HW_Week2 - Free surface VIGUFIE P258 zero? Explain. . 2.60...

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Unformatted text preview: Free surface VIGUFIE P258 zero? Explain. . 2.60 A pump supplies water under pressure to a large tank as shown in Fig. P260. The circular-plate valve fitted in the short held shut against the water pressure by a latch at B. Show that t : force on the latch is independent of the supply pressure, p, and the height of the tank, it. ' Supply Pressure ,0 , ‘ h FIGURE P2.60 {2.6 homogeneous, 4«ft~wide, 8-ft—long rectangular gate weigh- “ittg‘ 860 lb is held in place by a horizontal flexible cable as shown discharge pipe on the tank pivots about its diameter AHA and ' ' Problems 85 . A6“. 8ft EFIGURE P2.6‘l in Fig. P161. Water acts against the gate which is hinged at point A. Friction in the hinge is negligible. Determine the tension in the cable. T2132 Sometimes it is difficult to open an exterior door of a building because the air distribution system maintains a pressure difference between the inside and outside of the building. Estimate how big this pressure difference can be if it is “not too difficult” for an average person to open the door. 2.63 An area in the form of an isosceles triangle with a base width of 6 ft and an altitude of 8 ft lies in the plane forming one wall of a tank which contains a liquid having a specific weight of 79.81b/ft3. The side slopes upward, making an angle of 60° with the horizontal. The base of the triangle is horizontal and the vertex is above the base. Determine the resultant force the fluid exerts on the area when the fluid depth is 20 ft above the base of the triangu- lar area. Show, with the aid of a sketch, where the center of pres— sure is located. 2.64 Solve Problem 2.63 if the isosceles triangle is replaced with a right triangle having the same base width and altitude as the isqseles triangle. : vertical plane area having the shape shown in Fig. P265 is . ersed in an oil bath (specific weight : 8.75 kN/m3). Deter— mine the magnitude of the resultant force acting on one side of the area as a result of the oil. . healers—i a FIGURE P235 2.66 A 3~m—wide, 8-m-high rectangular gate is located at the end of a rectangular passage that is connected to a large open tank filled with water as shown in Fig. P2.66. The gate is hinged at its bottom and held closed by'h horizontal force, FH, located at the center of the gate. The maximum value for F” is 3500 RN. (a) Determine the maximum water depth, 1:, above the center of the gate that can exist without the gate opening. (b) Is the answer the same if the gate is hinged at the top? Explain your answer. ali'shafibe located? (b) What is the magnitude gg : when it opens? widei‘right-ang‘le gate with negligible mass is free frictiOnleSS hinge at point 0, as shown in Fig. nzontal ponies 0f the gate covrars a I—ft—diameter "hieontains air at atmospheric pressure. Determine Fi‘deptlt, h, at which the gate will pivot to allow at: I G u n E P2.73 2114 _ An open rectangular tank is 2 m wide and 4 m long. The tank contains water to a depth of 2 m and oil (86 : 0.8) on top of the water to a depth of l rn. Determine the magnitude and location of the resultant fluid force acting on one end of the tank. $2.75 An open rectangular settling tank contains a liquid suspen- sion that at a given time has a specific weight that varies approximately with depth according to the following data: “Y 0 ' 10.0 0.4 10.1 0.8 10.2 1.2 10.6 l.6 ‘ 1 1.3 2.0 12.3 2.4 12.7 2.8 12.9 3.2 13.0 The depth h = 0 corresponds to the free surface. Determine, by means of numerical integration, the magnitude and location of the resultant force that the liquid suspension exerts on a vertical wall of the tank that is 6 m wide. The depth of fluid in the tank is 3.6 m. 2.76 The closed vessel of Fig. P236 contains water with an air pressure of 10 psi at the water surface. One side of the vessel 6-in.-diameter gate FIGURE P2.76 Problems 87 contains a spout that is closed by a 6-in.—diameter circular gate that is hinged along one side as illustrated. The horizontal axis of the hinge is located 10 it below the water surface. Determine the minimum torque that must be applied at the hinge to hold the gte shut. Neglect the weight of the gate and friction at the hinge. - A 4-ft—tall, 8-in.