An equation in fluid dynamic ~ me ~

In summary, the conversation discusses a difficult equation in fluid dynamics and a possible relationship between it and Gauss's Divergence Theorem. The solution is suggested to be found through the application of the divergence theorem and the conservation of mass. The conversation ends with a request for a clearer explanation or for the solution to be provided.
  • #1
abcdefg10645
43
0
When I studied the fluid dynamic , I saw a quite hard equation (typed in attached file) ,

I don't know how to prove it , maybe there's a somehow relationship between this eq with Gauss's Divergence Theorem ...

Can anyone help me ?
 

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  • #2
abcdefg10645 said:
When I studied the fluid dynamic , I saw a quite hard equation (typed in attached file) ,

I don't know how to prove it , maybe there's a somehow relationship between this eq with Gauss's Divergence Theorem ...

Can anyone help me ?

Your equation is a relation between vectors, but you can prove it by considering each vector component separately and applying the divergence theorem.
 
  • #3
Iirc, you can get at it from conservation of mass:

dm=o
d(pV) =0
(product rule)
etc...
 
  • #4
Pythagorean said:
Iirc, you can get at it from conservation of mass:

dm=o
d(pV) =0
(product rule)
etc...

Well,I cannot fully understand what the term "etc" mean , could you be more explicit , or can you just type the solution to this annoying question ?


Thanks again if I get any reply~
 
  • #5


As a scientist who has also studied fluid dynamics, I can understand your struggle with this equation. It is common for equations in this field to be complex and difficult to prove. In regards to your question about a possible relationship with Gauss's Divergence Theorem, it is possible that this equation is related to the principle of conservation of mass in fluid flow. This theorem states that the net flow of a fluid into a closed surface is equal to the rate of change of fluid within the surface. This principle is fundamental in understanding fluid dynamics and could potentially provide insight into proving the equation you are struggling with. I suggest consulting with your peers or a mentor for further assistance in understanding and potentially proving this equation.
 

1. What is an equation in fluid dynamics?

An equation in fluid dynamics is a mathematical representation of the behavior of fluids, such as liquids and gases, in motion. These equations describe how fluids move and interact with their surroundings, and are essential for understanding and predicting fluid flow in various applications.

2. What is the significance of fluid dynamics in scientific research?

Fluid dynamics plays a crucial role in many fields of science, such as meteorology, oceanography, and engineering. It helps us understand the behavior of fluids in nature and in man-made systems, and is essential in the design and optimization of various technologies, from airplanes to pipelines.

3. How are equations in fluid dynamics derived?

Equations in fluid dynamics are derived from fundamental principles, such as conservation of mass, momentum, and energy. These principles are applied to a specific system or problem, and the resulting equations are then solved using mathematical techniques, such as calculus and differential equations.

4. Can equations in fluid dynamics predict real-world fluid behavior accurately?

While equations in fluid dynamics provide a good approximation of real-world fluid behavior, they are not always accurate due to the complexity of fluid dynamics. Factors such as turbulence, viscosity, and boundary conditions can affect the accuracy of predictions made using these equations.

5. What are some practical applications of equations in fluid dynamics?

Equations in fluid dynamics have numerous practical applications, such as predicting weather patterns, designing efficient transportation systems, and optimizing chemical processes. They are also used in the development of new technologies, such as wind turbines and fuel-efficient vehicles.

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