A horizontal water jet impinges against a vertical flat plate at 30 ft/s and splashes off the sides in the verti- cal plane. If a horizontal force of 500 lbf is required to hold the plate against the water stream, determine the volume flow rate of the water.

8.6 ft³/s

Explanation:

The force due to the water jet F = mv where m = mass flow rate = ρQ where ρ = density of water = 62.4 lbm/ft³ and Q = volume flow rate. v = velocity of water jet = 30 ft/s

So, F = mv

F = ρQv

making Q subject of the formula, we have

Q = F/ρv

Since F = force due to water jet = force needed to hold the plate against the water stream = 500 lbf = 500 × 1 lbf = 500 × 32.2 lbmft/s² = 16100 lbmft/s²

Since

Q = F/ρv

Substituting the values of the variables into the equation for Q, we have

Q = F/ρv

Q = 16100 lbmft/s²/(62.4 lbm/ft³ × 30 ft/s)

Q = 16100 lbmft/s²/1872 lbm/ft²s

Q = 8.6 ft³/s

So, the volume flow rate is 8.6 ft³/s.

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