Energy conservation for a Newtonian fluid?

  • #1

Homework Statement


vsoqrs.png

ρ= density, vi = i-th velocity component, gi=i-th component of gravity vector, p=pressure, μ= viscosity, D/Dt = material derivative

Homework Equations


Continuity equation: div v = 0

The Attempt at a Solution


acbhwo.png
 

Answers and Replies

  • #2
21,489
4,867

Homework Statement


View attachment 203392
ρ= density, vi = i-th velocity component, gi=i-th component of gravity vector, p=pressure, μ= viscosity, D/Dt = material derivative

Homework Equations


Continuity equation: div v = 0

The Attempt at a Solution


View attachment 203393
The derivation you are looking for is in Transport Phenomena by Bird, Stewart, and Lightfoot. It involves dotting the equation of motion (momentum balance equation) with the velocity vector. Incidentally, this is called the Mechanical Energy Balance Equation. It can be combined with the Overall Energy Balance equation to yield the Thermal Energy Balance equation.
 

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