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This is the problem I'm trying to solve:

figure

I'm looking at the worked-out solution from my professor and it shows that the sum of the forces in the x-direction is equal to:

[d/dt(momentum) in the x-direction, out] - [d/dt(momentum) in the x-direction, in]

I don't understand what is meant by momentum out vs. momentum in and why one is positive and the other is negative.

Also, I apologize if this is a dumb question.

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If it is a solid body, the force applied on the body is the rate of change of momentum of the body in the direction of force(here we talk about the mass of the body and its velocity).In case of a fluid, we talk about the mass flow rate and velocity.So the initial momentum of the flow before the bend(and nozzle) is the momentum in and after interacting with the nozzle, the momentum of the flow leaving out is the momentum out.The difference will give the force acting on the fluid by the bend.I think you should include pressure force in x direction.

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