While taking a shower, you notice that the shower head is made up of 36 small ro

Question

While taking a shower, you notice that the shower head is made up of 36 small round openings, each with a radius of 1.4 mm. You also determine that it takes 7.00 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 6. m below the level of the shower head. The pump maintains an absolute pressure of 1.6 atm. Use g = 10 m/s2.

(a) What is the total area of the openings in the shower head?

(b) At what speed does the water emerge from the holes?
m/s

(b) At what speed is the water flowing through the pipe connected to the pump? assume it has a cross sectional area.

(d) What is the radius of the pipe?

(e) If you covered up six of the holes in the shower head with your thumb, with what speed would you expect the water to emerge from the remaining holes?

Explanation / Answer

a) A = 36*pi*r^2 = 36*3.14*1.4^2*10^-6 = 221.558e?6 m^2

b) volume rate = 10^-3/7 = 0.143*10^-3 s

A*v = 0.143*10^-3

v = 0.645 m/s

c) 0.5*m*V^2 = m g h

V = sqrt(2*g*h)= sqrt(2*9.8*6.2) = 11.02 m/s

d) aV = pi*R^2= 0.143*10^-3

R = 2.03255e?3 m = 2 mm

e) 30*pi*r^2*v = 0.143*10^-3

v = 0.774 m/s

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