Drag force on a two-dimensional structure

[fruitstreet]

"A two-dimensional structure is tested in a wind tunnel with an air density of 1 kg/m3. The wind tunnel is 1 m high, with upstream and downstream pressures of 1.5 kPa gage (i.e. above atmospheric) and 1 kPa gage respectively. If the mean velocity of the entering air is 30 m/s and the downstream velocity profile is as shown below, what is the drag per unit length of the structure? Neglect wind tunnel wall shear stress."

The object in the wind tunnel is a two-dimensional hexagon with an undefined length. I understand that Fd=Cd(rho)(V^2)A/2. I'm getting hung up on having a 1 dimensional area, and if I simply apply that equation then I'm not using the given pressures.

Any ideas? Thanks in advance.

 

[boneh3ad]

1 dimensional area is length.

 

[Senor]

I have the exact problem and am also struggling a bit. Who want's the challenge!

 

[Senor]

also the velocity profile at the exit is equal to zero at the center. It increases linearly to v1 at the outer edge because we ignore shear stress from the wall

 

[boneh3ad]

If you are familiar with the Reynolds Transport Theorem, use it on on the momentum in the profile before and after the object (which you are given) and an unknown body force term. If you solve for the force term, you end up with the drag.

A system with drag is dissipative (or non-conservative), so momentum in the flow is not conserved as some is removed by the drag on the object.

 

[Senor]

Thank you very much