Question

A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 m 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 × 103 kg/m 3 . The difference in pressure between the main line and the second floor is _______.

Answer 1

Answer:

 P₁- P₂ = 91.1 10³ Pa

Explanation:

For this exercise we will use Bernoulli's equation, where point 1 is at the bottom of the house and point 2 on the second floor

          P₁ + ½ ρ v₁² + ρ g y₁ = P₂ + ½ ρ v₂² + ρ g y₂

          P1-P2 = ½ ρ (v₂² - v₁²) + ρ g (y₂-y₁)

In the exercise they give us the speeds and the height of the turbid, so we can calculate the pressure difference

For heights let's set a reference system on the ground floor of the house, so we have 5m for the second floor and an entrance at -2m

 

        P₁-P₂ = ½ 1.0 10³ (7² - 2²) + 1.0 10³ 9.8 (5 + 2)

       P₁-P₂ = 22.5 10³ + 68.6 10³

       P₁- P₂ = 91.1 10³ Pa