Question

Determine the mass flow of nitrogen in an 8-in.-diameter duct if it has a velocity of 16 ft/s. The nitrogen has a temperature of 90∘F, and the gage pressure is 10 psi. The atmospheric pressure is 14.7 psi.

Answer 1

Mass flow = 0.0203 slug/s

Step-by-step explanation:

given data

diameter = 8 in

velocity = 16 ft/s

nitrogen temperature = 90°F = 549.67 °R

gage pressure = 10 psi

atmospheric pressure = 14.7 psi

solution

we know absolute pressure that is express as

`\rho` absolute =
`\rho` gage +
`\rho` atmospheric ....................1

put here value we get

`\rho` absolute = 10 + 14.7

`\rho` absolute = 24.7 psi

`\rho` absolute = 3556.8 psf

and For nitrogen

R = 1775 ft-lb/slug °R

and we get gas equation that is express as

`\rho` absolute =
`\rho` R T ...............2

3556.8 =
`\rho` × 1775 × 549.67

`\rho` = 3.645 ×
`10^(-3)` slug/ft³

so here Mass flow that is express as

Mass flow =
`\rho`AV .................3

Mass flow = 3.645 ×
`10^(-3)` × (
`(\pi * ((8)/(12))^2)/(4)` ) × (16)

Mass flow = 0.0203 slug/s