Question

Air flows steadily through a horizontal 4-in.-diameter pipe and exits into the atmosphere through a 3-in.-diameter nozzle. The velocity at the nozzle exit is 150 ft/s. Determine the pressure in the pipe if viscous effects are negligible.

Answer 1

Answer:

$P=18.28\ lb/ft^2$

Explanation:

Given that

d₁ = 4 in

d₂ = 3 in

v₂ = 150 ft/s

We know that ,from continuity equation

A₁v₁= A₂v₂

d₁²v₁ = d₂²v₂

$v_1=\dfrac{3^2}{4^2}\times 150\ ft/s$

$v_1=84.37\ ft/s$

Now by using energy equation ,The pressure P is given as

$P=\dfrac{1}{2}(v_2^2-v_1^2)\times \rho\ lb/ft^2$

$P=\dfrac{1}{2}(150^2-84.37^2)\times 0.002377\ lb/ft^2$

$P=18.28\ lb/ft^2$