of fluid, (m/sec) D = inner diameter of pipe, (m) g = Acceleration due to gravity, (m/sec 2 ) The Darcy Friction factor used with Weisbach equation has now become the standard head loss equation for calculating head loss in pipes where the flow is turbulent. 9.4 Apparatus Description The experimental set up consists of a large number of pipes of different diameters. The pipes have tapping at certain distance so that a head loss can be measure with the help of a U Tube manometer. The flow of water through a pipeline is regulated by operating a control valve which is provided in main supply line. Actual discharge through pipeline is calculated by collecting the water in measuring tank and by noting the time for collection. 9.5 Technical Specification Pipe: MOC = Polyurethane (P.U.) Test length, L = 1000 mm Pipe Dia. Pipe 1: Internal Diameter, D1: 16 mm Pipe 2: Internal Diameter, D2: 21 mm Pipe 3: Internal Diameter, D3: 26.5 mm 9.6 Experimental Procedure 1. Fill the storage tank/sump with the water. 2. Switch on the pump and keep the control valve fully open and close the bypass valve to have maximum flow rate through the meter. 3. To find friction factor of pipe 1 open control valve of the same and close other to valves 4. Open the vent cocks provided for the particular pipe 1 of the manometer. 5. Note down the difference of level of mercury in the manometer limbs. 6. Keep the drain valve of the collection tank open till it s time to start collecting the water. 7. Close the drain valve of the collection tank and collect known quantity of water 9-2

37 Pipe Friction Losses 8. Note down the time required for the same. 9. Change the flow rate of water through the meter with the help of control valve and repeat the above procedure. 10. Similarly for pipe 2 and 3. Repeat the same procedure indicated in step Take about 2-3 readings for different flow rates. Sr. No Observations Table Length of test section L = 1000 mm = 1 m Pipe 1 Internal Diameter of Pipe, D1 = 16 mm Cross Sectional Area of Pipe, A1 = mm 2 = 2.0 x 10-4 m 2 h 1 (cm of Hg) Manometric Reading h 2 (cm of Hg) Manometer Difference (m of Hg) x = h 2 h time for 10 lit, t, (sec) Sr. No 1 2 Pipe 2 Internal Diameter of Pipe, D2 = 21 mm Cross Sectional Area of Pipe, A2 = mm 2 = 3.46 x 10-4 m 2 h 1 (cm of Hg) Manometric Reading h 2 (cm of Hg) Manometer Difference (m of Hg) x = h 2 h time for 10 lit, t, (sec) Sr. No 1 2 Pipe 3 Internal Diameter of Pipe, D3 = 26.5 mm Cross Sectional Area of Pipe, A3 = mm 2 = 5.52 x 10-4 m 2 h 1 (cm of Hg) Manometric Reading h 2 (cm of Hg) Manometer Difference (m of Hg) x = h 2 h time for 10 lit, t, (sec) 9-3

38 Pipe Friction Losses 9.8 Calculations 1. Actual Discharge 2. Mean velocity Volume of Water in m3 Q act = Time in Sec = 0.01 t 3. Difference in Pressure Head, 4. Friction factor 9.9 Result Table V act = Q act A h f = x [ S h S o 1] = x [ ] f = 2gDh f 4LV 2 Sr. No. Actual Discharge Q act, m 3 /sec Actual Velocity V act, m/sec Diff. in Pressure Head, h f, m of Water Friction Factor, f 1 2 Pipe Pipe Pipe Conclusion.. 9-4

39 10.1 Objective EXPERIMENT NO. 10 To determine loss coefficients for different pipe fittings. Minor Losses 10.2 Introduction While installing a pipeline for conveying a fluid, it is generally not possible to install a long pipeline of same size all over a straight for various reasons, like space restrictions, aesthetics, location of outlet etc. Hence, the pipe size varies and it also changes its direction. Also, various fittings are required to be used. All these variations of sizes and the fittings cause the loss of fluid head. Losses due to change in cross-section, bends, elbows, valves and fittings of all types fall into the category of minor losses in pipelines. In long pipeline, the friction losses are much larger than these minor losses and hence, the latter are often neglected. But, in shorter pipelines, their consideration is necessary for the correct estimate of losses. The minor loses are, generally expressed as Where, HL is the minor loss (i.e. head loss) H L = K L ( V2 2g ) KL, the loss coefficient, V is the velocity of flow in the pipe 10.3 Apparatus Description The experimental set-up consists of a pipe of diameter about 24.3 mm fitted with 1. A right angle bend 2. An elbow 3. A Gate Valve 4. A sudden expansion (larger pipe having diameter of about 24.3 mm) and 5. A sudden contraction (from about 24.3 mm to about 13.8 mm) Sufficient length of the pipeline is provided between various pipe fittings. The pressure taps on either side of these fittings are suitably provided and the same may be connected to a multi tube manometer bank. Supply to the line is made through a storage tank and discharge is regulated by means of outlet valve provided near the outlet end. 10-1

