7.37.5A canal gate is shown in the drawing. The gate is designed to maintain a constant depth of waterin the canal by rotating open automatically under the action of the hydrostatic forces on it when thedepth 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 lbf, applied at the lifting eye as shown, torotate the gate open. At what depth of water will the gate start to open automatically?(Ans. 11.5 ft.)7.6The 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 andindicate 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 lbf, 2260 lbfupward, 0)
7.47.7A 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 wouldyou recommend for the top, middle and bottom rings if the tank is fabricated from rings of steel 2m high. Use some some engineering judgment in selecting the thicknesses, in addition to lookingat the strict minimum allowable thicknesses obtained from the calculations.(Ans. 2-3 mm, 5 mm, 10 mm (minimum 8.82 mm))7.8A balloon has a volume of 4000 m3. If it is at an altitude of 2000 m, what weight can it lift if it isfilled 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 40oC?Note that since the balloon material is very flexible, the gas inside it must be at essentially thesame pressure as the surrounding air. The following values of the gas constant may be used: forH2, 4125 J/kgK; for He, 2077 J/kgK; for air, 287 J/kgK.(Ans. 36.7 kN, 34 kN, 4.8 kN)7.9Ignoring the friction between the cylindrical log and the wall, findthe density of the log. What is the force between the log andthe wall, per unit length?(Ans. 1068 kg/m3, 1226 N/m)7.10A filled oil barge is shown in cross-section. The air space above the oil is at atmosphericprressure. How deep will the barge float when it is empty? Assume that the top deck is used tohold the sides of the barge together or apart at the top. Assume also that the lower corners of thehull cannot transmit a moment (ie. they effectively act as hinges). What is the force in the topdeck per unit length of the barge (that is, in the direction normal to the page) for the conditionsshown in the diagram?(Ans. 2.09 m, 22 kN/m compression)
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