Question

At cruise conditions, air flows into a jet engine at a steady rate of 60 lbm/s. Fuel enters the engine at a steady rate of 0.59 lbm/s. The average velocity of the exhaust gases is 1485 ft/s relative to the engine. If the engine exhaust effective cross-sectional area is 4.0 ft2, estimate the density of the exhaust gases in lbm/ft3.

Answer 1

ρ=0.0102lbm/ft^3

Step-by-step explanation:

To solve this problem we must take into account the equation of continuity, this indicates that the sum of the mass flows that enter a system is equal to the sum of all those that leave.

Therefore, to find the mass flow of exhaust gases we must add the mass flows of air and fuel.

m=0.59+60=60.59lbm/s( mass flow of exhaust gases)

The equation that defines the mass flow (amount of mass that passes through a pipe per unit of time) is as follows

m=ρVA

Where

ρ=density

V=velocity

m=mass flow

A=cross-sectional area

solving for density

ρ=m/VA

ρ=60.59/{(1485)(4)}

ρ=0.0102lbm/ft^3