40 Minor Loss 10.4 Experimental Procedure 1. Fill up sufficient clean water in the sump tank 2. Fill up mercury in the manometer 3. Connect the electric supply. See that the flow control valve and bypass valve are fully open and all the manometer cocks are closed. Keep the water collecting funnel in the sump tank side 4. Start the pump and adjust the flow rate. Now slowly open the manometer tapping connection of small bend. Open both the cocks simultaneously 5. Open air vent cocks. Remove air bubbles and slowly & simultaneously close the cocks. Note down the manometer reading and flow rate. 6. Close the cocks and similarly, note down the readings for other fittings. Repeat the procedure for different flow rates Observations 1. Type of fitting Elbow Diameter of the elbow, d = 33.4 mm = m Mean Area of elbow, A = π 4 d2 = 8.76 x 10 4 m 2 Sr. No. Manometer Reading h 1 (cm of Hg) h 2 (cm of Hg) Manometer difference (m of Hg) x = h 2 h Time for 10 lit, t (sec) Type of fitting Bend Diameter of the bend, d = 33.4 mm = m For bend, mean area A = π 4 d2 = 8.76 x 10 4 m 2 Sr. No. Manometer Reading h 1 (cm of Hg) h 2 (cm of Hg) Manometer difference (m of Hg) x = h 2 h Time for 10 lit, t (sec)

41 3. Type of fitting Valve Diameter of the valve opening, d = 33.4 mm = m For gate valve mean area, A = π 4 d2 = 8.76 x 10 4 m 2 Minor Losses Sr. No. Manometer Reading h 1 (cm of Hg) h 2 (cm of Hg) Manometer difference (m of Hg) x = h 2 h Time for 10 lit, t (sec) Type of fitting Sudden Contraction Inlet diameter = 24.3 mm = m; Therefore Ai = 4.64 X 10-4 m 2 Outlet diameter = 13.8 mm = m; Therefore Ao = 1.50 x 10-4 m 2 Sr. No. Manometer Reading h 1 (cm of Hg) h 2 (cm of Hg) Manometer difference (m of Hg) x = h 2 h Time for 10 lit, t (sec) Type of fitting Sudden Expansion Inlet diameter = 24.3 mm = m; Therefore Ai = 4.64 X 10-4 m 2 Outlet diameter = 13.8 mm = m; Therefore Ao = 1.50 x 10-4 m 2 Sr. No. Manometer Reading h 1 (cm of Hg) h 2 (cm of Hg) Manometer difference (m of Hg) x = h 2 h Time for 10 lit, t (sec)

42 Minor Loss 10.6 Calculations 1. Elbow Actual discharge, Mean velocity of flow, Q = L time required to collect L ltrs of water in m3 /sec V = Q A m/s Difference (loss) in pressure head, The loss coefficient of the elbow, H L = x [ S h S o 1] = x [ ] H L = K L ( V2 ) meter of water 2g 2. Pipe Bend Actual discharge, Mean velocity of flow, Q = Difference in pressure head, Loss coefficient of the bend, L time required to collect L ltrs of water in m3 /sec V = Q A m/s H L = x [ S h S o 1] = x [ ] H L = K L ( V2 ) meter of water 2g 3. Valve Actual discharge, Q = Mean velocity of flow, L time required to collect L ltrs of water in m3 /sec V = Q A m/s Difference in pressure head, 10-4

43 H L = x [ S h S o 1] = x [ ] The loss coefficient of the valve, Minor Losses H L = K L ( V2 ) meter of water 2g 4. Sudden Contraction Actual discharge, Q = Velocity of fluid at inlet, L time required to collect L ltrs of water in m3 /sec V i = Q m s A i Velocity of fluid at outlet, V o = Q m s A o Loss of head due to increase in velocity, h v = v i 2 2g v 2 o 2g Difference in pressure head, H L = x [ S h S o 1] = x [ ] Loss of head due to sudden contraction, H LC = H L h v The loss coefficient of sudden contraction, H Lc = K L ( V o 2 2g ) 5. Sudden Expansion Actual discharge, Q = Velocity of fluid at inlet, L time required to collect L ltrs of water in m3 /sec V i = Q m s A i Velocity of fluid at outlet, 10-5

