Find Mass Flow Rate and the Exit Flow Area

Click For Summary
SUMMARY

The discussion focuses on calculating the mass flow rate and exit flow area for air in a control volume under steady-state conditions. The mass flow rate is determined using the equation m' = ρvA, where ρ is the air density calculated from the ideal gas law (ρ = p/RT). The calculated mass flow rate is 0.351 kg/s, and it is confirmed that the mass flow rate remains constant in steady-state conditions. The exit flow area can be derived from the mass flow rate and exit conditions.

PREREQUISITES
  • Understanding of ideal gas behavior and the ideal gas law (p = ρRT)
  • Familiarity with fluid dynamics concepts, particularly mass flow rate calculations
  • Knowledge of steady-state operation principles in control volumes
  • Basic proficiency in unit conversions, particularly between cubic centimeters and square centimeters
NEXT STEPS
  • Research the application of the ideal gas law in different thermodynamic scenarios
  • Learn about the conservation of mass in fluid dynamics
  • Explore methods for calculating flow areas in various engineering applications
  • Study the implications of varying pressure and temperature on gas density and flow rates
USEFUL FOR

Students in engineering disciplines, particularly those studying thermodynamics and fluid mechanics, as well as professionals involved in HVAC systems and aerodynamics who require a solid understanding of mass flow rates and control volume analysis.

Northbysouth
Messages
241
Reaction score
2

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?
 
Physics news on Phys.org
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?
 
Northbysouth said:
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.
 
Areas are usually measured in square cm, rather than cubic cm.
 

Similar threads

Replies
1
Views
2K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 5 ·
Replies
5
Views
3K
Replies
12
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 2 ·
Replies
2
Views
5K
Replies
4
Views
1K
Replies
3
Views
2K
Replies
1
Views
5K