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

Answer:

$P_1 =322095.92\ Pa$

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

$P_1 + \rho\dfrac{v_1^2}{2} = P_2 + \rho\dfrac{v_2^2}{2g} + \rho gz$

$P_1 = P_2 + \rho \dfrac{v_2^2-v_1^2}{2g} + \rho gz$

$P_1 =207000+1000\times \dfrac{12^2-1^2}{2\times 9.8} + 1000\times 9.8\times 11$

$P_1 =322095.92\ Pa$

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