# Integral form of momentum equation

## Main Question or Discussion Point

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

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Chestermiller
Mentor
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.

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
Mentor
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
Mentor
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
Mentor