Is Linear Momentum Converted to Angular Momentum?

Most recent answer: 09/11/2013

Hi Van, A question on angular vs linear momentum. If a fluid in a pipe passes through an inductive turbine/water wheel is the velocity of the fluid flow slowed down? Is this a conversion of linear to angular momentum, or how are they both conserved? Is there a linear force exerted on the axle of the wheel perpendicular to the long axis? Thanks, Chris
- Chris C (age 31)
Broomfield, CO, USA

The two conservation laws- linear and angular momentum- are absolutely separate. Neither one can be converted to the other.

A turbine inserted into a pipe will make the fluid flow slower than it would without the turbine. However, the fluid flow through different parts of the tube will not be different, because otherwise fluid would be building up in some part of the tube.

Linear momentum conservation is simple: the fluid pushes on the turbine. If you quit pushung on the fluid it will come to rest, dumping its momentum into the earth via the turbine.

It's not clear to me what the geometry is for your last question. For the simple turbine, placed symmetrically along the fluid flow, the angular momentum along its axis picked up by the turbine is exactly balanced by angular momentum picked  up by the fluid. You can see how that would work by imagining how the fluid would come out the back of the turbine, at an angle sort of sliding along the surface of the blades. Gradually that angular momentum will get transferred out to the whole earth via viscous friction with the walls of the tube. 

Heres a little experiment that you might be able to do. Take some fairly smooth, non-rotating airflow, maybe from an air-conditioner vent. Put a simple little rotary fan in front of it, not turned on. You should see the fan start to spin a little, driven by the wind. Now using some ribbons that blow in the wind measure the airflow behind the fan. You should see a bit of rotation, opposite to the fan rotation. Remove the fan and that rotation should go away. And let us know how it comes out.

Mike W.

(published on 09/11/2013)