Resistance Force on Gas in Magnetohydrodynamic Generator

[bucky3052]

TL;DR Summary

How much does velocity of a fluid drop as it passes through a magnetohydrodynamic generator

I am attempting to derive equations of state for a flow loop that incorporates a magnetohydrodynamic (MHD) generator to extract energy from the working fluid, an ionized gas. I have been able to find the following equation to define the power output of the generator:

(where K is load factor, σ is conductivity, u is velocity, and B is applied magnetic field)

However, in order to complete my equations of state, I need to balance this power against the change in the fluid's enthalpy and pressure/velocity:

(where m is constant mass flow rate, h is specific enthalpy, and v is velocity [sorry for inconsistent variables])

Just from some basic reading, it seems like the fluid should have to "push" against some force as it goes through the MHD generator in order to produce power, which should reduce its velocity. If this is true and significant, I need to account for it in my equations of state, but I'm not sure how to model this

Is there a well-defined "resistance" force (opposing the direction of travel) experienced by the gas, or a way to quantify slowing through the MHD generator?

 

[Baluncore]

Charge is being forced up a potential energy step. That is balanced by a pressure gradient that forms in the fluid, tending to oppose the fluid flow.

The mass flow of the fluid is fixed by conservation. Changes in pressure, density, temperature, and velocity, are coupled by the cross-section of the flow, through conservation of energy, in line with Bernoulli's principle.

 

[bucky3052]

Charge is being forced up a potential energy step. That is balanced by a pressure gradient that forms in the fluid, tending to oppose the fluid flow.

The mass flow of the fluid is fixed by conservation. Changes in pressure, density, temperature, and velocity, are coupled by the cross-section of the flow, through conservation of energy, in line with Bernoulli's principle.

Ah yes, I should have realized that the hall voltage being created along the MHD was a potential that the ions in the gas would have to climb.

If I assume a perfect MHD generator, and that there is no net change in flow area, then the only "slowing" felt by the fluid should be from the electric potential. Is this accurate?

Then it should be a simple conservation of energy for the free positive ions as they push along the potential to determine how fluid velocity is affected.