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Jet pumps or venturi pumps are often stated as having a "terribly low" efficiency, steam jet pumps specifically are usually describes as "only justifiable when there's an abundant steam supply anyway" - however, I hardly find any numbers, and no formulas.

My question: Is there a general form to describe the work done by a (non-steam) jet pump an the pumped medium as a function of the work used to pump the working fluid (gas or liquid)

Is there a general form to describe the work done by a steam pumpe as a function of the thermal energyinput into the workng fluid?

While real-world numbers are interesting, I'm mostly after the limits posed to jet pumps by thermodynamics, not engineering.

EDIT: Can a jet pump be describes meaningfully in a p - V diagram? Put another way, can the changes of impulse in the media be expressed solely as functions of the pressures (before/after)?

Thus, can a (steam-)jet pump be described as a thermal (steam-)engine?

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This paper might have what you want: dx.doi.org/10.1063/1.1150141 – user2963 Feb 14 '12 at 13:49
    
there's a paywall and it seems to bother more with engineering aspects. – mart Feb 14 '12 at 14:18
    
they give an efficiency of $\eta = \frac{\dot{m_e}(P_d-P_e)}{\dot{m_j}(P_j-P_d)}$ e = entrainment j = jet d = discharge – user2963 Feb 14 '12 at 14:20
    
If that's what you are looking for and you want to see the derivation, I can give you a link to the pdf – user2963 Feb 14 '12 at 14:23
    
P refers to impulse, or pressure? This refers to compressible fluids also? I assume it doen'st hold true for condensing jets. I'd be interested in the derivation (so I'd know how to play this thinking in purely mechanical terms, and maybe find the solution for steam jets afterward). Thanks a lot so far, I think I need to rephrasse my question, like what's the highest entrained mass flow possible for given pressures (and why). – mart Feb 14 '12 at 15:34

"Terribly low efficiency" is quite relative. You can easily Reach a 85% peak-efficiency for such a pump. Nobody actually claims that ie. steam-turbine's have a "terribly low" efficiency, and this is why ie. 90% of the electricity in US is produced by them; ie. all nuclear powerplants all over the world use them to convert the thermal energy to kinetic energy and then to Electricity.

But these machines do have also a "terribly low efficiency", as if they are used in locomotives or in boats; There is only one gas-turbine driven boat build in the world. The reason is that though they have a good peak efficiency, they have "Terribly low" Partial load efficiency.

The reason for terribly low partial load efficiency of gas/steam turbines can be tracked to the fact that any flow velocity which is different than the design velocity causes counterflows and turbulence inside the machine. This same suits to "steam jet pump", it has a good efficiency, but it's really difficult to found a case where this could be reached; ie. if you pump something to tank or from tank; as the tank fills up or empites, the pressure varies, and you are immidietly of from the best efficiency.

Your detailed questions;

Is there a general form to describe the work done by a steam pumpe as a function of the thermal energyinput into the working fluid?

$P_{out}$ = $P_{in}$ x efficiency

Can a jet pump be describes meaningfully in a p - V diagram? Put another way, can the changes of impulse in the media be expressed solely as functions of the pressures (before/after)?

p- V diagramm would by only a single line. The meaningfulness of this line is relative.

Thus, can a (steam-)jet pump be described as a thermal (steam-)engine?

The thermal reactions doesn't really have any remarkable influence to the process itself, if you pump water, the steam will condensate, and thus the pressure after the pump will be lower and will theoretically help the pumping-process, but practically it only causes the pump to work outside the best-efficiency-point, as you might not be able to design the pump to work with this effect in use.

Ps. Turbines are mainly used only in constant velocity cases; like Airplanes and Electricity production. But you can have even a motorbike with a gas turbine,,,, But even there it has terribly low efficiency; Turbo-charged piston engines make it better;

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