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Horizontal Force Necessary to Hold the Plate in Place

Problem:

A hose and nozzle discharge a horizontal water jet against a nearby vertical plate, as shown in figure below. The flow rate of water is 0.035 m3/s, and the diameter of the nozzle tip is 25 mm. Calculate the horizontal force necessary to hold the plate in place.

Solution:

F = ρQ (v2 – v1)  = R

Where,

F =  the net external force acting on the fluid

   =  this is also the horizontal force necessary to hold the plate in place, R.

ρ = 1,000 kg/m3, the density of water at 4 °C (39 °F)

As shown in the figure, force F acts toward the left, assume this direction is taken to be positive.

First, solve for velocities of water:

V1 = Q/A1  

    =  0.035 / [π(0.025)2/4]

    =  71.30 m/s

V= 0

We can now calculate the horizontal force necessary to hold the plate in place, R.

R = 1000 (0.035)[0 – (-71.30)]

    =  2,495.5 N (leftward).

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