FACULTY OF CIVIL ENGINEERING & TECHNOLOGY LABORATORY MODULE AMJ20204 FLUID MECHANICS ENGINEERING Semester 1 Academic Session 2022/2023 Dr. Ain Nihla Kamarudzaman Dr. Zulkarnain Hassan Mrs. Siti Hasmah Abdul Hamid Mr. Zalizam Ghazali
FLOWMETER MEASUREMENT APPARATUS 1.0 OBJECTIVES 1.1 To obtain the flow rate by utilizing rotameter, venturi meter and orifice meter. 1.2 To determine the total head loss and loss coefficient when fluid flows through 90 degree elbow. 2.0 INTRODUCTION Rotameter The rotameter is a flow meter in which a rotating free float is the indicating element. Basically, a rotameter consists of a transparent tapered vertical tube through which fluid flows upward. Within the tube is placed a freely suspended “float” of pump-bob shape. When there is no flow, the float rests on a stop at the bottom end. As flow commences, the float rises upward and buoyancy forces on it are balanced by its weight. The float rises only a short distance if the rate of flow is small, and vice versa. The points of equilibrium can be noted as a function of flow rate. With a well-calibrated marked glass tube, the level of the float becomes a direct measure of flow rate. Figure 1: The rotameter Venturi Meter The venturi meter consists of a venturi tube and a suitable differential pressure gauge. The venturi tube has a converging portion, a throat and a diverging portion as shown in the Figure 2. The function of the converging portion is to increase the velocity of the fluid and lower its static pressure. A pressure difference between inlet and throat is thus developed, which pressure difference is correlated with the rate of discharge. The diverging cone serves to change the area of the stream back to the entrance area and convert velocity head into pressure head. Tapered tube Flow Scale EXPERIMENT 1 AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 1
Figure 2: Venturi Meter Assuming incompressible flow and no frictional losses, from Bernoulli’s Equation 2 2 22 1 2 11 2 2 Z g v g p Z g v g p ++=++ ρ ρ (1) Use of the continuity Equation Q = A1V1 = A2V2, equation (1) becomes −=−+ − 2 1 2 2 2 21 21 1 2 A A g V ZZ g pp ρ (2) Ideally, 2/1 21 21 /1 2 2 1 2 222 1 2 −+ − −== − ZZ g pp g A A AVAQ ρ (3) However, in the case of real fluid flow, the flow rate will be expected to be less than that given by equation (2) because of frictional effects and consequent head loss between the inlet and throat. In metering practice, this non-ideality is accounted by insertion of an experimentally determined coefficient, Cd that is termed as the coefficient of discharge. With Z1 = Z2 (elevation of the centerline of the pipe) in this apparatus, equation (3) becomes 21 21 1 2 2 1 2 2 1 2 − −××= − g pp g A A d ACQ ρ (4) Since P = ρgh Then, Actual flow rate, [ ] ( ) s m g hh A A ACQ t td 3 21 21 21 2 1 2 − −××= − (5) where, Cd = Coefficient of discharge (0.98) D2 = Throat diameter (16 mm) D1 = Inlet diameter (26 mm) At = Throat area (2.011 x 10-4 m2 ) A = Inlet area (5.309 x 10-4 m2 ) g = 9.81 m/s2 1 2 Inlet Throat ρ = Density of water (1000 kg/m3 ) P1 = Inlet pressure (Pa) P2 = Throat pressure (Pa) h1, h2 = Manometer readings (m) AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 2
Orifice Meter The orifice for use as a metering device in a pipeline consists of a concentric square-edged circular hole in a thin plate, which is clamped between the flanges of the pipe as shown in the Figure 3. Figure 3: Orifice meter Pressure connections for attaching separate pressure gauges are made at holes in the pipe walls on both side of the orifice plate. The downstream pressure tap is placed at the minimum pressure position, which is assumed to be at the vena contracta. The centre of the inlet pressure tap is located between one-half and two pipe diameters from the upstream side of the orifice plate, usually a distance of one pipe diameter is employed. Equation (4) for the venturi meter can also be applied to the orifice meter where Actual flow rate, 21 21 1 2 2 1 2 2 1 2 − −××= − g pp g A A d ACQ ρ (6) The coefficient of discharge, Cd in the case of the orifice meter will be different from that for the case of a venturi meter. (7) where, Cd = Coefficient of discharge (0.63) D7 = Orifice diameter (16 mm) D6 = Orifice upstream diameter (26 mm) At = Orifice area (2.011 x 10-4 m2 ) A = Orifice upstream area (5.309 x 10-4 m2 ) (h6 – h7) = Pressure difference across orifice (m) A1 A2 Vena contracta [ ] ( ) s m g hh A A ACQ t td 3 21 76 21 2 1 2 − −××= − AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 3
90o elbow Figure 4 shows fluid flowing in a pipeline where there is some pipe fitting such as bend or valve, and change in pipe diameter. Included in the figure is the variation of piezometric head along the pipe run, as would be shown by numerous pressure tappings at the pipe wall. Figure 4: Piezometric head along a pipeline If the upstream and downstream lines of linear friction gradient are extrapolated to the plane of fitting, a loss of piezometric head, ∆h, due to the fitting is found. By introducing the velocity heads in the upstream and downstream runs of pipe, total head loss, ∆H can be determined in which g V g V hH 22 2 2 2 1 =∆ −+∆ (8) Energy losses are proportional to the velocity head of the fluid as it flows around an elbow, through an enlargement or contraction of the flow section, or through a valve. Experimental values for energy losses are usually expressed in terms of a dimensionless loss coefficient K, where gV H or gV H K /2/ 2 2 2 2 1 ∆ ∆ = (9) For results of better accuracy, long sections of straight pipe are required to establish with certainty the relative positions of the linear sections of the piezometric lines. However, in a compact apparatus as described, only two piezometers are used, one placed upstream and the other downstream of the fitting, at sufficient distances as to avoid severe disturbances. These piezometers measure the piezometric head loss, ∆h’ between the tapping. Thus ∆−∆=∆ hhh f ' (10) =∆ g V D L f fh 2 4 2 V2 2 / 2g V1 2 / 2g H h V V 2 1 g V 2 2 2 g V 2 2 1 H h V1 V2 AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 4
