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A hose goes down a 1.07 m hill as shown at right. The speed of the...

A hose goes down a 1.07 m hill as shown at right. The speed of the water entering the hose is 3.95 m/s and the speed of the water leaving the nozzle is 7.63 m/s.

If the water is at atmospheric pressure when it leaves the nozzle, what is the pressure at the faucet? [Give this answer to 4 sig figs.]

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Answer #1

using the Bernoulli's equation we have

P1 + 0.5pv1^2 + pgh1 = P2 + 0.5pv2^2 + pgh2

P1 + 0.5*1000*3.95^2 + 1000*9.8*-1.07 = 101325 + 0.5*1000*7.63^2 + 1000*9.8*0

P1 = 140347 N/m^2

so P1 =140347 / 1.01325 *10^5 = 1.385 atm

so the pressure at the faucet is 1.385 atm

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