38 



This result was obtained independently by several of the writers cited above. 

 The coefficient C D (<r) is the drag coefficient of the plate at cavitation num- 

 ber a, and C D (0) is the drag coefficient for cavitation number zero, or 

 ^ff = 0.88 (Kirchhoff flow). Here, 



where D is the drag, and I is the breadth of the plate. This expression 

 holds with excellent approximation for cavitation numbers less than one. At • 

 a = 1 , Wehausen found that the error between this approximation and the exact 

 calculation is less than 0.8 percent (see Wehausen's commentary 68 ). 



It is interesting that Reichardt 54 obtained precisely the above re- 

 sult for axisymmetric flow on the basis of a reasonable choice of assumption 

 of the variation of the pressures on the face of the model. Reichardt assumed 

 that, for small cavitation numbers, the pressure coefficient on the face of 

 the model <;„ at cavitation number a will vary from the pressure coefficient a* 

 for cavitation number zero according to the equation 



1 - <r f = (1 + <r)(1 - a*) 



or 



a„ + a = (1 + a)a* 



The drag is given by 



D = J" ( Pf " p c )dA 



where p f is the pressure on the face, 

 p is the cavity pressure, and 

 A is the area of the model. 



Dividing by "2pU 2 A , this equation may be written 



C D = ~A l (a f + ff)dA 



A 



which itfith the assumption above, becomes 



% - ^W 



so that a. 



C D (cr) = (1 + a)C D (0) [21] 



Another simple drag law which was proposed by Betz 70 is obtained by assuming 

 that the drag given for Kirchhoff flow is increased by the product of area 

 times the pressure reduction in the finite cavity. This leads to the result 



2 7T 



C D = n + k + a which agrees well with the above approximation for very small 

 cavitation numbers. 



