While taking a shower, you notice that the shower head is made up of 50 small ro

Question

While taking a shower, you notice that the shower head is made up of 50 small round openings, each with a radius of 2.00 mm. You also determine that it takes 3.00 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 5.20 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? 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

(A) volume flow rate = 1 L / (3 sec) = 3.33 x 10^-4 m^3 / s

A = 50 (pi (2x 10^-3)^2) = 6.283 x 10^-4 m^2

v= Q / v = 0.53 m/s

(b) from bernoulli's equation.

P + rho gh + rho v^2 / 2 = constant

1.50 x 10^5 + 0 + (1000 v^2 /2 ) = 1 x 10^5 + (1000 x 10 x 5.20) + (1000 x 0.53^2 / 2)

v = 2.07 m/s

(c) Q = A v

A = (3.33 x 10^-4) / 2.07 = 1.61 x 10^-4 m^2  

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