[19] 



« = at y = ^ 



u = V at y = S 



The pressure p and the velocity V at the outer edge of the boundary layer are related by 

 Bernouilli's equation for potential flow 



■p + — pV^ = constant [20] 



or 



-i^=f/^ [21] 



p ax ax 



Combining the equation of motion, [17], the continuity equation, [18], and the differential 

 Bemouilli equation, [21], produces 



i!i=ui«-i« (iJi + JL ^]dy - U ^ [22] 



y2 dx dy J \ dx r dx j dx 



A first approximation is to let 



dy^ 



[23] 



Integrating [23] twice and utilizing boundary conditions, [19], results in a linear velocity 

 profile 



V 8 



[24] 



A second approximation is obtained by substituting the linear velocity profile, [24], 

 into differential equation [22]. Integrating twice and utilizing boundary conditions, [19], as 

 before gives 



4 , .2 



V 24 dx 



-|iKfl%t^)[(lf-(l) 



[25] 



Applying the additional boundary condition that 



dy 



= at y = 5 



to the differentiated form of Equation [25] yields 



,2 



+ 

 dx V dx 





16 vf.. 



[26] 



[27] 



