While taking a shower, you notice that the shower head is made up of 34 small ro

Question

While taking a shower, you notice that the shower head is made up of 34 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 a pump that is 5.30 m below the level of the shower head. The pump maintains an absolute pressure of 1.50 atm. Use g 10 m/s, and assume that 1 atmosphere is 1.0 x 105 Pa. (a) At what speed does the water emerge from the shower head? 0.468 m/s (b) What is the speed of the water in the pipe connected to the pump? 3.45 x m/s (c) What is the cross-sectional area of the pipe connected to the pump? 00005796x m2 Additional Materials eBook Submit Answer Save Progress

Explanation / Answer

v1 = 0.468 m/s

Applying bernoulli's equation,

P1 + rho g h1 + rho v^2 /2 = constant

(1.5 x 10^5) + (1000 x 10 x - 5.30) + (1000 v^2 /2 ) = (1 x 10^5) + (1000 x 10 x 0) + (1000 x 0.468^2 /2 )

v = 2.49 m/s ........Ans(b)

(C) Q = A v

Q = 1 x 10^-3 m^3 / 5 s = 2 x 10^-4 m^3 / s

A = Q / v = 8.03 x 10^-5 m^2

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