Find Mass Flow Rate and the Exit Flow Area

[Northbysouth]

Homework Statement

Air enters aone-inlet, one-exit contreol volume at 6 bar, 500K and 30m/s through a flow area of 28cm³. At the exit the pressure is 3 bar, the temperature is 456.5 K and the velocity is 300 m/s. The air behaves as an ideal gas. For steady state operation determine

a) the mass flow rate, in kg/s
b) the exit flow area, in cm³

Homework Equations

m' = dm/dt = ρvA

The Attempt at a Solution

I have the area of the cross section, A, and the velocity at both ends, but I'm not sure about the ρ.

Can I use:

ρ = p/RT to find the air density?

 

[Northbysouth]

I've managed to find the mass flow rate, using the density equation given above, I found the air density and then plugged this number into m' =ρvA

m' = (4.1803 kg/m³)(30 m/s)(28cm²)

m' = 0.351 kg/s

Does the mass flow rate stay constant? Can I rework these equations to find the Exit flow area?

 

[haruspex]

Does the mass flow rate stay constant?

Mass is a a conserved quantity. In steady state, the mass within the volume is neither increasing nor decreasing, so the mass flow rate in must equal the mass flow rate out.

 

[SteamKing]

Areas are usually measured in square cm, rather than cubic cm.