44 Minor Loss V o = Q m s A o Loss of head due to decrease in velocity, h v = v i 2 2g v 2 o 2g Difference in pressure head, H L = x [ S h S o 1] = x [ ] Loss of head due to sudden expansion H Le = h v H L The loss coefficient of sudden expansion, 10.7 Result Table Sr No H Le = K L (V i V o ) 2 2g Bend Elbow Valve Sudden Contraction Sudden Expansion HL KL HL KL HL KL HLc KL HLe KL 10.8 Conclusion

45 11.1 Objective EXPERIMENT NO. 11 To study pressure and pressure measurement devices. Pressure Measurement 11.2 Introduction Fluid pressure can be defined as the measure of force per-unit-area exerted by a fluid, acting perpendicularly to any surface it contacts The standard SI unit for pressure measurement is the Pascal (Pa) which is equivalent to one Newton per square meter (N/m2) or the Kilopascal (kpa) where 1 kpa = 1000 Pa. Pressure can be expressed in many different units including in terms of a height of a column of liquid. The Table below lists commonly used units of pressure measurement and the conversion between the units. Pressure measurements can be divided into three different categories: absolute pressure, gage pressure and differential pressure. Absolute pressure refers to the absolute value of the force per-unit-area exerted on a surface by a fluid. Therefore the absolute pressure is the difference between the pressure at a given point in a fluid and the absolute zero of pressure or a perfect vacuum. Gauge pressure is the measurement of the difference between the absolute pressure and the local atmospheric pressure. Local atmospheric pressure can vary depending on ambient temperature, altitude and local weather conditions. A gage pressure by convention is always positive. A negative gage pressure is defined as vacuum. Vacuum is the measurement of the amount by which the local atmospheric pressure exceeds the absolute pressure. A perfect vacuum is zero absolute pressure. Figure below shows the relationship between absolute, gage pressures and vacuum. 11-1

46 Pressure Measurement Relationship between various pressure measurement devices Differential pressure is simply the measurement of one unknown pressure with reference to another unknown pressure. The pressure measured is the difference between the two unknown pressures. This type of pressure measurement is commonly used to measure the pressure drop in a fluid system. Since a differential pressure is a measure of one pressure referenced to another, it is not necessary to specify a pressure reference. For the English system of units this could simply be psi and for the SI system it could be kpa. In addition to the three types of pressure measurement, there are different types of fluid systems and fluid pressures. There are two types of fluid systems; static systems and dynamic systems. As the names imply, a static system is one in which the fluid is at rest and a dynamic system is on in which the fluid is moving Pressure Measurement Devices Manometer A Manometer is a device to measure pressures. A common simple manometer consists of a U shaped tube of glass filled with some liquid. Typically the liquid is mercury because of its high density. In the figure to the right we show such a U shaped tube filled with a liquid. Note that both ends of the tube are open to the atmosphere. Thus both points A and B are at atmospheric pressure. The two points also have the same vertical height 11-2

47 Pressure Measurement Now the top of the tube on the left has been closed. We imagine that there is a sample of gas in the closed end of the tube. The right side of the tube remains open to the atmosphere. The point A, then, is at atmospheric pressure. The point C is at the pressure of the gas in the closed end of the tube. The point B has a pressure greater than atmospheric pressure due to the weight of the column of liquid of height h. The point C is at the same height as B, so it has the same pressure as B. And this is equal to the pressure of the gas in the closed end of the tube. Thus, in this case the pressure of the gas that is trapped in the closed end of the tube is greater than atmospheric pressure by the amount of pressure exerted by the column of liquid of height h. Some "rules" to remember about U-tube manometry Manometer height difference does not depend on tube diameter. Manometer height difference does not depend on tube length. Manometer height difference does not depend on tube shape. Shape of a container does not matter in hydrostatics. This implies that a U-tube manometer does not have to be in a perfect U shape. There is a way to take advantage of this, namely one can construct an inclined manometer, as shown here. Although the column height difference between the two sides does not change, an inclined manometer has better resolution than does 11-3

48 Pressure Measurement a standard vertical manometer because of the inclined right side. Specifically, for a given ruler resolution, one "tick" mark on the ruler corresponds to a finer gradation of pressure for the inclined case. Burdon Pressure Gauge A Bourdon gauge uses a coiled tube, which, as it expands due to pressure increase causes a rotation of an arm connected to the tube. In 1849 the Bourdon tube pressure gauge was patented in France by Eugene Bourdon. Parts of Burdon tube The pressure sensing element is a closed coiled tube connected to the chamber or pipe in which pressure is to be sensed. As the gauge pressure increases the tube will tend to uncoil, while a reduced gauge pressure will cause the tube to coil more tightly. This motion is transferred through a linkage to a gear train connected to a pointer. The pointer is presented in front of a card face is inscribed with the pressure indications associated with particular pointer deflections Apparatus Description The manometers and gauges unit is a framed structure with a backboard, holding a: Vertical U-tube manometer U-tube manometer with an inclined limb Bourdon gauge for measuring vacuums Bourdon gauge for measuring positive pressure, and 11-4

