Magnetohydrodynamic Propulsion for Sea Vehicles 



Consider the MHD pump or propulsive duct integrated into a thrust- 

 producing propulsive unit, as shown in Fig. 2. The vehicle and propulsive unit 

 will be considered moving with constant speed V. The propulsive duct will be 

 considered as square and therefore of area 8 2. Ae is the exit area for the fluid 

 jet and Ue is the exit velocity. For steady motion, the thrust of the propulsion 

 unit must equal the drag on the vehicle. K w is the mass flow per unit time 

 through the unit, the thrust is (w = pUeAe), so that 



Thrust = T = Drag = w (Ue - V) 



(6) 



The drag can be expressed in terms of the wetted area of the vehicle S^ and 

 the drag coefficient c^ as Drag = (1/2) pV^ c^s^^, so that Eq. (6) becomes 



L-r\Oi 



D^W 



Ue / Ue 



2Ae — 1 



V \ V 



(7) 



Fig. 2 - Propulsion unit with propulsive duct 



For a given vehicle of known Cj, and S^^, the velocity ratio Ue/v is deter- 

 mined once the exit area of the propulsive unit is chosen. The propulsive ef- 

 ficiency of the unit vp is determined by this velocity ratio 



1 + 



Ue 



(8) 



Equation (7) could just as conveniently be written in terms of the propulsive 

 efficiency, or 



^D^W = 4Ae 



(2-7,p) (1- vp) 



(9) 



As mentioned above, although the velocity does not change through the duct, 

 the pressure does. The fluid enters the duct with a Bernoulli constant equal to 



1439 