where; ∆hf = Friction head loss which would be incurred in fully developed flow along the run of pipe between the piezometer tappings. f = Friction factor L = Distance between the piezometer, measured along the pipe center line D = Pipe diameter V = Average velocity of fluid flow in pipe. The friction head loss is estimated by choosing a suitable value of friction factor, f for fully developed flow along a smooth pipe. The method used here to determine the friction factor is the Prandtl equation; ( ) 4.0Relog4 1 = f − f (11) Typical values derived from this equation are tabulated in the table below: Re, x 104 0.5 1.0 1.5 2.0 2.5 3.0 3.5 F, x 10-3 9.27 7.73 6.96 6.48 6.14 5.88 5.67 In determination of the fraction factor, f, it is sufficient to establish the value of f at just one typical flow rate, as about the middle of the range of measurement due to the fact that f varies only slowly with Re, and the friction loss is generally fairly small in relation to the measured value of ∆h’. Characteristic of flow through elbow and at changes in diameter Figure 5 shows flow round a 90o elbow which has a constant circular cross section. Figure 5: 90o Elbow The value of loss coefficient K is dependent on the ratio of the bend radius, R to the pipe inside diameter D. As this ratio increase, the value of K will decrease and vice versa. 2/ gvKH 2 ×=∆ (12) Where, K = Coefficient of losses, v = velocity of flow and g = 9.81 m/s2 D V R AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 5
3.0 EQUIPMENTS Figure 6: Part Identification Diagram for the flow meter A. Part Identifications List 1 Manometer Tubes 7 90° Elbow 2 Discharge Valve 8 Orifice 3 Water Outlet 9 Venturi 4 Water Supply 5 Staddle Valve 6 Rotameter 1 2 3 4 5 6 7 8 9 AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 6
4.0 EXPERIMENTAL PROCEDURE General Start-up Procedure 4.1 Fully close the flow control valve of the hydraulic bench and fully open the discharge valve. 4.2 Ensure that discharge hose is properly directed to sump tank (made of fibreglass) before starting up the system. Also ensure that collection tank drain valve is left OPEN to allow flow discharge back into sump tank. 4.3 Once step (4.2) is completed start up the pump supply in the hydraulic bench. Open the bench valve slowly. At this point, you will see water flowing from hydraulic bench through to the flow apparatus and discharge into the collection tank of hydraulic bench and then drained back into sump tank. 4.4 Proceed to fully open the flow control valve. When the flow in the pipe is steady and there is no trapped air bubbles, start to close the bench valve in order to reduce the flow to the maximum measurable flow rate. 4.5 The water level in the manometer board will display different level of water heights. (If the water level in the manometer board is too high where it is out of visible point, adjust the water level by using the staddle valve. With the maximum measurable flow rate, retain maximum readings on manometer). 4.6 At this point, slowly reduce the flow by controlling the flow discharge valve of the apparatus, you may also close this discharge valve totally. 4.7 The water level in the manometer board will begin to level into a straight level. This level maybe at the lower or higher end of the manometer board range. (Take note that the pump from the hydraulic bench is at this time, still supplying water at a certain pressure in the system). 4.8 Also be on the lookout for “Trapped Bubbles” in the glass tube or plastic transfer tube. To remove it you can either slowly press the plastic tube to push the bubbles up or lightly “tab” the glass tube to release the bubbles upwards. To obtain the flow rate by utilizing rotameter, venturi meter and orifice meter. 4.9 When the flow in the pipe is steady and there is no trapped bubble, start to close the bench valve to reduce the flow to the maximum measurable flow rate. 4.10 Use the air bleed screw, adjust water level in the manometer board. Retain maximum readings on manometers with the maximum measurable flow rate. 4.11 Note readings on manometers (A - H), rotameter and measured flow rate. 4.12 Repeat 4.9 for different flow rates. The flow rates can be adjusted by utilizing both bench valve and discharge valve. AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 7
To determine the total head loss and loss coefficient when fluid flows through 90 degree elbow. 4.13 Note readings on manometers (I and J) and measured flow rate. 4.14 Repeated 4.11 for different flow rates. The flow rates can be adjusted by utilizing both bench valve and discharge valve. 4.15 Complete the tables below. 4.16 Plot graph ∆H against v2 for 90 degree elbow to determine the coefficient of losses. 2g Note: Probe A and C for venturi calculation Probe G and H for orifice calculation Probe I and J for 90 degree elbow calculation All other probe readings are for viewing of pressure curve ONLY. AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 8