49 Pressure Measurement Syringe assembly for pressurizing and reducing pressure in the measurement devices. Each gauge and manometer has a delivery point to connect to the syringe using plastic tubing (included). All connections are push-fit, and T-pieces are provided to enable two instruments to be connected to one point Experimental Procedure 1. Using the syring connects its plastic tubing to Pressure gauge. Push the syring arm to generate pressure. Observe the deflection on the gauge 2. Now connect the syring tubing to vacuum gauge. Release the arm of syring to generate vacuum and observe the change in deflection. 3. U tube Manometer can be connected to any of the flow meter devices. Switch the pump and observe the change in mercury levels in the manometer. Calculate the pressure difference. 4. Similarly connect the Inclined U tube manometer to any of the flow meter and calculate pressure difference 11.6 Observations: Density of liquid flowing in pipe = Density of liquid flowing in pipe = Manometric Reading Sr. No. Type of Manometer h1 h2 1 U tube Manometer 2 Inclined Tube Manometer 3 Pressure Gauge 4 Vacuum Gauge Pressure/Pressure Difference 11.7 Calculations 11-5

50 Pressure Measurement In the above figure, since the pressure at the height of the lower surface of the manometer fluid is the same in both arms of the manometer, we can write the following equation: P1 + ρ1gd1 = P2 + ρ2gd2 + ρf g h Here, ρ1 = ρ2 = ρw = Density of water; P1 - P2 = ρwgd2 + ρf g h ρwgd1 Also d1- d2 = h P1 - P2 = (ρf - ρw) g h Here ρf = Density of Mercury; Substituting Standard Values P1-P2 = (kg/m 3 ) x g (m/s 2 ) x h/1000 (m) = g h (in N/m 2 ) Where g =9.81 m/s 2 ; h in mm 11.8 Conclusion

51 Free and Forced Vortex Flow EXPERIMENT NO Objective To obtain surface profile of free and forced vortex flow Introduction A vortex is a spinning, often turbulent, flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex. When a liquid contained in a cylindrical vessel is given the rotation surface of water no longer remains horizontal but it depresses at the centre and rises near the walls of the vessel. A rotating mass of fluid is called vortex and motion of rotating mass of fluid is vortex motion. Vortices are of two type viz., forced vortex and free vortex. When a cylinder is in rotation then a vortex is called forced vortex. If water enters a stationary cylinder then a vortex is called free vortex. Forced vortex flow is an example of rotational flow and can be generated by rotating a cylinder containing a fluid about its axis (e.g., in a kitchen mixing machine) or by rotating a paddle in a large volume of fluid (e.g., the stirring of tea cup). Under Steady conditions, each particle will move with the same angular velocity and there will not be any relative motion between fluid particles. Streamlines for such a flow will be concentric circles and total energy is constant along a streamline but varies from one streamline to another. Figure 12.1 Forced vortex: total energy line and surface profile 12-1

52 Free and Forced vortex Flow 12.3 Apparatus Description The apparatus consists of a Perspex cylinder with drain at centre of bottom. The cylinder is fixed over a rotating platform which can be rotated with the help of a D.C. motor at different speeds. A tangential water supply rip is provided with flow control valve. The whole unit is mounted over the main frame. Water is supplied by a pump. Exit orifice of different sizes are provided which can be easily replaced. Figure 12.2 Vortex measurement 12.4 Experimental Procedure A. Forced Vortex 1. Close the drain valve of the cylinder vessel. Fill up some water (Say 4-5 cms height from the bottom) in vessel 2. Switch ON the supply and slowly increase motor speed. Do not start the pump. 3. Keep motor speed constant and wait till the vortex formed in the cylinder stabilizes. Once the vortex is stabilized note down the co-ordinates of the vortex and complete the observation table 4. With the surface speed attachment of tachometer, measure outside surface speed of vessel and note down in observation table (Tachometer is not supplied with the unit). 12-2

