Momentum for a control volume (Fluid Mechanics)

[PhyIsOhSoHard]

Homework Statement

http://i988.photobucket.com/albums/af10/postop/equationsmomentum_zpse8c8d44a.png

Homework Equations

The Attempt at a Solution

Can somebody explain to me in the two equations above what is the "u" and what is the "v"?
In the question, it says that the water at the nozzle has a speed of 25 m/s and the vane maintains the speed at 5 m/s.

It just doesn't make any sense because my textbook writes the following when calculating the reaction force for the x-axis:

But with the reaction force for the y-axis it writes:

And they argue that it is because [itex]v_1=0[/itex]
Why is there no A1 segment for the y-axis?
I just don't understand, what is "v" and "u" in these equations and how did [itex]v_1=0[/itex] happen?

 

[mark726]

Thank you for your question. The "u" and "v" in the equations refer to the initial and final velocities of the water at the nozzle and the vane, respectively. In this case, "u" is equal to 25 m/s because that is the initial velocity of the water at the nozzle, and "v" is equal to 5 m/s because that is the final velocity of the water at the vane.

As for the reaction forces for the x-axis and y-axis, the reason why there is no A1 segment for the y-axis is because the water is not moving in the y-direction. Therefore, there is no need to consider the initial velocity in that direction, and v1 is equal to 0.

I hope this explanation helps to clarify your doubts. If you have any further questions, please don't hesitate to ask. Keep up the good work with your studies!