Resler 



voltage is v and the current is determined by this voltage, the back emf (elec- 

 tromotive force) generated by the fluid motion, and the resistance R in accord 

 with Ohms law, and is: 



^ V - UB5 V - UB5 ^ / V \ ,^. 



o-Se 



Consider a constant area duct. Then for incompressible fluids the velocity 

 u will be constant through the duct. The force IBS will act on the fluid to in- 

 crease its pressure in going through the duct. The MHD duct serves as a pump 

 without blades or vanes, the force on the fluid being a direct body force acting 

 throughout the flow where the electrical currents flow in the presence of the 

 magnetic field B. The work done on the fluid per unit time (Pp) is the IBS force 

 multiplied by the velocity U or 



Pp = (IBS)U = aSe BUS (- - Ub] (2) 



The power supplied by the source of current is just IV, so the pumping ef- 

 ficiency, the ratio of work done on the fluid to the power supplied by the source, 



,,. . IBSU UB U 



-.•-:., T) = erriciency = = = — . .„. 



IV \_ y_ (3) 



S SB 



The efficiency is therefore the ratio of the electric field induced by the mo- 

 tion (UB) to the applied electric field V/S or, alternatively, the velocity of the 

 fluid u divided by the velocity (V/S)/B. The choice of voltage for the power 

 source thus determines the efficiency of the pumping action and is under the op- 

 erator's control. Using Eq. (3) to eliminate the voltage v from the equation for 

 Pp, Eq. (2) gives 



Pp - (ctUS) (U) (B^Se) (^y (4) 



The expression for Pp has been written as the product of four terms, each 

 enclosed in parentheses. The first term is the so-called magnetic Reynolds 

 number Rm = ous and is a measure of how efficiently the electromagnetic forces 

 are coupled to the fluid. The second term is the fluid velocity u, the useful 

 power Pp being the force acting multiplied by this velocity. The term B^Se is 

 the magnetic pressure B^ multiplied by the area Se, in a certain sense the 

 maximum force expected. The last term involving the efficiency is controlled 

 by proper choice of voltage V . The force on the fluid supplied by the forces in 

 the propulsive duct or MHD pump is then 



F = (aUS) (B2Se) LZJH . (5) 



1438 



