Question

A water faucet has an inner area of 3.0cm2. The flow of water through the faucet is such that it fills a 500mL container in 15s.

(a) What is the flow rate of the water as it comes out of the faucet?

(b) What is the velocity with which the water emerges from the faucet?

(c) What is the velocity of the water 20cm below the faucet?

(d) What is the area of the water stream 20cm below the faucet?

Answer 1

given

cross sectional area of the pipe, A = 3 cm^2

= 3*10^-4 m^2

Volume of water, V = 500 mL = 0.5 L = 0.5*10^-3 m^3

time taken, t = 15 s

a) volume flow rate = dV/dt

= 0.5*10^-3/15

= 3.33*10^-5 m^3/s or 3.33*10^-2 L/s or or 33.3 mL/s

b) we know, dV/dt = A*v

v = (dV/dt)/A

= 3.33*10^-5/(3*10^-4)

= 0.111 m/s or 11.1 cm/s

c) use, vf^2 - vi^2 = 2*a*d

vf = sqrt(vi^2 + 2*a*d)

= sqrt(0.111^2 + 2*9.8*0.2)

= 1.983 m/s

d) use continuty equation

A2*v2 = A1*v1

A2 = A1*v1/v2

= 2*0.111/1.983

= 0.113 cm^2