conservation of energy

[tkdhwjd]

Dear collegues,

In ejector design, velocity (kinetic energy) is converted into pressure (potential energy). In terms of energy conservation, this perfectly makes sense. But mathematically, this seems quite difficult to grasp... at least for me. For example, let us assume that the equipment is ruptured at a known pressure. If you can assume the fragment mass & shape and initial angle of projectile, you should be able to calculate the expected travel distance. Yet, I am unable to derive initial velocity from rupture pressure. Unit-wise, it seems not possible to convert pressure into velocity. So, how is a typical ejector designed? Any tips will be greatly appreciated.

 

[zdas04]

This is a very confused question. How did you get from how does an eductor work to how far will a projectile go in a rupture?

I find ejectors easier to explain than eductors. The difference is that ejectors use a gas as a power fluid and eductors us a liquid power fluid.

For a critical-flow ejector (most of them are critical flow), the power fluid exits the nozzle at sonic velocity. A sonic stream is very dense and will not mix with anything. Consequently, the suction gas at low-to-zero velocity within the steam chamber sees a no-flow boundary at the edge of the sonic stream and is accelerated into the converger. Within the convergent section, the accelerated gas is further sped up by a decreasing cross sectional area (think of Bernoulli's equation). Then in the straight throat the suction gas and the power gas begin to mix. At the exit of the throat the mixed gas enters the divergent section where it trades velocity for pressure.

Eductors and non-critical ejectors are similar, but the shape of the pieces are a bit different.

With your "initial velocity of a rupture" question, if you can determine the area of the projectile and the differential pressure then F=P*A. Then calculate the mass of the projectile and F=m*a so a(0)=P*A/m. Velocity is the integral of acceleration with respect to time so you have to come up with an expression for the change in acceleration normal to the failure (not a trivial task) then it is easy.

David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

The harder I work, the luckier I seem

 

[rmw]

The ejector converts kinetic energy to pressure via the shock wave. The hydraulic jump in a fluid flow channel is an easy way to visualize the concept, or at least it is for me.

rmw