Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr.

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1 Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr. Sert) Study Set 2 Reading Assignments You can find the answers of some of the following questions in your textbook. For others you need to go to other references. R1. Pascal s law states that For a fluid at rest, pressure at a point is independent of direction. Study its proof in your textbook. R2. Learn the working principle of piezoresistive type pressure transducers. Visit manufacturer web sites (such as the following) to see the available models and their working pressure ranges and prices. R3. Read about the U.S. Standard atmosphere in your textbook. R4. Read the Stability section in your textbook. 1. Provide 1 or 2 sentence definitions of the following terms Pressure Absolute & gage pressure Incompressible fluid Piezometer Pressure head Aneroid barometer Bourdon gage Pressure transducer Center of pressure Hydrometer 2. Perorm the following units conversions 1 atm = Pa 1 bar = Pa 1 psi = Pa 1 mmhg = Pa 1 mmh2o = Pa 3. Considering air to be ideal gas and assuming that it is behaving as U.S. Standard Atmosphere, determine the pressure at the peak of mount Everest (8848 m). Photo credit: 1

2 4. (Elger) for the shown setup, the ratio of container diameter to tube diameter is 10. When air in the container is at atmospheric pressure, the free surface in the tube is at position 1. When the container is pressurized, the liquid in the tube moves 0.9 m up the tube from position 1 to position 2. What is the container pressure that causes this deflection? The specific weight of the liquid is 7850 N/m (Munson) An air-filled, hemispherical shell is attached to the ocean floor at a depth of 10 m. A mercury barometer located inside the shell reads 765 mm Hg, and a mercury U tube manometer designed to give the outside water pressure indicates a differential reading of 735 mm Hg as illustrated. Based on these data what is the atmospheric pressure at the ocean surface? 6. (Fox) Water flows downward along a pipe that is inclined at 30 o below the horizontal, as shown. Pressure difference p A p B is due partly to gravity and partly to friction. Derive an expression for the pressure difference. Evaluate the pressure difference if L= 1.5 m and h = 0.15 m. 2

3 7. (Munson) Water backs up behind a concrete (specific weight 23.7 kn/m 3 ) dam. Leakage under the foundation gives a pressure distribution under the dam as shown. If the water depth, h, is too great, the dam will topple over about its toe (point A). For the dimensions given, determine the maximum water depth h for the following widths of the dam, l = 6, 9, 12, 15, and 18 m. 8. (Fox) As water rises on the left side of the shown gate, it will open automatically. At what depth above the hinge will this occur? Neglect the mass of the gate. 9. (Aksel) A sliding gate has a weight of 3500 N per unit length. a) Determine the elevation h of water at which the gate will open. b) For the elevation calculated in part (a) determine the resultant horizontal force per unit length on the gate and its line of action from the bottom. 10. (Munson) A pressurized tank contains oil and has a square, 0.6 m by 0.6 m planar plate bolted to its side. The pressure gage on the top of the tank reads 50 kpa g, and the outside of the tank is at atmospheric pressure. What is the magnitude and location of the resultant force on the attached plate? 3

4 11. (Fox) Gates in the Poe Lock at Sault Ste. Marie, Michigan, close a channel W = 34 m wide, L = 360 m long, and D = 10 m deep. The geometry of one pair of gates is shown. Each gate is hinged at the channel wall. When closed, the gate edges are forced together at the center of the channel by water pressure. Evaluate the force exerted by the water on gate A. Determine the magnitude and direction of the force components exerted by the gate on the hinge. (Neglect the weight of the gate.) You can read about these locks at (Çengel) A 4 m long quarter circular gate of radius 3 m and of negligible weight is hinged about its upper edge A. The gate controls the flow of water over the wall at B, where the gate is pressed by a spring. Determine the minimum spring force required to keep the gate closed when the water level rises to the level of point A. 13. (Çengel) A long solid cylinder of radius 0.8 m hinged at point A is used as an automatic gate. When the water level reaches 5 m, the circular gate opens by turning about the hinge at point A. Determine c) the pressure force acting on the cylinder and its line of action when the gate opens. d) the weight of the cylinder per m length of the cylinder. 14. (Munson) The concrete (specific weight 23.7 kn/m 3 ) seawall has a curved surface and restrains seawater at a depth of 7.3 m. The trace of the surface is a parabola. Determine the moment of the fluid force (per unit length) with respect to an axis through the toe at point A. 4

5 15. (Fox) A Tainter gate used to control water flow from the Uniontown Dam on the Ohio River is shown. The gate width is W = 35 m. Determine the magnitude, direction, and line of action of the force from the water acting on the gate. You can watch the simulation of an opening tainter gate here youtube.com/watch?v=uzgt09ik8iu 16. (Aksel) A float regulated gate is used to keep water level in the reservoir constant. The water level in the upper reservoir is kept at 1 m above the hinge of the gate. The length of the float arm is 0.25 m and the weight of the float is 50 N. Neglect the weight of the arm. Determine the immersed volume of the float when the gate just opens. 17. (Çengel) In a logging operation, timber floats downstream to a lumber mill. It is a dry year, and the river is running low, as low as 60 cm in some locations. What is the largest diameter log that may be transported in this fashion (leaving a minimum 5 cm clearance between the log and the bottom of the river)? For the wood, specific gravity is (Çengel) A 170 kg granite rock (ρ = 2700 kg/m 3 ) is dropped into a lake. A man dives in and tries to lift the rock. Determine how much force he needs to apply to lift it from the bottom of the lake. Do you think he can do it? 19. (Fox) The cross-sectional shape of a canoe is modeled by the curve y = ax 2, where a = 3.89 m 1, and the coordinates are in meters. Assume the width of the canoe is constant at w = 0.6 m over its entire length L = 5.25 m. Set up a general algebraic expression relating the total mass of the floating canoe and its contents to the distance d. Calculate the maximum total mass allowable without swamping the canoe. 5

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