-wide concrete (150 1b/ft3) retaining wall is uiit as shown in Fig. P237. During a heavy rain, water fills the space between the wall and the earth behind it to a depth I2. Deter- mine the maximum depth of water possible without the wall tipping over. The wail simply rests on the ground without being anchored to it. FIGURE P2.77 *2.78 Water backs up behind a concrete darn as shown in Fig. P238. Leakage under the foundation gives a pressure distribu» tion 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: t? = 20, 30, 40, 50, and 60 ft. Base your analysis on a unit length of the dam. The specific weight of the concrete is 150 lb/ft3. FIGURE P278 2.79 (See Fluids in the News article titled “The Three Gorges Dam,” Section 2.8.) (a) Determine the horizontal hydrostatic force on the 2309um-long Three Gorges Dam when the average depth of the water against it is 175 m. (b) If all of the 6.4 billion people on Earth were to push horizontally against the Three Gorges Dam, could they generate enough force to hold it in place? Support your answer with appropriate calculatiops. Section 2.10 Hydrostatic Force on a Curved Surface 2.80 Obtain a photograph/image of a situation in which the hydrostatic force on a curved surface is important. Print this photo and write a brief paragraph that describes the situation involved. Chapter 2 a Fluid Statics W. (c) EFIGURE P2.95 river barge, whose cross section is approximately rectan- . ;. ar, carries a load of grain. The barge is 28 ft wide and ubmergence) 90 ft long. When unloaded its draft (depth of s is 5 ft, and with the load of grain the draft is 7 ft. Determine: (a) the unloaded Weight of the barge, and (b) the weight of the grain. specific weight 73 as cylinder of specific Weight 72 and volu uid (see Fig. P2.99b), the liquid level rises by Ah : (72/ 3'1) V/A- EFIGURE P239 2.100 When the Tueurui Brazil, the lake that was crea hardwood trees. It was found that even a the trees were perfectly preserved and und started. During the logging process a tree 1 and anchored with ropes to prevent like a missile when cut. Assume proximated as'a truncate diameter of 2 ft, and a heig vertical force that the ropes mus merged tree is cut. The specific gr mater 0.6. T1101 Estimate the minimum water do carrying two people and their camping gear. List all as and show all calculations. an amount Dam was constructed in northern ted covered a large forest of valuable fter 15 years underwater erwater logging was ‘5 selected, trimmed, it from shooting to the surface that a typical large tree can be ap- d cone with a base diameter of 8 ft, a top hr of 100 ft. Determine the resultant t resist when the completely sub- avity of the wood is approxi- pth needed to float a canoe sumptions rtially filled with air floats in a plas- e as shown in Video V2.7 and Fig. the tube has been adjusted so that it 1y fastened. A slight squeezing of 2.102 An inverted test tube pa tic water-filled soft drink bottl P2102. The amount of air in just floats. The bottle cap is secure the plastic bottle will cause the test bottle. Explain this phenomenon. tube to sink to the bottom of the Test tube Water Plastic bottle piece of a solid material weighs 8.05 1h 2.103 An irregularly shaped leter submerged in water. Determine in air and 5.26 lb when comp the density of the material. 2.104 A l-m—diameter cylindrical mass, M, is connected to a 2- m-wide rectangular gate as shown in Fig. P1104. The gate is to open when the water level, it, drops below 2.5 m. Determine the required value for M. Neglect friction at the gate hinge and the pulley. a . EFIGUHE P2.104 d Video V2.8) have 2.105 When a hydrometer (see Fig. P1105 an ater, the stem pro- ing a stem diameter of 0.30 in. is placed in w trades 3.15 in. above the water surface. If the water is replaced with a liquid having a specific gravity of 1.10, how much of the stem would protrude above the liquid surface? The hydrometer weighs 0.042 1b. Fluid sudace Hydrometer ...
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This note was uploaded on 09/22/2009 for the course ME 3340 taught by Professor Smith during the Fall '09 term at Georgia Institute of Technology.

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HW_Week2 - Free surface VIGUFIE P258 zero? Explain. . 2.60...

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