Question

Consider a tank full of water, cylindrical in shape, 3.0 meters high and 1.0 meter in diameter. Suppose there is a hole of area 1.0 cm2 at the bottom of the tank. Calculate (a) the speed with which water is discharged, then (b) the volume of water discharged each second.

Answer 1

a) Let the speed of the water discharged is v.

The height of the tank is h=3.0 m.

The area of the hole is a=1.0 cm²=0.0001 m².

From the Bernoulli's theorem, we can say the speed is

  

The speed of the water discharged is 7.668115805 m/s or 7.67 m/s approximately.

b) Let the volume of water discharged each second is V.

We know the volume of water discharged per second is

  

  

The volume of water discharged each second is 7.6710^-4 m³ approximately.