Relation between Fluid mechanics and Thermodynamics

• Prasant
In summary: Entropy is not redundant- it is a fundamental part of the equations. The lost energy generates heat and entropy, so you can apply the thermodynamic equations to fluids based on those two concepts.
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?

Prasant said:
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?

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.

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.

Prasant said:
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?

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.

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 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:

1. What is the basic difference between fluid mechanics and thermodynamics?

The main difference between fluid mechanics and thermodynamics is that fluid mechanics deals with the behavior and properties of fluids (liquids and gases) in motion, while thermodynamics deals with the transfer of heat and energy in a system.

2. How are fluid mechanics and thermodynamics related?

Fluid mechanics and thermodynamics are closely related, as both fields deal with the study of energy and its transfer. In fluid mechanics, the focus is on the flow of fluids and the forces acting on them, while in thermodynamics, the focus is on the transfer of heat and energy between systems.

3. What are some real-world applications of the relation between fluid mechanics and thermodynamics?

The relation between fluid mechanics and thermodynamics has many practical applications, such as designing efficient engines and turbines, understanding weather patterns and climate change, and developing technologies for energy production and transportation.

4. How does the study of fluid mechanics contribute to our understanding of thermodynamics?

Fluid mechanics provides a foundation for understanding the behavior of fluids in different systems, which is essential for studying thermodynamics. The principles of fluid mechanics, such as Bernoulli's equation and the laws of conservation of mass and momentum, are used to analyze and solve problems in thermodynamics.

5. Can you give an example of how fluid mechanics and thermodynamics are applied together in engineering?

One example of the application of fluid mechanics and thermodynamics in engineering is in the design of a gas turbine engine. The principles of fluid mechanics are used to study the flow of air through the engine, while thermodynamics is used to analyze the transfer of heat and energy within the engine to increase its efficiency.

• Thermodynamics
Replies
3
Views
1K
• Thermodynamics
Replies
4
Views
1K
• Thermodynamics
Replies
5
Views
2K
• Thermodynamics
Replies
4
Views
1K
• Thermodynamics
Replies
8
Views
1K
• Classical Physics
Replies
16
Views
4K
• Science and Math Textbooks
Replies
2
Views
1K
• Thermodynamics
Replies
4
Views
2K
• Thermodynamics
Replies
2
Views
1K
• Thermodynamics
Replies
1
Views
1K