5.0 RESULTS Data: Table 1, 2 Table 1: Manometer reading Manometer reading (mm) A B C D E F G H I J Ro ( AMJ20204: FLUID MECHANICS ENGINEERING 9
gs and flow rate calculation Flow rate calculated using the Bernoulli's Equation (L/min) otameter (L/min) Vol (L) Time (min) Flow rate, Q (L/min) Venturi Orifice Laboratory Module
Table 2: Determination of the loss coefficient when fluid flows through a 90 degree elbow. Show all your calculations in separate sheets. Plot graph using Excel 6.0 DISCUSSION (Include a discussion on the result noting trends in measured data, and comparing measurements with theoretical predictions when possible. Include the physical interpretation of the result, the reasons for deviations of your findings from expected results, your recommendations on further experimentation for verifying your results, and your findings.) 7.0 CONCLUSION (Based on data and discussion, make your overall conclusion) 8.0 QUESTIONS 8.1 Which are the terms in the Bernoulli’s Equation denote pressure head, velocity head elevation head and piezometric head? 8.2 What does Coefficient of discharge (Cd) mean? 8.3 What is vena contracta? 8.4 Give any two differences between Venturi and Orifice meter. 8.5 How does the pressure and velocity of water change at the throat of the conduit shown below? Represent it using a graph. Flowrate, Q(L/min) Differential Piezometer Head, ∆h' (mm) Elbow (hI-hJ) V (m/s) V 2 /2g (mm) ∆hf (mm) ∆H (mm) Flow rate P & V ? AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 10
BERNOULLI’S THEOREM DEMONSTRATION 1.0 OBJECTIVES 1.1 To determine the discharge coefficient of the venturi meter. 1.2 To measure flow rate with venturi meter. 1.3 To demonstrate Bernoulli’s Theorem. 2.0 INTRODUCTION Bernoulli’s Law Bernoulli’s Law states that if a non-viscous fluid is flowing along a pipe of varying cross section, then the pressure is lower at the constrictions where the velocity is higher, and the pressure is higher where the pipe opens out and the fluid stagnates. This is expressed with the following equation. ∗ =++ hz g V g p 2 2 ρ = constant (1) where, P – Fluid static pressure at the cross section, ρ – Density of the moving fluid, g – Acceleration due to gravity, V – Mean velocity of fluid flow at the cross section, z – Elevation head of the centre at the cross section with respect to the datum, h* - Total (stagnation) head. = g p ρ Pressure Head g V 2 2 = velocity head, hv where, z = Elevation head h* = Total head (sum of all the terms) z = 0 (since the centre line of the cross section lie on the same horizontal plane). Therefore equation 1 becomes, ==+ * 2 2 h g V g p ρ constant (2) This represents the total head at the cross section. EXPERIMENT 2 AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 11
Derivation of Bernoulli’s equation using streamline coordinates Euler’s equation for steady flow along a streamline is given by, s v V s z g s p ∂ ∂ = ∂ ∂ − ∂ ∂ − ρ 1 (3) If a fluid particle moves a distance ds along a streamline, ds s p ∂ ∂ = dP (change in pressure) = ∂ ∂ ds s z dz (change in elevation) = ∂ ∂ ds s v dv (change in velocity) After multiplying equation (3) by ∂s, we get =∂+∂+ 0 ∂ g vVz p ρ (4) Integrating equation (4) ∫∫∫ =∂+∂+ ∂ g vVz p ρ constant =++ 2 2 V gz p ρ constant (5) For the case where flow is incompressible, ρ is constant and equation (5) becomes, z =++ g V g p 2 2 ρ constant (6) Equation (6) is the Bernoulli’s equation. Following are the assumptions made in the derivation of Bernoulli’s equation. (a) The flow is steady (b) The flow is incompressible (c) The fluid is ideal, i.e. viscosity is zero (d) The flow is irrotational, i.e. flow along a streamline. AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 12
Measurement of static, stagnation and dynamic pressures There is no pressure variation normal to straight streamlines. This fact makes it possible to measure the static pressure in a flowing fluid using a wall pressure tapping placed in a region where the flow streamlines are straight as shown in Figure 1. The pressure tap is a small hole, drilled carefully in the wall, with its axis perpendicular to the surface. If the hole is perpendicular to the duct and free from burrs, accurate measurements of static pressure can be made by connecting the tap to a suitable measuring instrument. Figure 1: Wall pressure tapping for measuring static pressure In a fluid stream far from a wall, or where streamlines are curved, accurate static pressure measurements can be made by careful use of a static pressure probe as shown in Figure 2. Such probes are designed so that the measuring holes are placed correctly with respect to the probe tip and stem to avoid erroneous results. Measuring section must be aligned with the local flow direction. Figure 2: Measurement of static pressure using probes Stagnation pressure is obtained when a flowing fluid is decelerated to zero speed by a frictionless process. In incompressible flow, Bernoulli’s equation can be used to relate changes in speed and pressure along a streamline for such a process. Neglecting elevation differences, equation (5) becomes: =+ 2 2 Vp ρ constant (7) Flow streamlines Pressure tap Fluid flow Small holes Stem To manometer or pressure gauge AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 13
