Conservation of Momentum Question

[member 428835]

In the x direction, we know that the volumetric rate of flow into the blade system from the left must equal the flow out on the right. In the y direction there is no requirement that volumetric rate of flow up the left side of the blades must equal that on the right side.

Ok, I think I have it! I wrote up a proof, starting with the momentum equation, assuming incompressible, steady, non-viscous flow and neglecting body forces. I'll attach it since typing it took some time. Let me know what you think, as I have one question with what I wrote.

 

[haruspex]

Ok, I think I have it! I wrote up a proof, starting with the momentum equation, assuming incompressible, steady, non-viscous flow and neglecting body forces. I'll attach it since typing it took some time. Let me know what you think, as I have one question with what I wrote.

Yes, that all looks correct to me.

 

[member 428835]

Yes, that all looks correct to me.

Awesome, thanks so much for your help! I really appreciate it!

 

[Chestermiller]

I get the opposite signs than you have obtained for the components of the external force necessary to hold the vane in place.

 

[haruspex]

I get the opposite signs than you have obtained for the components of the external force necessary to hold the vane in place.

Good point. I read the diagram as indicating Rx and Ry are the forces the flow exerts on the vanes, and did not notice that wording.

 

[member 428835]

Shoot, thanks! I'll fix this!