on EF: 



if U + q h^U -h^q 



q < V, X = — \ h, \n + A„ In 



^ n\^^ U -q 2 h^U + h^q 



On DE, 1 < t < a, r IS imaginary and t = iq/U, and 



^ 1 ^ 



A, tan — - A„ tan 



The force on DE due to the Bernoulli pressure in steady motion is most easily found 

 from the conservation of momentum. Consider the fluid between two transverse planes drawn 

 far away from DE and on opposite sides of it. 



In a second, the net effect of the motion is the same as if a volume Aj V of this fluid 

 were removed from the neighborhood of the rear plane (at the right) and inserted just ahead 

 of the forward plane, gaining thereby momentum 



ph. U {— U-U]=ph,U^i— - 1 I . [108o] 



The momentum in the remainder of the space between the planes is unaltered. During the 

 same time the difference of pressure between the fwo planes delivers momentum to the fluid 

 of magnitude equal to the differential force multiplied by the time or 



[108p] 



The remainder of the gain in momentum must be furnished by a force due to negative pressure 

 over DE\ the reaction is a force of suction on DE, directed oppositely to the stream, of 

 magnitude equal to Equation [108o] minus Equation [lOBp] or, per unit of length perpendicular 

 to the flow, 



F, = - p ^2 1 (^^ _ ^^)_ [logq] 



The force F^ exceeds the force of suction on an equal area in the approaching stream 

 by AFj =Fi -- pU^ {h,-h^)or 



269 