If the static pressure (p) at a point in the flow where the speed is V, then the stagnation pressure (p0), where the stagnation speed, V0 is zero, may be computed from the following equation. 22 2 2 Vp 00 Vp +=+ ρρ Therefore, 2 0 2 1 += ρVpp (8) Equation (8) is a mathematical statement of stagnation pressure, valid for incompressible flow. The term ½ ρV² generally is the dynamic pressure. Solving the dynamic pressure gives: ρ 0 pp )(2 V − = (9) Thus, if the stagnation pressure and the static pressure could be measured at a point, Equation (9) would give the local flow speed. Stagnation pressure is measured in the laboratory using a probe with a hole that faces directly upstream as shown in Figure 3. Such a probe is called a stagnation pressure probe (hypodermic probe) or Pitot tube. The measuring section must be aligned with the local flow direction. Figure 3: Measurement of stagnation pressure using probe Two possible experimental setups are shown below. In Figure 4 the static pressure corresponding to point A is read from the wall static pressure tap. The stagnation pressure is measured directly at A by the total head tube, as shown. (The stem of the total head tube is placed downstream from the measurement location to minimize disturbance of the local flow) 0 Fluid flow Stem To manometer or pressure gauge Small hole AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 14
Figure 4: Measurement of static and stagnation pressures Two probes often are combined, as in the Pitot-static tube shown in Figure 5. The inner tube is used to measure the stagnation pressure at point B, while the static pressure at C is sensed using the tapping on the wall. In flow fields where the static pressure variation in the streamwise direction is small, the Pitot-static tube may be used to infer the speed at point B in the flow by assuming pB = pC and using Equation (9). (Note that when pB ≠ pC, this procedure will give erroneous results) Figure 5: Simultaneous measurement of static and stagnation pressures Bernoulli equation applies only for incompressible flow (Mach number, Ma ≤ 0.3). Note: -c u u Ma = (10) where, u = fluid velocity and c = sonic velocity Pressure Varies Along the Pipe A number of factors can cause for pressure to vary along the pipe such as: a) Friction from the pipe’s inner surface, b) The diameter of the pipe; if it is small the pressure is lower because the velocity is increased (Bernoulli’s Theory), c) Density of the fluid in the pipe, d) The height of the pipe at which the pipe stands or the height at which the flow through i.e. gravity, e) Turbulence of the fluid Flow p A p0 Total head tube flow Stem Small holes B C p p0 AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 15
Venturi Meter The venturi meter consists of a venturi tube and differential pressure gauge. The venturi tube has a converging portion, a throat and a diverging portion as shown in the Figure 6. The function of the converging portion is to increase the velocity of the fluid and lower its static pressure. A pressure difference between inlet and throat is thus developed; the pressure difference is correlated with the rate of discharge. The diverging cone serves to change the area of the stream back to the entrance area and convert velocity head into pressure head. Figure 6: The Venturi Tube Assuming incompressible flow and no frictional losses, from Bernoulli’s Equation 2 2 22 1 2 11 2 2 Z g vp Z g vp ++=++ ρ ρ (11) Using continuity Equation Q = A1V1 = A2V2, equation (11) becomes −=−+ − 2 1 2 2 2 21 21 1 2 A A g V ZZ pp ρ (12) Ideally, 2/1 21 21 /1 2 2 1 2 222 1 2 −+ − −== − ZZ pp g A A i AVAQ ρ (13) However, in the case of real fluid flow, the flow rate will be expected to be less than that given by equation (13) because of frictional effects and consequent head loss between inlet and throat. Therefore, 2/1 21 21 /1 2 2 1 2 2 1 2 −+ − −××= − ZZ pp g A A da ACQ ρ (14) Inlet Throat Discharge 1 2 3 AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 16
Non-ideality of flow rate is accounted by insertion of an experimentally determined discharge coefficient, Cd that is termed as the coefficient of discharge. With Z1 = Z2 in this apparatus, the discharge coefficient is determined as follow: i a d Q Q C = (15) Discharge coefficient, Cd usually lies in the range between 0.9 and 0.99. 3.0 EQUIPMENTS Figure 7: Unit Assembly of Bernoulli’s Theorem Demonstration A. Part Identifications List 1 Manometer Tubes 7 Gland nut 2 Test section 8 Hypodermic probe 3 Water inlet 9 Adjustable feet 4 Unions 5 Air bleed screw 6 Flow control valve 1 2 3 4 4 5 6 7 8 9 AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 17
4.0 EXPERIMENTAL PROCEDURE General Start-up Procedures 4.1 Ensure that the clear acrylic test section is installed with the converging section upstream. Check that the unions are tighten (hand tight only). If necessary to dismantle the test section then the total pressure probe must be withdrawn fully (but not pulled out of its guide in the downstream coupling) before releasing the couplings. 4.2 Locate the apparatus on the flat top of the bench. 4.3 Attach a spirit level to baseboard and level the unit on top of the bench by adjusting the feet. 4.4 Fill water into the volumetric tank of the hydraulic bench until approximately 90% full. 4.5 Connect the flexible inlet tube using the quick release coupling in the bed of the channel. 4.6 Connect a flexible hose to the outlet and make sure that it is directed into the channel. 