Question

water jet leaves a horizontal nozzle with a velocity of 12 m/s and mass flow rate of 30 kg/sstrikes the vertical wall of a cart moving at a fixed direction. After the strike, the water splatters ofin all directions on the surface of the cart wall. Determine the force which must be applied to thecart to: (a) keep it moving at a constant velocity of 4 m/s, (b) to keep it motionless at a fixed posi-tion. Assume that the density of water is 1000 kg/m3.

Answer 1

a) 160 N

b) 360 N

Step-by-step explanation:

v = 12 m/s

`\dot{m}` = 30 kg/s

ρ = 1000 kg/m^3

a) when the water jet is moving at a constant velocity, then force exerted by the jet in the moving plane,

Fx = ρA(v- 4)^2

`\dot{m}` =ρAv

30 = 1000*A*12

A=2.5*10^(-3)

Fx = ρA(v-4)

Fx = 1000*2.5*10^(-3)*(12 - 4)^2

Fx = 160 N

b) When water jet striking on a stationary vertical plate, the force in the direction of jet:

Fx = ρAv^2

Fx = 1000*2.5*10^(-3)*12^2

Fx = 360 N