A vertical cylindrical tank with a diameter of 120 m and dep

A vertical cylindrical tank with a diameter of 12.0 m and depth of 4 0 m is filled to the brim with water at 30degree C (density = 995 7 kg/m^3). If the water is instantly heated to 70degreeC (density = 977.8 kg/m^3), how much volume of water will spill over the edge of the tank?

Solution

sol:

Multiple each of the unit weights U1 and U2 by the volume to get the amount of water in the tank at each temperature.

radius of the cylinder = d/2 = 6m

height of the cylinder = 4m

Volume of the cylindrical tank (V) = pi* r²* h

V = (22/7)*(6²)*(4)

V = 452.57 m³

W1 = V*U1 = 452.57* 995.7 = 450625.3714 kg
W2 = V*U2 = 452.57*977.8 = 442522.946 kg

Now subtract these to get the amount of water that spilled over.

Spilled water = W1 - W2

= 450625.3714 -  442522.946

= 8102.42 kg