Fluid flow problem with the momentum balance equation

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SUMMARY

The discussion centers on the fluid flow problem utilizing the momentum balance equation, specifically addressing the formula for the area of a circle in terms of diameter. The correct formula is identified as Fp = -ρvj²(π/4)(D1² - D2²), where ρ represents fluid density and v is velocity. The conversation highlights a unique scenario where the change in momentum is expressed as vΔm rather than the conventional mΔv, indicating a nuanced understanding of fluid dynamics.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with momentum balance equations
  • Knowledge of geometric formulas, specifically for circles
  • Basic algebra for manipulating equations
NEXT STEPS
  • Research the derivation of the momentum balance equation in fluid dynamics
  • Study the implications of using vΔm in momentum calculations
  • Learn about applications of the area of a circle in engineering contexts
  • Explore advanced fluid flow problems involving varying diameters
USEFUL FOR

Students and professionals in engineering, particularly those specializing in fluid mechanics, as well as anyone involved in solving complex fluid flow problems using momentum balance equations.

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All problem info, and my work is done in the attached pdf.

Basically, I'm not sure that I have done it correctly.
 

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What is the formula for the area of a circle in terms of diameter?
 
Ooops

So the answer is then:


Fp = -\rhovj2\frac{\pi}{4}(D12 - D22)
 
Looks good to me.
 
Comment: interesting problem; case where change in momentum is vΔm instead of the usual mΔv.
 

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