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I know momentum is conserved in an isolated system wherein there in not mass nor energy flow and the net resultant external forces are equaly to zero.

My doubt is when I'm studying a (fixed) constrol volumen instead a system. I understand perfecly the mass and energy laws conservation when they're applied to the fixed control volume. My problem is when I have to deal with momentum. Since the fluid is flowing throught the boundaries of the control volume this "closed" fluid in experimenting a net external force usually not equal to zero (due to de surface forces [pressures and viscous stresses distributions) and body forces]. How can momentum be conserved in the control volume if it exist a net force aplied to the control volume?

I don't know if I've explained well myself (my english is very bad).

Thank you.

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    $\begingroup$ Your English is not bad - it is certainly much better than my Spanish, French, or German. And, you have asked a good, thoughtful question. $\endgroup$ Jul 14, 2016 at 20:12

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The forces acting on the fluid are changing its momentum. There are forces acting on the stationary portions of the control volume boundary, and there are also forces being applied to force fluid into, and acting to prevent it from flowing out of the control volume. The total rate of change of momentum in the control volume at any instant of time is equal to the net rate of momentum entering plus the time derivative of the momentum per unit volume integrated over the control volume.

Now, regarding overall conservation of momentum, to consider this, one must include not only the material inside the control volume but also all the rest of the equipment and fluid outside the control volume (the surrounding universe). The sum of these rates of change plus those for the control volume must be equal to zero. For example, if the control volume consists of a pipe of non-constant cross section through which fluid is flowing (say at steady state), the reaction force that the fluid exerts on the pipe (which is connected to the earth) causes the momentum of the pipe and earth to change.

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@ChesterMiller: answer is good, but I would just simplify it. What you say is that the total momentum is the momentum of the contents of the control volume plus the sum of that which traverses the boundaries. If you take the change in momentum per unit time, you have momentum flux, which equals force.

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