Question

A tank 1.5 m stands on a trolly and is full of water. It has an orifice of diameter 0.1 m at 0.3 m from the bottom of the tank. If the orifice is suddenly opened and coefficient of velocity is 0.60, then the propelling force on the trolley will be
1. 69.37 N
2. 66.51 N
3. 63.79 N
4. 65.39 N

Answer 1

Correct Answer - Option 2 : 66.51 N

Concept:

When the orifice is suddenly opened, the water will come out and a propelling force will act on the tank in opposite direction.

The magnitude of propelling force is, F = ρAV² 

where, A = area of orifice, V = velocity of water

Calculation:

Given:

H = 1.5 - 0.3 = 1.2 m, C_v = 0.6, d = 0.1 m

Velocity, \(V = {C_v}\sqrt {2gH} \)

\(V = 0.60\sqrt {2 \times 9.81 \times 1.2} = 2.91~{\rm{m}}{\rm{s\;}}\;\)

Force = ρAV²

\(F = 1000 \times \frac{\pi }{4} \times {0.1^2} \times {2.91^2} = 66.5 N\)