Turbomachinery velocity triangle problem

  • Thread starter MacLaddy
  • Start date
  • #1
MacLaddy
Gold Member
291
11
Capture.PNG

Homework Statement



Air (assumed incompressible) flows across the rotor shown in the figure such that the magnitude of the absolute velocity increases from 15 m/s to 25 m/s. Measurements indicate that the absolute velocity at the inlet is in the direction shown. Determine the direction of the absolute velocity at the outlet if the fluid puts no torque on the rotor. Is the rotation CW or CCW? Is this device a pump or a turbine?


Homework Equations



Euler's Torque equation

[itex]T=\dot{m}(r_2V_{\theta2}-r_1V_{\theta1})[/itex]

The Attempt at a Solution


[/B]
As torque = 0

[itex]T=\dot{m}(r_2V_{\theta2}-r_1V_{\theta1})=0[/itex]

[itex](r_2V_{\theta2})=(r_1V_{\theta1})[/itex]

[itex]V_{\theta2}=V_{\theta1}*\frac{r_1}{r_2}=15\sin{60}*\frac{1.9}{1.2}=20.57 m/s[/itex]

No idea where to take it from here. I can't tell from the problem statement if the direction of [itex]V_2[/itex] is as indicated.

If there is no torque, as indicated, then I would assume that this must be a pump--as the fluid isn't doing any work on the rotor. However, I believe I need to prove this with velocity triangles and the like.

Any help would be appreciated.
Mac
 

Answers and Replies

  • #2
RUber
Homework Helper
1,687
344
It looks like you found the velocity in the same direction as V1. The problem gives you the full velocity. You can complete the triangle using the Pythagorean thm, and find the angle from that.
 

Related Threads on Turbomachinery velocity triangle problem

  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
3
Views
9K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
10
Views
5K
  • Last Post
Replies
1
Views
758
  • Last Post
Replies
22
Views
1K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
1
Views
500
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
1
Views
1K
Top