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.

Mass flow = 0.0203 slug/s

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

absolute = gage + atmospheric    ....................1

put here value we get

absolute = 10 + 14.7

absolute = 24.7 psi

absolute = 3556.8 psf

and For nitrogen

R = 1775 ft-lb/slug °R

and we get gas equation that is express as  

absolute  = R T      ...............2

3556.8 = × 1775 × 549.67    

= 3.645 ×  slug/ft³

so here Mass flow that is express as

Mass flow = AV      .................3

Mass flow = 3.645 ×  ×  ( ) ×  (16)

Mass flow = 0.0203 slug/s