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
The difference in pressure between the main line and the second floor is 91,100 Pa.
The given parameters;
Apply Bernoulli's equation to determine the difference in pressure between the main line and the second floor is calculated as follows;
[tex]P_1 \ + \ \frac{1}{2} \rho v_1^2 + \rho gh_1 = P_2 \ + \ \frac{1}{2} \rho v_2^2 + \rho gh_2\\\\P_1 - P_2 = \frac{1}{2} \rho v_2^2 \ - \ \frac{1}{2} \rho v_1^2 \ + \ \rho gh_2 - \rho gh_1 \\\\P_1 - P_2 = \frac{1}{2} \rho(v_2^2 - v_1^2) \ + \ \rho g(h_2 -h_1)\\\\P_1 - P_2 = \frac{1}{2} (1000)(7^2- 2^2) + \ (1000\times 9.8)(5- (-2))\\\\P_1 - P_2 = 91,100 \ Pa[/tex]
Thus, the difference in pressure between the main line and the second floor is 91,100 Pa.
Learn more about Bernoulli's equation: https://brainly.com/question/15396422
