A cart is moving with a constant velocity of Vc A nozzle iss

A cart is moving with a constant velocity of V_c. A nozzle issues a jet of water at a velocity of V_j. Find the resistive force at the wheels, given the specific weight of water, gamma_w, and the area of the jet, A_j. State the applicable assumptions. Sketch the needed diagrams and write the corresponding, simplified equation in terms of what is known.

Solution

Assume that the wind resistance on the cart is negligible.

Use conservation of momentum for the control volume / surface shown below moving to the right with a speed of V_c

The cross sectional area of the nozzle, A_Nozzle = Pi*R²/4

Specific Weight of water = = 1000 kg/m3

Water flow through nozzle in kg/s = m = * A_Nozzle * V_j

The jet is exposed to atmospheric pressure. There is no accumulation in the tube. Thus, the speed of the fluid relative to the control volume exiting the same as that entering. V_j,in = V_{j,out =} V_j

Applying momentum principle along X direction

F_{x =} m (-V_j,out - V_j,in)

F_X=2mV_J acting to the left