2.25 Problem Sets - Section 5
Problem 5.2
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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. |
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(a)
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
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(b)
Demonstrate that 
always, that is, in order to hold
the system in place, one must always push on it toward the left,
regardless of volume flow rate or angle.
(c) For the simple case Q=0 (no flow, but system filled with static liquid to height h), our answer predicts that the external force required to hold it in place is
Consider a system mounted on a support with frictionless wheels. The result (1) suggests that if such a system is held in place and filled with water, and the external holding force removed, it will tend to move to the right. Does this make sense? Explain. |
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(d) Now consider another special case:
a straight horizontal pipe, that is,
regardless of the shape of the system between 1 and 2. Explain on physical grounds why this makes sense. |
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and 
