Mass flow rate through De Laval Nozzle

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SUMMARY

The discussion centers on calculating the mass flow rate through a De Laval nozzle, specifically addressing the discrepancies between theoretical and experimental results. Key parameters include a throat diameter of 4.79 mm, an exit diameter of 5.54 mm, and a coefficient of discharge of 0.6. The user, Max, initially miscalculated the pressure difference by using Pascals instead of the correct unit, kilopascals, which led to significant errors in his calculations. After correcting this unit error, Max achieved sensible results, highlighting the importance of unit consistency in fluid dynamics calculations.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly choked flow.
  • Familiarity with De Laval nozzle design and operation.
  • Knowledge of pressure measurement units, specifically Pascals and kilopascals.
  • Basic proficiency in using equations related to mass flow rate and density.
NEXT STEPS
  • Research the principles of choked flow in De Laval nozzles.
  • Learn how to calculate mass flow rate using the appropriate equations.
  • Study the impact of diameter variations on flow characteristics in nozzles.
  • Explore the significance of unit conversions in engineering calculations.
USEFUL FOR

Engineers, fluid dynamics students, and anyone involved in nozzle design or performance analysis will benefit from this discussion, particularly those focusing on mass flow rate calculations in fluid systems.

darksupernova
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Hey guys,


Ive got a little stuck calculating the mass flow rate of a choked flow through a de laval nozzle.

I have been given a formula to use for theoretical max and experimental but they seem to be SO far apart, I am sure I am missing something.

Given data:

Density of water 1000 kg/m^3
Throat diameter (nozzle) 4.79mm
Exit diameter (nozzle) 5.54mm
Probe diameter 3.30mm
Coefficient of discharge of orifice plate 0.6
orifice diameter 27.03mm
pipe diameter 76.2mm
gamma ratio of specific heats 1.4
gas constant 287 J/(kg K)
Absolute zero 273 degrees c / 0 K
Delta H = 2" = 0.0508m

See useful equations in attached image.

The manometer had water in it, and thus rho g H uses water density and delta H as above.

Please also see my attempt in the attached images for the theoretical and experimental equations.

The problem, they seem to be miles apart, am I using the correct diameters?

What am I getting wrong?

I hope you can help!

Thanks,

Max
 

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Update: I found the error. For p1-p2 I had the pressure difference in Pascals when of course the difference would be in Kilo Pascals, this unit change fixed the errors and gave me sensible answers. Little sad that nobody on here was any help! :(

Also I cannot see how to mark this thread as [Solved], it won't let me edit my original post.
 

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