Water enters a cylindrical tank at point 1 through a 3-inch-diameter pipe at an
ID: 2993033 • Letter: W
Question
Water enters a cylindrical tank at point 1 through a 3-inch-diameter pipe at an average
velocity of V1 and leaves the tank through pipes 2 and 3. Pipe 2 has a volumetric flow
rate of Q2.Let the water velocity at point 3, V3, be 10 ft/s and connect pipe 4 to the
top to let the air out of the tank.Consider the tank for a non-steady flow case.If the tank diameter, D, is 12 inches, V1=20 ft/s, Q2=78gpm, d3=2.5 in and d4=2 in, d1=3 in
a) Calculate the rate of change of h of the free surface (dh/dt),
b) Calculate the average air velocity through the vent pipe.
Explanation / Answer
a) 1 gallon = 0.1337 ft^3
78 gpm = 78*0.1337/60 ft^3/s = 0.1738 ft^3/s
Rate of accumulation of water in tank = Rate of water entering the tank - Rate of water leaving the tank
(/4*D^2)*(dh/dt) = (/4*d1^2)*V1 - Q2 - (/4*d3^2)*V3
(/4*(12/12)^2)*(dh/dt) = (/4*(3/12)^2)*20 - 0.1738 - (/4*(2.5/12)^2)*10
dh/dt = 0.5945 ft/s
b) Rate of exit of air = Rate of rise of water in tank
(/4*d4^2)*V4 = (/4*(12/12)^2)*(dh/dt)
(/4*(2/12)^2)*V4 = (/4*(12/12)^2)*0.5945
V4 = 21.4 ft/s
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