Ans 127 kn 73 75 a canal gate is shown in the drawing

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(Ans. 127 kN)
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7.3 7.5 A canal gate is shown in the drawing. The gate is designed to maintain a constant depth of water in the canal by rotating open automatically under the action of the hydrostatic forces on it when the depth exceeds some value. The canal is 30 ft. wide and the gate spans the full width of the canal. When the canal is empty it requires a force of 30,000 lb f , applied at the lifting eye as shown, to rotate the gate open. At what depth of water will the gate start to open automatically? (Ans. 11.5 ft.) 7.6 The hydraulic gate shown in the drawing is known as a Tainter gate. (a) Find the horizontal component of the hydraulic force acting on 1 ft. width of the gate. (b) Find the vertical component of the hydraulic force acting on 1 ft. width of the gate and indicate its direction. (c) Find the moment about the hinge H due to the hydraulic forces for 1 ft. width of the gate. (d) Explain from first principles why the moment in (c) had to be zero. (Ans. 12,480 lb f , 2260 lb f upward, 0)
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7.4 7.7 A cylindrical steel silo (storage tank) 20 m high and 6 m in diameter holds silage with S.G. = 1.5. If the steel of the tank has an allowable working stress level of 100 Mpa, what thickness would you recommend for the top, middle and bottom rings if the tank is fabricated from rings of steel 2 m high. Use some some engineering judgment in selecting the thicknesses, in addition to looking at the strict minimum allowable thicknesses obtained from the calculations. (Ans. 2-3 mm, 5 mm, 10 mm (minimum 8.82 mm)) 7.8 A balloon has a volume of 4000 m 3 . If it is at an altitude of 2000 m, what weight can it lift if it is filled with: (i) hydrogen at the same temperature as the surrounding air? (ii) helium at the same temperature as the surrounding air? (iii) hot air, at 40 o C? Note that since the balloon material is very flexible, the gas inside it must be at essentially the same pressure as the surrounding air. The following values of the gas constant may be used: for H 2 , 4125 J/kgK; for He, 2077 J/kgK; for air, 287 J/kgK. (Ans. 36.7 kN, 34 kN, 4.8 kN) 7.9 Ignoring the friction between the cylindrical log and the wall, find the density of the log. What is the force between the log and the wall, per unit length? (Ans. 1068 kg/m 3 , 1226 N/m) 7.10 A filled oil barge is shown in cross-section. The air space above the oil is at atmospheric prressure. How deep will the barge float when it is empty? Assume that the top deck is used to hold the sides of the barge together or apart at the top. Assume also that the lower corners of the hull cannot transmit a moment (ie. they effectively act as hinges). What is the force in the top deck per unit length of the barge (that is, in the direction normal to the page) for the conditions shown in the diagram? (Ans. 2.09 m, 22 kN/m compression)
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