# Relation between Fluid mechanics and Thermodynamics

1. Feb 7, 2008

### Prasant

Is there any valid formula which can apply to both thermodynamics and fluid mechanics, as they are both based on the nature of flow of a substance? If yes, please mention the formula and it's derivation?

2. Feb 7, 2008

### John Creighto

I’m not sure what you’re looking for. The Navier-Stokes equations relate the forces (pressure, and shear) in the fluid to the acceleration of the fluid. Knowing the acceleration you can get the flows. The lost energy generates heat and entropy so you should be able to apply the thermodynamic equations once you know the flows.

3. Feb 7, 2008

### h2oski1326

um, sure. Any fundamental law can be applied to any situation if applied correctly. However, the information you can get from those laws may not be very useful.

The 1st and 2nd laws of thermodynamic as well as Newtons second law can be written in a slightly more general form to allow an easy Control Volume analysis of a fluid system.

For example the 1st law of thermodynamics can be written in the following form:

$$\frac{d}{dt}\int_{CV}e \rho dV + \int_{CS}(h+\frac{1}{2} V^2 + gz)(\rho \hat{u}_{\\rel} \cdot d \hat{A}) = \dot Q_{into CV} + \dot W_{other,on CV}$$

And while it may look different than what you may have learned in Thermodynamics it is the same, just written in a form which makes it a bit easier to understand in the context of a fluid mechanics course.

4. Feb 8, 2008

### Andy Resnick

Material flow: conservation of mass, conservation of momentum
Nonmaterial flow: conservation of energy.

Those three equations can be written in either a differential way or integral (much like h2oski1326) way. One can also institute "jump conditions" across material or nonmaterial bounderies.

I'm not going to write any formulas- it would take too much time, and there's no need. My go-to book for all this is "Interfacial Transport Phenomena" by Slattery. Brenner and Edwards "Macrotransport Processes" is also very good.

5. Feb 9, 2008

### John Creighto

The integral form of the equations can be found here:

http://en.wikipedia.org/wiki/Reynolds_transport_theorem

The differential form of the momentum equation is the Navier-Stokes equations:

http://en.wikipedia.org/wiki/Navier-Stokes_equations
http://en.wikipedia.org/wiki/Navier-Stokes_equations/Derivation

The differential form of the mas equation is the continuity equation found here:

http://en.wikipedia.org/wiki/Continuity_equation#Fluid_dynamics

I cannot find the differential form of the energy equation. I expect it to look something like [URL [Broken] equation[/url]

I presume equations involving entropy would be redundant but I came across a paper before which used minimum entropy generation as a principle for deriving empirical forms of convection expressions from computation fluid dynamic techniques.

Last edited by a moderator: May 3, 2017