Integral form of momentum equation

[Ali Durrani]

Hello guys!
can i get the derivation for this equation ?

 

[Chestermiller]

I think the first term should be a partial derivative with respect to time t (not x), and represents the rate of accumulation of x-momentum within the control volume. The second term represents the net rate of x-momentum leaving the control volume.

 

[Ali Durrani]

I think the first term should be a partial derivative with respect to time t (not x), and represents the rate of accumulation of x-momentum within the control volume. The second term represents the net rate of x-momentum leaving the control volume.

yes sir as you said the 1st term should be the partial derivative with respect to time but i don't know why our teacher in the fluid class wrote the equation in this form, and it was not a mistake because he used it again and again, can you explain the logic behind it as he is a very senior teacher and he wouldn't make such a silly mistake

 

[Chestermiller]

yes sir as you said the 1st term should be the partial derivative with respect to time but i don't know why our teacher in the fluid class wrote the equation in this form, and it was not a mistake because he used it again and again, can you explain the logic behind it as he is a very senior teacher and he wouldn't make such a silly mistake

I stand by what I said. I can't account for what your teacher does. All I can do is confidence in what I am saying.

My questions for you are:

1. How does his equation account for the time rate of accumulation of x momentum within the control volume?

2. When he writes the corresponding equation for the conservation of mass within the control volume, does his equation have a partial derivative with respect to x or a partial derivative with respect to t?

 

[Chestermiller]

Here's a couple of more questions for you:

1. What are the units of the term as your teacher has written it?

2. Are those units of force?

 

[Chestermiller]

So... What are your answers to my questions?

 

[Ali Durrani]

sorry i asked him and he said its partial by partial t and not x his writing style is different so i mistakenly wrote it as partial by partial x

 

[Chestermiller]

sorry i asked him and he said its partial by partial t and not x his writing style is different so i mistakenly wrote it as partial by partial x

No problem.