NEWTON”S SECOND LAW:Bernoulli
1. (a) Explain how the Bernoulli Energy Equation can be obtained from considerations of the forces acting on a streamtube of fluid. Ensure that your answer explains the significance of the terms in the Equation and its limitations. What principle could be used to create a differential head flowmeter based on this Equation ?
1. (b) Water flows through a pipe of inside diameter 200 mm at a rate of 100 m^{3}h^{1}. The flow abruptly enters a section which reduces the pipe diameter to 150 mm, for which the head loss is equivalent to 0.2 velocity heads based on the smaller pipe. If the gauge pressure is 80 kNm^{2} upstream of the reducing section, find the force needed to hold the section in position.
2. (a) You are required to create a differential head flowmeter based on a convergence in a section of pipe. Starting with an expression for the forces acting on an ideal fluid, show how you would estimate the volumetric flowrate based on measurements of differential pressure. How would you modify your answer to account for the fact that a real fluid will have viscosity and how would you ensure that energy degradation is minimised?
2.(b) A manometer uses a manometric fluid of density 1075 kg/m^{3} to measure the pressure drop across an orifice plate with a throat diameter of 75 mm. The orifice plate is placed inside a vertical pipe with a diameter of 225 mm and oil with a density of 860 kg/m^{3} is flowing upwards inside the pipe. The deflection of the manometer fluid is 0.5 m and the discharge coefficient of the orifice is 0.659. What is the flowrate of the oil?
3. (a) Beginning with Newton’s Second Law calculate the force required to stabilise a 90o horizontal pipe bend against movement due to hydrodynamic reaction forces. State any assumptions you would make and explain how you would calculate the direction of the force.
3. (b) A jet of water of 22.5 cm diameter impinges normally on a flat plate moving at 0.6 m s^{1} in the same direction as the jet. If the discharge is 0.14 m^{3} s^{1} find the force and the work done per second on the plate.
4. (a) Explain how you would create a differential head flowmeter based on convergence at an orifice plate placed in a section of pipe. Starting with an expression for the forces acting on an ideal fluid, show how you would estimate the volumetric flowrate based on measurements of differential pressure.
4. (b) A horizontal venturi meter with a discharge coefficient of 0.96 is to be used to measure the flowrate of water up to 0.025m^{3}s^{1} in a pipe of internal diameter 100 mm. The meter is connected to a differential manometer containing mercury (Specific Gravity,SG = 13.6). If the maximum allowable difference in mercury levels is 80 cm, what is the diameter of the throat ?
5. (a) Using Newton’s Second Law as a starting point, explain how you would create a flowmeter based on a converging section of pipe for a real (nonideal) fluid. Your answer must explain how the degradation of energy is minimised and how you would estimate the volumetric flowrate based on measurements of differential pressure.
5. (b) Obtain an expression for the force exerted by a jet of liquid which leaves a nozzle and strikes a stationary flat plate normally with a velocity v. How would this expression be modified if the plate were to be moving in the same direction as the jet with a velocity u ? Explain any assumptions which you make.
5. (c) Two pressure gauges are located at tapping points 50 cm apart on a vertical Venturi tube which has an inlet diameter of 150 mm, a throat diameter of 70 mm and a discharge coefficient of 0.98. If a liquid of density 1,000 kgm^{3} flows upward through the Venturi tube at a rate of 0.075 m^{3}s^{1} what is the difference in reading of the two pressure gauges ?
5. (d) Droplets of oil (density = 960 kg/m^{3}) are dispersed as an emulsion in a solution with a density and shear viscosity the same as water. Calculate how long an 80 µm spherical droplet will take to rise from the bottom of a tank to the surface 1.4 m above in still liquid. Neglect acceleration effects and state any assumptions you make.
