Question

A water faucet in a house is h=8 m below the water surface in the local water tower. The radius of the orifice in the fully opened faucet is r=0.01 m. We assume non-viscous flow in this problem.

a) How long does it take to fill a 20 liter bucket with water using this faucet?

Answer 1

From Bernouli's equation

rho g h1 + 1/2   rho v1^2 = rho g h2 + 1/2 rho m v2^2,    here v1 = 0, h2 = 0

rho g h1 = 1/2 rho v2^2

v2^2 = 2*g*h1 = 2*9.8*8 = 156.8

v2 = 12.52 m/s

now mass flow rate m/t = rho *A*V              rho density of water , A area of cross section, V is speed

                                            = 1000 *3.14*0.01^2*12.52

                                            = 3.931 kg/s

time taken to fill 20 lts of water is 20 / 3.931 = 5.08 s

(treated 1kg of water as 1 ltr)