2 1 

 cos o(E = (1 + _N )2 _ N 



Ho^ Ho (22) 



f2N 

 „ , — - Gosoce . (23) 



tan a 9 = -cot od £ (21) 



The phenomenon is seen to be a function of the Jimensionless ratio N/Kq for 

 the condition assumed. 



Acceleration . - In the preceding analysis of the problem, it was assumed 

 that the instantaneous rate of flow in accelerated motion is the same as in 

 steady motion, under the same head. This assumption neglects the head necessary 

 to accelerate the flow. The magnitude of the error will now be analyzed for 

 the case of laminar floWo 



The equations of motion are, 



h - h' = L dV 



g clt (2A) 



h' = 8U LV 



w r2 



2 

 V ^ A dH' dV = A d H' 



a dt dt 



dt" 



h - 8 LA dH' = L A d^H' 



wa r2 dt g a dt^ (2^?,) 



From the first approximation, 



hp = Hq cos <x £ h = ho sin oc (t + £ ) 



Ho' = Ho sin ex £ H' = Hq' sincx (t - G) 



If these relationships are substituted in equation 2<^a, the equation becomes 

 an inequality since the first approximation was obtained on the assumption 

 that dv = 0. Making the substitution 

 dt 



Hq cos c<6 sin oc {t ^ S ) - oC 8 U LA H^ sin ol cos oC (t - 6) 



5 waR ^ 



+ oC L A Hq sin odf sin oC (t - 0) ^ (25) 

 g a 



29 



