Drag force on a cylinder in an air tunnel

[ussername]

Homework Statement

Let's have a cylinder in air tunnel. The air is flowing around cylinder. I want to calculate a net force acting on the cylinder. Part of the incoming air hits the cylinder and its trajectory direction changes. For that reason we can see straight behind the cylinder lower velocity (29 m/s) that is increasing with y coordinate.

The air density is constant 1.23 kg/m3.

Homework Equations

In order to calculate (through the linear momentum bilance) the net force acting on cylinder, I have to consider control volume, that has mass outlet just behind the cylinder (that is above and under cylinder there are no mass flows). For that I need to consider sufficiently big height (Δy) of the control volume. Unfortunately I missed the teacher explanation of how to calculate this. Moreover I don't understand the given v2 function - I'm sure its wrong because at first v2 increases with y to some maximal value and then it convergate back to 30 m/s again - so this v2 function is deffinitely wrong.
Do you have some experience with that type of tasks?

The Attempt at a Solution

Through mass bilance I have to find minimal height of control volume with outlet only behind the cylinder.
Then from control surface dimensions and given velocities I calculate the net force acting on the cylinder.
The correct result is F=95.78 N

 

[mfb]

What is the exact problem statement? Please copy it instead of describing it. Sometimes details can be important.

The flow velocity has to be larger than the wind tunnel velocity in some parts behind the obstacle, otherwise you would put more air into the tunnel than air goes out.

The region of y considered should be large enough to cover all relevant perturbations of the object I guess.

 

[ussername]

 

[mfb]

If you are just given the velocity profile in this 2 m meter region, I guess that is all you can use. Looks odd, but if the problem statement wants that...