Force exerted on U-shaped pipe by steady air-flow help please

[ds7202]

Force exerted on U-shaped pipe by steady air-flow... help please! :)

Hello! I have attempted this problem, and my result makes sense in my twisted mind. However, it seems like it came too easy!

Homework Statement

Consider a length of pipe bent into a U-shape. The inside diameter of the pipe is 0.2m. Air enters one leg of the pipe at a mean velocity of 10 m/s and exits the other leg at the same magnitude of velocity, but moving in the opposite direction. The pressure of the flow at the inlet and exit is the ambient pressure of the surroundings. Calculate the magnitude and direction of the force exerted on the pipe by the airflow. The air density is 1.23 kg/m^3.

Homework Equations

I attempted this problem using the steady-flow momentum equation, \sum\vec{F} = \int\rho\vec{v}(\vec{v}\cdot\vec{n})dA

The Attempt at a Solution

My attempt at the solution can be viewed here:
http://i.imgur.com/SHItH.jpg


Pleeeeease help! Thanks! :D

 

[DiracRules]

I looked through your calculation, they don't seem wrong, but I didn't study that equation so I don't know if it is correct to use it.

However, I think that a pipe like the one in the problem would move in some way, because it seems very close to the problem of a ball rebounding on a wall: the initial and final condition of the ball are the same, except from the velocity that is the opposite. In these kind of problem, since the velocity varies, you have some forces acting (Newton's second law).
I'd use this way of reasoning - but I'm not sure it is correct. In addition, to perform my calculation I need the length of the pipe, and you did not provided it. So maybe my way is not the correct one. Nevertheless, I think that it must be considered some kind of non-zero force, because the air actually changes its velocity!

Hope you understand (my English is not perfect :D:D:D )

 

[ds7202]

I realize what I did wrong. I used the velocity's normal vector instead of the control surface's normal vector, haha