4.7 Partially open the outlet flow control valve at the Bernoulli’s Theorem Demonstration unit. 4.8 Fully close the bench flow control valve, V1 then switch on the pump. 4.9 Gradually open V1 and allow the piping to fill with water until all air has been expelled from the system. 4.10 Check for “Trapped Bubbles” in the glass tube or plastic transfer tube. Remove them from the system for better accuracy. Note: To remove air bubbles, you will have to bleed the air out as follows: a) Use a pen or screw driver to press the air bleed valve at the top right side of manometer board. b) Press air bleed valve lightly to allow fluid and trapped air to escape out. (Take care or you will wet yourself or the premise). c) Allow sufficient time for bleeding until all bubbles escape. 4.11 At this point, you will see water flowing into the venturi and discharge into the collection tank of hydraulic bench. 4.12 Increase the water flow rate. When the flow in the pipe is steady and there is no trapped bubble, start to close the discharge valve to reduce the flow to the maximum measurable flow rate. 4.13 You will see that water level in the manometer tubes will begin to display different level of water heights. If the water level in the manometer board is too low where it is out of visible point, open V1 to increase the static pressure. If the water level is too high, open the outlet control valve to lower the static pressure. (Note: The water level can be adjusted facilitate by the air bleed valve.) AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 18
4.14 Adjust V1 and outlet control valve to obtain a flow through the test section and observe that the static pressure profile along the converging and diverging sections is indicated on its respective manometers. The total head pressure along the venture tube can be measured by traversing the hypodermic tube. (Note: The manometer tube connected to the tapping adjacent to the outlet flow control valve is used as a datum when setting up equivalent conditions for flow through test section.) 4.15 The actual flow of water can be measured using the volumetric tank with a stop watch. Discharge Coefficient Determination 4.16 Perform the General Start-up Procedures (4.1 - 4.15) 4.17 Withdraw the hypodermic tube from the test section. 4.18 Adjust the discharge valve to the maximum measurable flow rate of the venturi. This is achieved when manometer tube 1 and 3 give the maximum observable water head difference. (Note: Refer to the venturi specification for the designed flow rate.) 4.19 After the level stabilizes, measure the water flow rate using volumetric method and record the manometers reading. 4.20 Repeat step 4.19 with at least three decreasing flow rates by regulating the venturi discharge valve. 4.21 Obtain the actual flow rate, Qa from the volumetric flow measurement method. 4.22 Calculate the ideal flow rate, Qi from the head difference between h1 and h3 using Equation (13). 4.23 Plot Qa Vs Qi and obtain the discharge coefficient, Cd which is the slope. AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 19
Flow Rate Measurement with Venturi Meter 4.24 Adjust the discharge valve to a high measurable flow rate. 4.25 After the level stabilizes, measure the water flow rate using volumetric method and record the manometers reading. 4.26 Repeat step 4.25 with three other decreasing flow rates by regulating the venturi discharge valve. 4.27 Calculate the venturi meter flow rate of each data by applying the discharge coefficient obtained. 4.28 Compare the volumetric flow rate with venturi meter flow rate. Bernoulli’s Theorem Demonstration 4.29 Adjust the discharge valve to a high measurable flow rate. 4.30 After the level stabilizes, measure the water flow rate using volumetric method. 4.31 Gently slide the hypodermic tube (total head measuring) connected to manometer #G, so that its end reaches the cross section of the Venturi tube (Figure 7) at #A. Wait for some time and note down the readings from manometer #G and #A. The reading shown by manometer #G is the sum of the static head and velocity heads, i.e. the total (or stagnation) head (h* ), because the hypodermic tube is held against the flow of fluid forcing it to a stop (zero velocity). The reading in manometer #A measures just the pressure head (hi) because it is connected to the Venturi tube pressure tap, which does not obstruct the flow, thus measuring the flow static pressure. 4.32 Repeat step 5 for other cross sections (#B, #C, #D, #E and #F). 4.33 Repeat step 3 to 6 with three other decreasing flow rates by regulating the venturi discharge valve. 4.34 Calculate the velocity, ViB using the Bernoulli’s equation where; )(2 iB 8 i −××= hhgV 4.35 Calculate the velocity, ViC using the continuity equation where ViC = Qav / Ai 4.36 Determined the difference between two calculated velocities. AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 20
Figure 8: Ventur AMJ20204: FLUID MECHANICS ENGINEERING 21
ri Meter Drawing Laboratory Module 1
5.0 RESULTS Data: Table 1, 2, 3 Table 1: Discharge Coefficient, Cd Determination Water Head (mm) Qa (LPM) A B C D E F hA-hC (m) Qi (LPM) 2/1 21 21 /1 2 2 1 2 222 1 2 −+ − −== − ZZ pp g A A i AVAQ ρ [ ] ( ) 2/1 2/1 2 1 2 i 2 1 2 hhg cA A A AQ − −= − m3 /s Draw graph with Qi (X-axis) and Qa (Y-axis) and determine the slope, which is Cd Show all your calculations in separate sheets. Throat dia, D3 (mm) = 16 Inlet dia, D1 (mm) = 26 Throat area, A2 (m2 ) = 2.01 x 10-4 Inlet area, A1 (m2 ) = 5.31 x 10-4 g (m/s2 ) = 9.81 ρ (kg/m3 ) = 1000 1 m3 /s = 60000 LPM AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 22
