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Unformatted text preview: Fluid Mechanics (CLD 10603) Experiment 1: Demonstration of Bernoulli’s Theorem in Fluid Flow Experiment 1 Demonstration of Bernoulli’s Theorem in Fluid Flow Objective Determine the fluid velocity using the Bernoulli’s theorem and the Continuity equation. Overview The Bernoulli effect is simply a result of the conservation of energy. The work done on a fluid (a fluid is a liquid or a gas), the pressure times the volume, is equal to the change in kinetic energy of the fluid. In a real flow, friction plays a large role ‐ a lot of times you must have a large pressure drop (decrease in pressure) just to overcome friction. This is the case in your house. Most water pipes have small diameters (large friction), hence it is called ʺwater pressureʺ ‐ it is the energy from that pressure drop that goes to friction. Experimental Procedure 1. 2. 3. 4. Fill water into the volumetric tank of the hydraulic bench until it is approximately 90% full. Open the outlet flow control valve fully at the right hand end of the apparatus. Close the inlet flow control valve then start the pump. Gradually open then inlet flow control valve and allow the pipework (Venturi and manometer) to fill with water until all air has been expelled from the pipework. Check that all manometer tubing is properly connected to the corresponding pressure taps and are air‐bubble free. If needed press air bleeds screw slowly to flush the air‐bubbles. 5. 1 Fluid Mechanics (CLD 10603) Experiment 1: Demonstration of Bernoulli’s Theorem in Fluid Flow 6. 7. After ensure that air is being expelled from the pipework, close the inlet valve fully and stop the pump. With the outlet valve open, press the air bleed screw slightly until the manometer levels reach mid height. Wait for some time for the level in manometer tube to stabilize (it takes some time for it to reach steady state). Start the pump and slowly adjust the inlet valve (you may adjust both inlet and outlet valves) so that you get the maximum difference in levels between tapping point 7 and 8. Wait for some time for the level in manometer tube 8 to stabilize (it takes some time for it to reach steady state). After the steady state is achieved, redirect the water outlet hose into a container whose capacity is known (20 liter, for example) and record the time taken for the water to fill it up. Take at least 3 measurements and record the timings in order to calculate (average) flow rate. 8. 9. 10. Air bleed screw Manometer tubes Unions Gland Nut Hypodermic probe Water inlet Test section Adjustable feet Figure 1: Bernoulli’s Theorem Apparatus 2 Fluid Mechanics (CLD 10603) Experiment 1: Demonstration of Bernoulli’s Theorem in Fluid Flow 11. Gently push the Pitot (total head measuring) tube, connected to manometer 8, so that its end reaches the cross section of the Venturi tube at 1, for example. Wait for some time and note down the readings from manometer 8 and 1. The reading shown by manometer 8 is the sum of the pressure and velocity heads, i.e. the total (or stagnation) head (h*), because the Pitot tube is held against the flow of fluid forcing it to a stop (zero velocity). The reading in manometer 1 measures just the pressure head (h) because it is connected to the Venturi tube pressure tap, which does not obstruct the flow, thus measuring the flow static pressure. Repeat step 11 for other cross sections. Repeat step 1 ‐12 for other flowrate (another two different flowrate). Record all the measurements acquired. Calculate the velocity, ViB using the Bernoulli’s equation where: ViB = 2 × g × (h 8 − h i ) 12. 13. 14. 15. 16. 17. Calculate the velocity, ViC using the continuity equation where ViC = Qav / Ai Determined the difference between two calculated velocity and the percentage differ of it. 3 Fluid Mechanics (CLD 10603) Experiment 1: Demonstration of Bernoulli’s Theorem in Fluid Flow Results Flowrate (Q) = _____________________ L/min = _____________________ m3/s Cross Section I A B C D E F Flowrate (Q) = _____________________ L/min = _____________________ m3/s Cross Section I A B C D E F h =h8 * Using Bernoulli equation Using Continuity equation Ai = =π Di2 / 4 mm2 530.93 366.44 201.06 314.16 380.13 530.93 ViC = Qav / Ai m/s Difference h =h8 * hi mm ViB = =√ [2*g*(h* ‐ hi )] m/s (ViB‐ViC)/ ViC % mm Using Bernoulli equation Using Continuity equation Ai = =π Di2 / 4 mm2 530.93 366.44 201.06 314.16 380.13 530.93 ViC = Qav / Ai m/s Difference hi mm ViB = =√ [2*g*(h* ‐ hi )] m/s (ViB‐ViC)/ ViC % mm 4 Fluid Mechanics (CLD 10603) Experiment 1: Demonstration of Bernoulli’s Theorem in Fluid Flow Flowrate (Q) = _____________________ L/min = _____________________ m3/s Cross Section I A B C D E F Where: Cross‐section A B C D E F Distance (mm) 60.0 83.0 105.0 148.6 166.4 215.0 Diameter of cross‐ section (mm) 26.0 21.6 16.0 20.0 22.0 26.0 h =h8 * Using Bernoulli equation Using Continuity equation Ai = =π Di2 / 4 mm2 530.93 366.44 201.06 314.16 380.13 530.93 ViC = Qav / Ai m/s Difference hi mm ViB = =√ [2*g*(h* ‐ hi )] m/s (ViB‐ViC)/ ViC % mm *The distance is from the beginning tip to the respective tapings. 5 Fluid Mechanics (CLD 10603) Experiment 1: Demonstration of Bernoulli’s Theorem in Fluid Flow Discussion 6 Fluid Mechanics (CLD 10603) Experiment 1: Demonstration of Bernoulli’s Theorem in Fluid Flow Tutorial 1. 2. 3. a) Discharge can be measured either in terms of mass flow rate and volumetric flow rate. Define discharge. List down three factors which cause pressure to vary along a pipe. What is meant by stagnation pressure? 7 Fluid Mechanics (CLD 10603) Experiment 1: Demonstration of Bernoulli’s Theorem in Fluid Flow b) Benzene flows through a 100 mm diameter pipe. The mean velocity of flow is 3 ms‐1. Find the volumetric flow rate and mass flow rate. Mass density of benzene is 879 kgm‐3. Conclusion 8 Fluid Mechanics (CLD 10603) Experiment 1: Demonstration of Bernoulli’s Theorem in Fluid Flow References 1. Joseph B. Franzini. Fluid Mechanics. 10th Ed. McGrawHill (2002) 2. John F. Douglas. Fluid Mechanics with Engineering Applications. 4th Ed. Prentice Hall (2001). 3. Noel de Nevers. Fluid Mechanics for Chemical Engineers. 2nd Ed. McGraw Hill (1991). 4. McCabe, W.L., Smith, J.C. and Harriot. Unit Operations of Chemical Engineering. 5th Ed., Mc Graw Hill (1993) 9 ...
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