# Turbomachinery velocity triangle problem

1. Jan 31, 2016

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

Euler's Torque equation

$T=\dot{m}(r_2V_{\theta2}-r_1V_{\theta1})$

3. The attempt at a solution

As torque = 0

$T=\dot{m}(r_2V_{\theta2}-r_1V_{\theta1})=0$

$(r_2V_{\theta2})=(r_1V_{\theta1})$

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

No idea where to take it from here. I can't tell from the problem statement if the direction of $V_2$ 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

2. Feb 2, 2016

### RUber

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.