The pressure from water mains located at street level may be insufficient for de

Question

The pressure from water mains located at street level may be insufficient for delivering water to the upper floors of tall building. In such a case, water may be pumped up to a tank that feed water to the building by gravity. For an open storage tank atop a 300 ft tall building, determine the pressure, in Ibf/in, at the bottom of the tank when filled to a depth of 20ft. The density of water is 62.2Ib/ft g = 32.0ft/s2, and the local atmosphere pressure is 14.7Ibf/in2. Figure P1.44 show a tank used to collect rainwater having a diameter of 4m.as shown in the figure, the depth of the tank varies linearly from 3.5m at its center to 3m along the perimeter. The local atmosphere pressure is 1 bar, the acceleration of gravity is 9.8m/s2, and the density of the water is 987.1kg/m3. When the tank is filled with water, determine. The pressure in kPa, at the bottom center of the tank .the total force in kN, acting on the bottom of the tank. Fig P1.44 If the water pressure at the base of the water tower shown the pressure of the air

Explanation / Answer

(a) The pressure is

P = patm+gh = 100000Pa + 987.1*9.8*3.5 = 133857.53 Pa = 133.86 kPa

(b) The total force acting on the botom of the tank includes the force from the water and the force from air. Since there is air all over the tank, the net force on the bottom from air is zero. The force from the water equals the weight of water in tank,

F = gV = g[R2h+R2(H-h)/3] = gR2[h+(H-h)/3]

   =987.1*9.8**22[3+(3.5-3)/3] = 384945.7N = 384.9 kN

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