Momentum Equation Homework: Questions & Solutions

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SUMMARY

The discussion revolves around the momentum equation in fluid dynamics, specifically addressing the confusion regarding the presence of a 1/2 factor in the left-hand side of the equation. Participants clarify that the term D(vivi)/Dt represents the substantial derivative of velocity, which incorporates both convective and local acceleration. The conversation emphasizes the importance of understanding how diffusion affects momentum and velocity terms in the equation.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with the momentum equation
  • Knowledge of substantial derivatives
  • Basic grasp of diffusion concepts
NEXT STEPS
  • Study the derivation of the momentum equation in fluid dynamics
  • Learn about substantial derivatives and their applications
  • Explore the role of diffusion in momentum transfer
  • Investigate advanced fluid dynamics topics, such as turbulence and boundary layers
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Students studying fluid dynamics, educators teaching momentum equations, and professionals working in fields related to fluid mechanics and engineering.

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Homework Statement


The questions are in the attachment. please help!

Homework Equations


M term is the diffusion.


The Attempt at a Solution


for the right hand side terms, it is just adding another velocity term, however on the left hand side term, i dun understand y there will be a 1/2 since momentum equation is just substantial derivative of velocity.
 

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oxxiissiixxo said:
… on the left hand side term, i dun understand y there will be a 1/2 since momentum equation is just substantial derivative of velocity.

Hi oxxiissiixxo! :smile:

Because D(vivi)/Dt = … ? :wink:
 

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