Question

A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 above ground on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 × 103kg/m3. Find the difference in pressure between the main line and the second floor.

Answer 1

By Bernoulli's equation: 

$$p_1+0.5\rho v_1^2+\rho gh=p_0+0.5\rho v_0^2$$

$$p_0-p_1=0.5\rho( v_1^2- v_0^2)+\rho gh$$

$$p_0-p_1=0.5(1000)( 7^2- 2^2)+(1000)(9.8)(2+5)=9.1\cdot 10^4\ Pa$$