Resler 



that in the free stream, namely 9f^ + (1/2) pY^, where iP^ is the ambient 

 pressure. At the exit of the propulsion unit the Bernoulli constant is y^ + 

 (1/2) pu J. These two Bernoulli constants differ by the pressure rise across 

 the propulsive duct which is equal to F, Eq. (5), divided by the duct area s^, 

 so 



AipMHD = ^ = A (c^SXB^Se) ^^"^ 



(10) 



In accordance with the above discussion, 



^A^ |PV2 + ^= y^^ ipUe2 



(11) 



The fluid is incompressible, so the velocities Ue and V are related by the con- 

 tinuity equation as 



UeAe = U5 2 



(12) 



Using Eqs. (10) and (12) in Eq. (11) gives 



B2 \ 1-77 



, Ae \ / Se 



I PV2 



Ue- 



- 1 - 



(13) 



Equation (7) can be solved for Ue /v , giving 



Ue 1 



1 + / 1 + 



2Cj^Sy 

 Ae 



(14) 



Using Eq. (14), Eq. (13) can be alternatively written 



-|p)(S 



1 - 77 



Ae 



+ /I + 



2CQSy 



Ae 



ipV^ 



1 + /I + 



2Cj^S^ 



Ae 



(15) 



Equation (15), which is general, can be rearranged to be used to compute the 

 required magnetic field B to propel a vehicle, giving for b: 



2^ I 1 - Tj \Ae j\Se j aVh 



~A^ 



2Cr^S 



+ /I + 



D^W 



Ae 



1 + /I + 



Ae 



(16) 



1440 



