While taking a shower, you notice that the shower head is made up of 42 small ro

Question

While taking a shower, you notice that the shower head is made up of 42 small round openings, each with a radius of 2.00 mm. You also determine that it takes 5.00 s for the shower to completely fill a 1.00-liter container you hold in the water stream. The water for the shower is pumped by pump that is 5 10 m below the eve of the shower head. The pump maintains an absolute pressure of 1.50 atm. Use g 10 m/s2 and assume that 1 atmosphere 1.0 × 105 Pa. (a) At what speed does the water emerge from the shower head? m/s (b) What is the speed of the water in the pipe connected to the pump? m/s (c) What is the cross-sectional area of the pipe connected to the pump? m2

Explanation / Answer

Flow rate

Q=(1*10-3)/5 =2*10-4 m/s

speed of water emerge from shower head

V=Q/NA =(2*10-4)/42*(pi*0.0022)

V=0.3789 m/s

b)

From Bernoulli's equation

P1+(1/2)pV12+pgh1=P2+(1/2)pV22+pgh2

(P2-P1)+pg(h2-h1)+(1/2)pV22 =(1/2)pV12

(105-1.5*105)+1000*10*5.1+(1/2)*1000*0.37892=(1/2)*1000*V12

V1=1.464 m/s

c)

From continuity equation

A1V1=A2V2

A1*1.466=0.3789*(42*pi*0.0022)

A1=1.364*10-4 m2

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