A fountain produces a vertical jet of water, which rises to a height of 30 m bef

ID: 1857427 • Letter: A

Question

A fountain produces a vertical jet of water, which rises to a height of 30 m before

falling back into a pond. If the jet of water is produced by a nozzle whose velocity

coefficient is 0.95, find the pressure with which the water is fed into the nozzle. You

may assume that the jet of water is not affected by friction once it has left the nozzle

and that there is a negligible change in the potential energy of water as it passes through

the nozzle.

(Hint: Tackle the problem by splitting it into two parts: (i) from the entry to the nozzle

to a point just after the water has left the nozzle; (ii) from just after the water has left the

nozzle to the top of the water jet. Analyse part (ii) first noting that the flow is

frictionless and that the pressure is atmospheric everywhere. Prove that the velocity just

after the nozzle is 24.26 m/sec and then analyse the flow through the nozzle itself).

(ans.: 3.26 bar)

velocity just after nozzle=sqrt(2gh)

=sqrt(2*9.8*30)=24.26 m/s

velocity just before coming outt= 24.26/0.95=25.53 m/s

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