Question

"Water moves in a pipe from the ground up to a height" of 11 m. At the bottom of the pipe the water has a velocity of 1 m/s. As the pipe goes up it reduces in diameter and at the top of the pipe it has a velocity of 12 m/s and a pressure of 207000 Pa. Find the necessary pressure at the bottom of the pipe to deiver the water to the top.

Answer 1

`P_1 =322095.92\ Pa`

Step-by-step explanation:

given,

height = z = 11 m

velocity at bottom = v₁ = 1 m/s

velocity at the top = v₂ = 12 m/s

pressure at the top = P₂ = 207000 Pa

Pressure at the bottom = P₁ = ?

using Bernoulli equation

`P_1 + \rho(v_1^2)/(2) = P_2 + \rho(v_2^2)/(2g) + \rho gz`

`P_1 = P_2 + \rho (v_2^2-v_1^2)/(2g) + \rho gz`

`P_1 =207000+1000* (12^2-1^2)/(2* 9.8) + 1000* 9.8* 11`

`P_1 =322095.92\ Pa`

Pressure at the bottom is equal to
`P_1 =322095.92\ Pa`