# BERNOULLIS EQUATION AND CONSERVATION OF MASS, ENERGY AND MOMENTUM

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MECH 1215 Thermofluids 1 MECH1215: Thermofluids 1 Laboratory 3 Page 1 of 7 LABORATORY FOUR BERNOULLI’S EQUATION AND CONSERVATION OF MASS, ENERGY AND MOMENTUM 1. OBJECTIVE On completion of the laboratory the students will have familiarised themselves with the application of Bernoullis equation and have determined the accuracy of the momentum equations by investigating the fluid mechanics of a jet of water impacting on a target. 2. STRUCTURE Students will work in groups of three or four, depending on laboratory group size, and each group will carry out 3 experiments: 1. Water flow through a tapered venturi nozzle in a small diameter pipe 2. Force on a target from an impinging jet of water 3. DELIVERABLES Each student is required to submit one document covering the all three experiments which should be concise and accurate. Write two individual lab reports which are bound together into one document. Important note: Each report should have: Aim Explain what your hope to achieve from the lab practical Apparatus A list of the apparatus used and a diagram of the experimental system Results in a concise form for each task, with the important data clearly highlighted, example calculations provided and all questions within that task answered Conclusions concise list of the conclusions arising from each experiment. When reporting data, please ensure you use the correct number of decimal places. The report should be placed in the Student Coursework Submission Postbox outside Lecture Theatre A as per the instructions on the VLE. Standard University penalties will be applied to work handed in after the deadline without mitigating circumstances. MECH 1215 Thermofluids 1 MECH1215: Thermofluids 1 Laboratory 3 Page 2 of 7 EXPERIMENT ONE: WATER FLOW THROUGH A TAPERED VENTURI NOZZLE IN A SMALL DIAMETER PIPE You will be provided with a tapered venture nozzle which has manometers attached at various locations along the length of the pipe. Nb. Information on mass flow rate, conservation of mass, Bernoulli’s equation, pitot tubes and pitot-static tubes is attached as an Appendix. P1 (static) P2 (static) P3 (static) P4 (static) P5 (static) P6 (static) P7 (static) Pitot tube MECH 1215 Thermofluids 1 MECH1215: Thermofluids 1 Laboratory 3 Page 3 of 7 Task 1: Establish a flow rate in the venturi meter where water is partially present in at least the first 3 columns of the manometers. Do not worry if water is not present in every column (4 and 5 may be difficult to fill without overflowing other manometers). Task 2: Select two manometer columns from which you can take measurements and state the diameters of the pipe at the points where these manometer are measuring static pressure. Record the heights of the fluid in each manometer. Task 3: By application of Bernoulli’s equation and the conservation of mass at these two positions, determine the fluid velocity at both points in the system. Report the computed values as well as the measurements and calculations undertaken. Task 4: Based on the velocity measurements taken, calculate the mass flow rate, m , of the flow at both points in the system. Report the computed values and the calculations undertaken. Task 5: Determine the mass flow rate, m , by measurement (1000 litres = 1 m3 ). Report the value determined and the measurements and calculations undertaken. How do the two values of mass flow rate compare with one another? Can you explain any discrepancies? Task 6: Move the pitot tube from upstream of the taper to a position downstream. What do you observe in the manometer connected to the pitot tube? What is the pitot tube measuring? MECH 1215 Thermofluids 1 MECH1215: Thermofluids 1 Laboratory 3 Page 4 of 7 EXPERIMENT TWO FORCE ON A TARGET FROM AN IMPINGING JET OF WATER An example of the application of the momentum equation arises with the impact of jets and their subsequent deflection on targets of various shapes. In the experiment in the laboratory a vertical water jet is aimed at a target. The vertical force exerted on the target by the water is measured by placing weights on a pan until the force of the jet is matched by the downward weight. By Newton’s second law, the force exerted on the fluid = rate of change of momentum in the x-direction: 1212 fluidonForce vvVumum , and by Newton’s third law, the force exerted on the plate is equal and opposite to this, i.e. plateonForce uuVumum 2121 MECH 1215 Thermofluids 1 MECH1215: Thermofluids 1 Laboratory 3 Page 5 of 7 The velocity of the jet hitting the plate is given by u1 , after striking the plate the velocity of the fluid leaving the system (neglecting any frictional losses) in the xdirection is given by u1cos, where is the angle that the water is turned through. Consequently the force on the plate is given by: )cos1(cosplateonForce uVuuVumum 11121 Recognising that 1 3 uAV velocityareanozzle/s][mrateflow A general expression for the force can be written: )cos1(plateonForce 2 A V In this experiment the force on the plate is equal to the weight on the platform. For a particular target, by plotting the force on the plate on the y-axis and the quantity A Q 2 on the x axis, the gradient should be equal to )cos1( (remember the equation for a straight line on a graph is y=mx + c where m is the gradient). Water turned through 90 Water turned through 180 MECH 1215 Thermofluids 1 MECH1215: Thermofluids 1 Laboratory 3 Page 6 of 7 Results table nozzle diameter = nozzle area A = g = = Target angle = mass on pan M (kg) volume (m3 ) time (s) flow rate Q (m3 /s) Q 2 0.10 0.20 0.30 0.40 0.50 0.60 Task 1: The aim of this task is to determine the accuracy of the momentum equations used to predict the force of a jet of water impacting on a target. For a particular target, plot the force on the plate on the y-axis and the quantity A V 2 on the x axis. Measure the gradient of this line and compare it to the theoretical value for your particular target. Task 2: Repeat the experiment for a different target shape and discuss your observations when comparing the theoretical value with that which was experimentally obtained. Task 3: What angle gives the maximum force exerted on the plate? Why? MECH 1215 Thermofluids 1 MECH1215: Thermofluids 1 Laboratory 3 Page 7 of 7 APPENDIX: THEORY 1 flow 2 Mass Flow Rate m uA Conservation of Mass m m 1 2 u A u A 1 1 2 2 Bernoulli’s Equation (with no significant height difference between positions 1 and 2) p u p u 1 1 2 2 2 2 1 2 1 2 Pitot Tube Measures total pressure = p u 1 2 2 Pitot-Static Tube Measures the difference between total and static pressure = 1 2 2 u

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