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5_02 - Problem 5.2 Force on firemans hose We are interested...

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Problem 5.2 Force on fireman’s hose We are interested in how the shape of the nozzle and the direction of the stream affects the force required to hold a fireman’s hose. The sketch shows a test rig where a hose- nozzle combination is held firmly by a support. The bellows transmits no force to the parts mounted on the support (the hose to the left of it is supported separately). Water is supplied at a volume flow rate Q (m 3 s -1 )via a horizontal hose of radius R 1 , the flow within being in the x-direction, to a nozzle with a smaller exit radius R 2 and an outward normal vector v n 2 = v i cos + v j sin . The coordinates are indicated in the figure. The nozzle exit plane is at an elevation h relative to the horizontal supply hose, where y=0. The density of water is , and the atmospheric pressure is p a . The weight of material (water, hose, and nozzle) between the bellows and the nozzle’s exit plane is W . (a) Assuming that the flow between stations 1 and 2 is incompressible and inviscid, derive an expression for the force ( F S ) x exerted on the fire-hose by the support. Write the
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