53 Free and Forced Vortex Flow B. Free Vortex 1. Open the bypass valve and start the pump 2. Slowly close the water bypass valve and drain valve of the cylinder. Water is now getting admitted through the tangential entry pipe to the cylinder 3. Properly adjust the bottom drain valve of vessel so that a stable vortex is formed 4. Note down co-ordinate of the vortex. Also measure time required for L lit level rise in measuring tank and complete observation table Observation Table: A. Forced Vortex Sr. No. RPM of motor (N ) Radius (X coordinate) cms Height (z) (Y coordinate) cms 1 Sr. No B. Free Vortex Radius (X coordinate), cms Height (z) (Y coordinate), cms Time for L= lit. level rise, t (sec) Calculations A. Forced Vortex 12-3

54 Free and Forced vortex Flow B. Free Vortex Pipe diameter, d = 1.6 cm; A=2.01 x 10-4 m 2 (Note- For forced vortex, linear velocity of the cylinder does not equal the actual water velocity near I.D. of cylinder. Also for free vortex, as water does not enter exactly tangentially & velocity changes after it enters the cylinder which is not known, it is very difficult to calculate velocity of water exactly, the theoretical calculations deviate much from the observations. It can be readily observed that water comes out from pipe with high velocity, but velocity of water near the walls of cylinder appears to be very less) 12.7 Conclusion Precautions 1. While making the experiment forced vortex, see that water does not spill away from the vessel. Do not increase the speed of rotation excessively. 2. Do not start pump for forced vortex experiment Graph of Forced and Free Vortex: 12-4

55 Reynolds s Apparatus EXPERIMENT NO Objective To study Laminar and Turbulent flow and it s visualization on Reynolds s apparatus 13.2 Introduction The properties of density and specific gravity are measures of the heaviness of fluid. These properties are however not sufficient to uniquely characterize how fluids behave since two fluids (such as water and oil) can have approximately the same value of density but behaves quite differently when flowing. There is apparently some additional property that is needed to describe the fluidity of the fluid. Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid. It is an inherent property of each fluid. Its effect is similar to the frictional resistance of one body sliding over other body, as viscosity offers frictional resistance to the motion of the fluid consequently. In order to maintain the flow, extra energy is to be supplied to overcome effect of viscosity. The frictional energy generated comes out in form of heat and dissipated to the atmosphere through boundary surfaces Types of flow Laminar flow Laminar flow is that type of flow in which the particle of the fluid moves along well defined parts or streamlines. In laminar flow all streamlines are straight and parallel. In laminar flow one layer of fluid is sliding over another layer, whenever the Reynolds number is less than 2000, the flow is said to be laminar. In laminar flow, energy loss is low and it is directly proportional to the velocity of the fluid. The following reasons are for the laminar flow, fluid has low velocity, fluid has high viscosity and diameter of pipe is large Turbulent Flow: The flow is said to be turbulent flow it he flow moves in a zigzag way. Due to movement of the particles in a zigzag way, the eddies formation take place which are responsible of highenergy losses. 13-1

56 Reynolds s Apparatus In turbulent flow, energy loss is directly proportional to the square of velocity of fluid. If Reynolds number is greater than 4000, then flow is said to be turbulent 13.4 Reynolds s Number Reynolds was first to determine the translation from laminar to turbulent depends not only on the mean velocity but on the quality Where, = Density of Fluid D = Diameter of pipe =Dynamic Viscosity Re = VD The term is dimensionless and it is called Reynolds Number (Re). It is the ration of the inertia force to the viscous force Re = Intertia Force Viscous Force Re = V2 ( V D ) Re = VD 13.5 Apparatus Description The apparatus consists of 1. A tank containing water at constant head 2. Die container 3. A glass tube 4. The water from the tank is allowed to flow through the glass tube. The velocity of flow can be varied by regulating valve. A liquid die having same specific weight as that of water has to be introduced to glass tube. Additional materials or Equipment required are 1. Stop Watch 2. Measuring Flask 3. Color Dye 4. Water Supply 13-2

57 Reynolds s Apparatus 13.6 Experimental Procedure 1. Switch on the pump and fill the head tank. Manually also fill the dye tank with some amount of bright dye liquid provided. 2. Open the control valve slowly at the bottom of the tube and release small flow of dye. 3. Observe the flow in the tube. 4. Note down the time for 1 liter of discharge with the help of stopwatch and measuring flask. 5. Repeat the above process for various discharges 13.7 Observations The following observations are made: 1. When the velocity of flow is low, the die filament in the glass tube is in the form of a straight line of die filament is parallel to the glass tube which is the case of laminar flow as shown in fig Figure 13.1 Laminar flow 2. With the increase of velocity of flow the die filament is no longer straight line but it becomes wavy one as shown in fig.13.2 this is shown that flow is no longer laminar. This is transition flow. Figure 13.2 Transition flow 3. With further increase of velocity of the way die filament is broken and finally mixes in water as shown in fig Figure 13.3 Turbulent flow 13-3