|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 3s-1)via a horizontal hose of radius R1, the flow within being in the x-direction, to a nozzle with a smaller exit radius R2 and an outward normal vector . 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 r, and the atmospheric pressure is pa. The weight of material (water, hose, and nozzle) between the bellows and the nozzle's exit plane is W.|
Assuming that the flow between stations 1 and 2 is incompressible
and inviscid, derive an expression for the force
exerted on the fire-hose by the
support. Write the answer in terms the given quantities
(d) Now consider another special case: a straight horizontal pipe, that is, and =0 . In this case part (a) predicts
regardless of the shape of the system between 1 and 2. Explain on physical grounds why this makes sense.