Table 2: Flow Rate Measurement with Venturi meter Water Head (mm) Qa (LPM) A B C D E F hA-hC (m) Calc. Qac (LPM) Error (%) (Qac-Qa)/Qac [ ] ( ) 2/1 2/1 2 1 2 dac 2 1 2 hhg CA A A ACQ − −×= − m3 /s Table 3: Comparison of velocity profiles using Bernoulli & Continuity equation Volume 20 L Average Time Min Flow rate (Qav) LPM Cross Section Using Bernoulli equation Using Continuity equation Difference i h*=hG (mm) hi (mm) ViB = √[2*g*(h* - hi )] (m/s) Ai = π Di 2 / 4 (m2 ) ViC = Qav / Ai (m/s) ViB-ViC (m/s) A B C D E F AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 23
Volume 15 L Average Time Min Flow rate (Qav) LPM 6.0 DISCUSSION (Include a discussion on the resulst noting trends in measured data, and comparing measurements with theoretical predictions when possible. Include the physical interpretation of the result, the reasons for deviations of your findings from expected results, your recommendations on further experimentation for verifying your results, and your findings.) 7.0 CONCLUSION (Based on data and discussion, make your overall conclusion) 8.0 QUESTIONS 8.1 Define compressible and incompressible flow and give an example for each type of flow. 8.2 List the measuring devices that use Bernoulli’s equation. 8.3 What are the main assumptions made in the derivation of Bernoulli’s equation? 8.4 Water is flowing through a pipe of 5 cm diameter under a pressure of 29.43 x 104 N/m2 and with mean velocity of 2 m/s. Find the pressure head, velocity head and the total head of the water at a cross-section, which is 5 m above the datum line. Data: ρ = 1000 kg/m3 , g = 9.81 m/s2 Cross Section Using Bernoulli equation Using Continuity equation Difference i H*=hG (mm) hi (mm) ViB = √[2*g*(h* - hi )] (m/s) Ai = π Di 2 / 4 (m2 ) ViC = Qav / Ai (m/s) ViB-ViC (m/s) A B C D E F AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 24
FRICTION LOSS APPARATUS 1.0 OBJECTIVE 1.1 To determine the pressure or head loss in different pipe diameters, joints, valves, orifice meter and venturi tube. 2.0 INTRODUCTION Transportation or flow of fluid in closed conduits is one of the major topics in Fluid Mechanics due to its vast application in many fields of study. Early work in the subject was essentially empirical and despite many advances in mathematical analysis the complexity of the flow of real fluids is such that very few complete solutions of flow situations exist and thus, a large part of the topic of fluid flow in closed conduits remains an empirical science. Effect of Pipe Diameter on Energy Losses Different pipe diameters would result in different amount of energy losses depending on the regime of flow. For a given flow rate, the mean velocity in the pipe is given by: 4 2 D Q Thus, 2 4 D Q (1) Energy Losses due to Sudden Change in Pipe Diameter (a) Head Loss at Sudden Enlargement Consider a sudden enlargement in pipe flow area from A1 to A2 Figure 1: Sudden Enlargement AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 25 EXPERIMENT 4
Equating forces where net force acting on the fluid equals the rate of increase of momentum, together with Bernoulli’s and Continuity equations, it can be shown that: 2 2 1 2 1 1 2 A A g u hf (2) (b) Head Loss at Sudden Contraction The momentum equation cannot be applied in the case of a gradual contraction because the pressure on the face of the annulus at the change in section varies in an unknown way; this is clearly the case since it is pressure forces on this face which cause the flow to contract. After the contraction, a ‘vena contract' is formed after which the flow diverges to fill the smaller diameter tube. The flow pattern is shown in Figure 2. Figure 2: Sudden Contraction Eddies that formed between the ‘Vena Contract' and the pipe wall caused the most energy dissipation. Between the vena contract and the downstream section (2) a flow pattern similar to that occurring after an abrupt enlargement is formed and thus loss occurs once again. g u K A A g u h C C f 2 1 2 2 2 2 2 2 2 (3) Ac represents the cross sectional area of the vena contract. However, the area of the vena contract is normally unknown; yet, it would appear reasonable to suggest that if the contraction area ratio A2 / A1 becomes smaller, then the vena contract will become more pronounced. The limiting value would be the same as that for a sharp edged pipe discharging from a large tank for which a good experimental value is 0.5. A useful empirical result has been found to be: 2 1 15.0 d d Kc (4) AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 26
Although the area A1 is not explicitly involved the value for Kc is dependent upon the area ratio, A2 / A1 (equals (d2/d1) 2 ) to as tabulated below for concentric contractions at high Reynolds numbers: Energy Losses in Fittings A piping system is normally made up of several connective components. All these components are generally referred to as fittings. Fittings are being used for a number of purposes such as to change the direction of flow of a fluid (bends) as well as to regulate the flow rate (valves) and etc. However, all these fittings inevitably impose resistance on the flowing fluid, resulting in losses of energy. All these losses have to be taken into account in order to develop an effective piping system. Losses in Bends, Elbows and Junctions Energy is lost whenever direction of flow in a pipe is