A water line with an internal radius of 5.29 x 10-3 m is connected to a shower head that has 15 holes. The speed of the water in the line is 0.651 m/s. (a) What is the volume flow rate in the line? (b) At what speed does the water leave one of the holes (effective hole radius = 4.13 x 10-4 m) in the head?

(a) 3.44 x 10^-3 m^3/s

(b) 8.4 m/s

Explanation:

area of water line, A = 5.29 x 10^-3 m

number of holes, N = 15

Speed of water in line, V = 0.651 m/s

(a) Volume flow rate is given by

V = area of water line x speed of water in water line

V = 5.29 x 10^-3 x 0.651 = 3.44 x 10^-3 m^3/s

(b) area of one hole, a = 4.13 x 10^-4 m

Let v be the velocity of water in each hole

According to the equation of continuity

A x V = a x v

5.29 x 10^-3 x 0.651 = 4.1 x 10^-4 x v

v = 8.4 m/s