Question

A stream of water flowing horizontally with the speed of 15 m/s gushes out of a tube of cross-sectional area \( 10^{-2} \, \text{m}^2 \) and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water? Assuming it does not rebound.

• A. 2250 N
• B. 2000 N
• C. 1500 N
• D. 1000 N

Hint:

The force exerted by a fluid on a surface is equal to the rate of change of momentum of the fluid as it strikes the surface.

Answer 1

The Correct Option is A

The force exerted on the wall is equal to the rate of change of momentum of the water hitting the wall.
The momentum flux is given by: \[ F = \dot{m} v \] where \( \dot{m} \) is the mass flow rate and \( v \) is the velocity of the water.
The mass flow rate is: \[ \dot{m} = \rho A v \] where \( \rho = 1000 \, \text{kg/m}^3 \) is the density of water, \( A = 10^{-2} \, \text{m}^2 \) is the cross-sectional area of the tube, and \( v = 15 \, \text{m/s} \) is the velocity. Substituting the values: \[ \dot{m} = 1000 \times 10^{-2} \times 15 = 150 \, \text{kg/s} \] Thus, the force is: \[ F = 150 \times 15 = 2250 \, \text{N} \] Therefore, the correct answer is (a).