altered. Referring to a 90o bend as shown in Figure 3. When fluid flows in a curved path, there is a radial force acting inwards on the fluid to provide inward acceleration. This is accompanied by an increase in pressure near the outer wall of the bend, staring from point A and rising to a maximum at B. Furthermore, there is a reduction in pressure near the inner wall giving a minimum pressure at C and a subsequent rise from C to D. Between A and B and between C and D, the pressure increases in the direction of flow (adverse pressure gradient). A large radius of curvature of the bend will cause separation of the flow from the boundary and therefore energy losses in turbulence. The magnitude of these losses is thus mainly dependent on the radius of curvature of the bend. Energy losses also arise from secondary flow where it is set up at right angles to the pipe cross section which increases the velocity gradient and hence the shear stress of the wall. Figure 3: 90o Bend 0 0.2 0.4 0.6 0.8 1.0 0.5 0.48 0.42 0.32 0.18 0 Eddies AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 27
A pipe bend, elbow or juction therefore causes an additional head loss. This extra loss is conveniently expressed in term of number of velocity heads loss, given as follow: g u f kh 2 2 (5) Where, k is the coefficient of frictions. The value of k depends on the total angel of bend as well as the relative radius of curvature R/d (where R is the radius of curvature of pipe centre and d is the pipe diameter). k also increases with surface roughness but varies slightly with Re. Miter Bend A Mitre or 90o elbow bend (shown in Figure 4) is used where there is insufficient space for large radius. This bend would result in a greater head loss as the direction of flow is changed abruptly. R/d for it is 0 while k is approximately 1.1. Figure 4: Mitre Bend Losses in valves Various types of valve are being installed in a piping system to regulate or control fluid flow. Common ones are gate, globe and ball valves. Each has their own characteristics and applications. However, all of them have the common problem, which is causing additional losses of head. Generally, the more intricate the passage through which fluid has to pass, the greater the head loss. For turbulent flow, the head loss can be represented by the equation; g u f kh 2 2 Here, u represents the mean velocity in the pipe. The k factor values depend critically on the exact shape of the flow passages. Figures below show the structure of some of the commonly found valves: AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 28
Figure 5: Structure of common valves In-line Strainer In-line strainer is a type of fitting used to mechanically remove unwanted solids from flowing fluids by means of a perforated or wire mesh straining element. It is installed in pipelines to protect pumps, meters, control valves, steam traps, regulators and other process equipment. Figure 6: Y Strainer Approximate loss coefficients (k) for some commercial pipe fittings are being given as follows: Component K Value a. Elbow Regular 90o , flanged 0.3 Regular 90o , threaded 1.5 Long radius 90o , flanged 0.2 Long radius 90o , threaded 0.7 Gate Valve Globe Ball Valve AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 29
Long radius 45o , flanged 0.2 Regular 45o , flanged 0.4 b. 180o return bends 180o return bend, flanged 0.2 180o return bend, threaded 1.5 c. Tees Line flow, flanged 0.2 Line flow, threaded 0.9 Branch flow, flanged 1 Branch flow, threaded 2 d. Union 0.08 e. Valves Globe, fully open 10 Gate, fully open 0.15 Gate, 1/4 closed 0.26 Gate, 1/2 closed 2.1 Gate, 3/4 closed 17 Ball, fully open 0.05 Equivalent Length (Le) Energy loss in pipe fittings can also be expressed in term of Equivalent Length (Le) or Number of Pipe Diameter (NPD). ∆hf = Leq hsp = (NPD d) hsp (6) This approach requires knowing the head loss per unit length of straight pipe (hsp). This may be calculated or measured experimentally. Dividing the head loss over the straight pipe by the known length will give hsp. For a fitting, the head loss across it could be represented by head loss measured in a known length of pipe of equal diameter, carrying the same fluid under the same velocity. Total Head Loss of the pipe, tube or duct system, is the same as that produced in a straight pipe or duct whose length is equal to the pipes of the original systems - plus the sum of the equivalent lengths of all the components in the system. AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 30
Orifice Meter Figure 7: Fluid flowing through an orifice meter Referring to Figure 7 above, fluid approaching an orifice will converge towards it. Since an instantaneous change in direction is impossible, the streamlines will continue to converge beyond the orifice until they become parallel at a particular section. The jet will subsequently diverge again beyond this short parallel section, thus forming a minimum area at this section. It is termed the vena contract. Applying Bernoulli principles between (1) and (2), it can be shown that the volumetric flow-rate of fluid across the orifice is given by following equation: 2 1 2 1 2 A A C hgAC Q o d od Where: Q = Volumetric flow-rate (m3 /s)o Cd = Coefficient of discharge (typical value is between 0.6 – 0.65) Ao = Cross sectional area of orifice (m2 ) A1 = Cross sectional area of pipe before orifice (m2 ) ∆h = Head loss across orifice (m) g = Gravitational acceleration (9.81 ms-2) However, normally the denominator term can be approximate to 1 since both Cd 2 and (Ao/A1) 2 are insignificantly small. Thus, the equation can be further simplified to: od 2 hgACQ Orifice meter (7) (8) AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 31
