Aeroengines/Fluid Mechanics - Steady Flow

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SUMMARY

The discussion centers on a fluid mechanics problem involving the calculation of velocity (V9) in a nozzle control volume with given temperatures (T5 = 1000K, T9 = 670K) and velocity (V5 = 120 m/s). The correct answer is 822.8 m/s, but the user consistently arrives at 120 m/s due to confusion between the universal gravitational constant (G) and the acceleration due to gravity on Earth (gc). Clarification is provided on the distinction between these constants, emphasizing their different applications in physics and engineering calculations.

PREREQUISITES
  • Understanding of thermodynamics and fluid mechanics principles
  • Familiarity with specific heat capacity (Cp) and its application in gas flow calculations
  • Knowledge of gravitational constants: universal gravitational constant (G) and acceleration due to gravity (gc)
  • Ability to interpret and solve equations related to nozzle flow dynamics
NEXT STEPS
  • Study the application of the energy equation in compressible flow scenarios
  • Learn about the principles of conservation of mass and energy in fluid mechanics
  • Explore the differences between G and gc in engineering contexts
  • Review the derivation and application of the ideal gas law in thermodynamic calculations
USEFUL FOR

Students and professionals in mechanical engineering, particularly those focusing on fluid mechanics and thermodynamics, as well as anyone involved in aerospace engineering and nozzle design calculations.

JRS192
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Homework Statement


See Fig.2.4a, let the gases flowing through the nozzle control volume be perfect with Cp = 1.004kJ/kg.K

Determine V9 if T5 = 1000K, T9 = 670K and V5 = 120ms^-1.

Homework Equations


I've detailed the equations in the attached pdf for clarity.

The Attempt at a Solution


See attached pdf. The question paper has the answer as 822.8m/s, but I'm consistently getting 120m/s. Where am I going wrong?

Thank you
 

Attachments

  • Fig2.4a.png
    Fig2.4a.png
    47.3 KB · Views: 546
  • doc00586420150126151206.pdf
    doc00586420150126151206.pdf
    329.4 KB · Views: 273
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You've confused the universal gravitational constant G for the acceleration due to gravity on earth, gc.
It's not clear why you don't understand the distinction between these two constants.
 
Hi SteamKing,

Thanks for that. I did some research and everything directed me to that figure, even to the point of using gc...
 
JRS192 said:
Hi SteamKing,

Thanks for that. I did some research and everything directed me to that figure, even to the point of using gc...

I doubt that. You have misinterpreted something in what you read.

The universal gravitational constant G (which is invariably capitalized) is typically used to find the force of gravitational attraction between two masses, as described by the formula

F = Gm1m2/r2

G is used more often in physics type calculations. G also has some rather unusual units: G = 6.67*10-11 m3/kg-s2

The acceleration due to gravity on earth, gc, which is invariably lower case, is typically commonly found in engineering type calculations, more so than G.
 
Thank you for your help.
 

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