How do you calculate the exit velocity in aerodynamics?

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SUMMARY

The exit velocity in aerodynamics can be calculated using the principle of conservation of mass, specifically for incompressible flow. Given an inlet area of 23 ft² and an inlet velocity of 107 ft/sec, the exit area is 12 ft². The calculated exit velocity is 205 ft/sec, derived from the equation (velocity)in x (Cross-sectional Area)in = (velocity)out x (Cross-sectional Area)out. The Mach number of 0.0959 confirms that the flow is incompressible.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Knowledge of the conservation of mass in fluid flow
  • Familiarity with calculating Mach numbers
  • Basic algebra for solving equations
NEXT STEPS
  • Study the principles of incompressible flow in fluid dynamics
  • Learn about the continuity equation in fluid mechanics
  • Explore the concept of Mach number and its implications
  • Investigate real-world applications of exit velocity calculations in aerodynamics
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Aerodynamics students, engineers in fluid mechanics, and anyone involved in calculating flow rates in various applications will benefit from this discussion.

freedevil
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Homework Statement



Given: Inlet area = 23 ft², Inlet velocity = 107 ft/sec, Exit area = 12 ft². Find exit velocity

The Attempt at a Solution



I am having a hard time solving this. Can someone explain how to do this? Thanks
 
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solved!

Mach number = 107/1116 = 0.0959
This is less than 0.3 so the flow is incompressible

(volumetric flow)in = (volumetric flow)out
(velocity)in x (Cross-sectional Area)in = (velocity)out x (Cross-sectional Area)out
107 x 23 = (velocity)out x 12
(velocity)out = 205 ft/s
 

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