Venturi Tube Figure 8: Venturi tube structure Referring to Figure 8, the venturi tube has a rapid converging conical inlet, a parallel cylindrical throat, and a slowly diverging recovery cone. It has no projections into the fluid, no sharp corners, and no sudden changes in contour. Fluid is being accelerated through the converging section; the high fluid velocity at this section will result in a drop in pressure. Therefore, venturi effect perfectly depicts the law of conservation of energy given by Bernoulli’s equation. One of the applications of venturi tube is for measuring flow in a pipe. Applying Bernoulli’s equation and equation of continuity between the two sections, the flow-rate for an incompressible fluid can be approximated by the following equation: 1 2 2 2 1 1 A A hg d ACQ Where: Q = Fluid flow-rate (m3 /s) Cd = Coefficient of discharge for venturi (approximately is 0.975) A1 = Cross sectional area of converging inlet (m2 ) A2 = Cross sectional area of diverging outlet (m2 ) ∆h = Head difference between parallel throat and other section (m) A A 2 (9) AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 32
3.0 EQUIPMENTS Figure 9: Friction Loss Apparatus A. Part Identification List A Sudden Contraction M Globe Valve B 9.8mm PVC Piping N In-Line Strainer C 12mm PVC Piping O Elbow Joint D 16.3mm PVC Piping P 90o Bend Joint E 18.9mm PVC Piping Q T-Joint F Sudden Enlargement R Venturi tube G Ball valve, V1 S Orifice H Ball valve, V2 T Flow meter I Ball valve, V3 U Pitot tube J Ball valve, V4 K Y- Joint L Gate Valve AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 33
4.0 EXPERIMENTAL PROCEDURE 4.1 Place the apparatus on a level table. 4.2 Plug the 3 pin plug of the apparatus to the laboratory 240 VAC power supply. Switch ON the power supply. 4.3 Fill the water tank of the apparatus until 3/4 of its full capacity. 4.4 Shut off all the valves of the trainer. 4.5 Switch ON the trainer main power supply. Ensure the water pump is running. 4.6 Adjust the By-pass Valve (BV) and Flow Regulating Valve (FRV) to obtain the desired liquid flow-rate. 4.7 Turn off all valves except V1, connect the pressure meter to measure the head loss across the contraction, 9.8 mm PVC pipe and enlargement. (Check the flow meter reading; adjust BV and FRV to maintain the flow) 4.8 Turn off V1, switch on V2, with the rest of the valves remain closed, measure the head loss across the contraction, 12 mm PVC pipe (both full and half length) and the enlargement portion. 4.9 Turn off V2, switch on V3, to measure the head loss across 16.3 mm pipe. 4.10 Turn off V3, switch on V4, measure head loss across 18.9 mm pipe, ball valve, 45o Y-joint and 90o bend. 4.11 Under the same setting, measure the head loss across the different points along the venturi tube with respect to the point at the throat. (Ensure that there are no cavitations inside the tube during measurement) 4.12 Turn off V4, fully turn on globe valve, measure the head loss in 90o mitre bend, 90o T-joint, in-line strainer, gate valve, globe valve and the orifice meter. 4.13 Repeat the experiment using different flow rate. 4.14 Record all the data obtained to the table provided. Note: Check the flow meter reading regularly after each setting to ensure that the desired flow-rate is maintained. AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 34
5.0 RESULTS Fitting Pressure Drop (mH2O) Flowrate 1 Flowrate 2 Flowrate 3 Flowrate 4 Straight Pipes 9.8 mm (PVC) 12 mm (PVC) 16.3 mm (PVC) 18.9 mm (PVC) Enlargement (12mm) Enlargement (9.8mm) Contraction (12mm) Contraction (9.8mm) Bends 45o elbow 90o Bend 90o Elbow 90o Mitre Bend 90o T-joint 45o Y-joint Valve Gate Ball Globe In-line Strainer Pitot Tube Venturi meter 1-2 2-3 Orifice 1-2 Flowrate (GPM) 35 AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module
GRAPH Based on your result that obtained from the experiment: i. Plot the graph of head loss against flow rate. Note: Please show all your calculations in separate sheets. 6.0 DISCUSSION (Include a discussion on the result noting trends in measured data, and comparing measurements with theoretical predictions when possible. Include the physical interpretation of the result, the reasons for deviations of your findings from expected results, your recommendations on further experimentation for verifying your results, and your findings.) 7.0 CONCLUSION (Based on data and discussion, make your overall conclusion) 8.0 QUESTIONS 8.1 Give three (3) examples of pressure measurement devices. 8.2 Show that the Reynolds number for flow in a circular pipe of diameter D can be expressed as NRe = D m . 4 8.3 Determine the friction loss that will occur as 100 L/min of water flows through a sudden expansion from a 2-in Schedule 40 steel pipe to a 4-in Schedule 40 steel pipe. 8.4 A vertical venturi meter equipped with a differential pressure gage is used to measure the flow rate of water at 15oC (ρ = 991.1kg/m3 ) through a 5 cm diameter horizontal pipe. The diameter of the venturi neck is 3 cm, and the measured pressure drop is 5 kPa. For discharge coefficient of 0.98, determine the volume flow rate (L/s) of the water and the average velocity (m/s) through pipe. AMJ20204: FLUID MECHANICS ENGINEERING Laboratory Module 36