Question

Water flows through a circular pipe with a radius of 10 cm at 12 m/s. (a) If the radius of the pipe increases to 20 cm, what is the new speed of the water in the pipe? (b) Does the volume flow rate or the mass flow rate change in the pipe? (c) Calculate both the volume flow rate and mass flow rate in the pipe?

Answer 1

here,

the radius of circular pipe , r1 = 10 cm = 0.1 m

the velocity of pipe , v1 = 12 m/s

a)

when the radius of pipe is increased , r2 = 20 cm = 0.2 m

let the new speed of water in pipe be v2

using equation of continuity

pi * r1^2 * v1 = pi * r2^2 * v2

0.1^2 * 12 = 0.2^2 * v2

v2 = 3 m/s

the new speed of water is 3 m/s

b)

No, the volume flow rate does not change

c)

the volume flow rate , V = pi * r1^2 * v1

V = pi * 0.1^2 * 12 m^3 /s

V = 0.38 m^3 /s

the mass flow rate , m = V * p

m = 0.38 * 1000 kg/s

m = 376.8 kg