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1 1. A suction cup is used to support a plate of weight as shown in below Figure. For the conditions shown, determine. 2. A tanker truck carries water, and the cross section of the truck s tank is shown in below Figure. Determine the magnitude of the force of the water against the vertical front end of the tank. 3. A gate having the shape shown in below Figure is located in the vertical side of an open tank containing water. The gate is mounted on a horizontal shaft. (a) When the water level is at the top of the gate, determine the magnitude of the fluid force on the rectangular portion of the gate above the shaft and the magnitude of the fluid force on the semicircular portion of the gate below the shaft. (b) For this same fluid depth determine the moment of the force acting on the semicircular portion of the gate with respect to an axis which coincides with the shaft. 4. Water backs up behind a concrete dam as shown in below Figure. Leakage under the foundation gives a pressure distribution under the dam as indicated. 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 for the following widths of the dam: 20, 30, 40, 50, and 60ft. Base your analysis on a unit length of the dam. The specific weight of the concrete is 150 lb/ ft 3. 1

2 5. A plug in the bottom of a pressurized tank is conical in shape as shown in below Figure. The air pressure is 50kPa and the liquid in the tank has a specific weight of 27kN/m 3. Determine the magnitude, direction, and line of action of the force exerted on the curved surface of the cone within the tank due to the 50kPa pressure and the liquid. 6. The thin-walled, 1-m-diameter tank of below Figure is closed at one end and has a mass of 90 kg. The open end of the tank is lowered into the water and held in the position shown by a steel block having a density of 7840kg /m 3. Assume that the air that is trapped in the tank is compressed at a constant temperature. Determine: (a) the reading on the pressure gage at the top of the tank, and (b) the volume of the steel block. 7. An inverted hollow cone is pushed into the water as is shown in below Figure. Determine the distance,, that the water rises in the cone as a function of the depth, d, of the lower edge of the cone. Plot the results for 0 when H is equal to 1.0m. Assume the temperature of the air within the cone remains constant. 2

3 8. An open-topped tank, in the form of a cube of 900mmside, has a mass of 340 kg. It contains 0.405m 3 of oil of relative density 0.85 and is accelerated uniformly up a long slope at arctan(1/3) to the horizontal. The base of the tank remains parallel to the slope, and the side faces are parallel to the direction of motion. Neglecting the thickness of the walls of the tank, estimate the net force (parallel of the slope) accelerating the tank if the oil is just on the point of spilling. 9. A hollow cylinder with closed ends is 300 mm diameter and 450 mm high, has a mass of 27 kg and has a small hole in the base. It is lowered into water so that its axis remains vertical. Calculate the depth to which it will sink, the height to which the water will rise inside it and the air pressure inside it. Disregard the effect of the thickness of the walls but assume that it is uniform and that the compression of the air is isothermal. (Atmospheric pressure = 101.3kPa.) 10. Gate AB is a three-eights circle, 3m wide into the paper, hinged at B and resting against the a smooth wall at A. Compute the reaction force at A. 11. In below system, tank width and balloon pressure are 1m and 130kP respectively. It accelerates to right at 5 m/s 2. At what angle will the balloon lean? 3

4 12. Find and specific gravity of wood when the system is at stationary state. Moreover, investigate the type of stability. 13. A 90 inverted cone contains water as shown. The volume of the water in the cone is given by /3. The original depth of the water is 10cm. A block with a volume of 200cm 3 and a specific gravity of 0.6 is floated in the water. What will be the change (in cm) in water surface height in the cone? 14. At a garage sale you purchase an ancient piece of stereo equipment known as a turntable. When the turntable is installed in your living room, you decide to place a partially filled glass of water (h=8 in., d=3 in.) on the center of the rotating surface. (a) If an angular velocity of 33 rpm raises the level of the water to the rim of the cup as shown in Figure P5.13, what was the height of the water in the cup when the fluid was at rest? (b) Determine the location and magnitude of the maximum pressure in this rotating fluid. 15. Consider the fluid container shown in below Figure. Determine the total hydrostatic force on gate A. What is the total hydrostatic force on gate B? Assume that A and B are two equilateral triangle gates with the side of 2 m. Specify the location of net force for two of them. If the right side is filled with gasoline and H =4m, calculate the total hydrostatic force on gates C and D. Assume the structure has a width of 4 m. 4

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