The rssistance to steady flow through a pipe line connecting ta'io res- 

 ervoirs is 



h = K V^ + flV^ + ^3" 



2g D2g . 2g 



Here, K represents the entrance, elbow and othar losses due to fittings, 

 f is the friction factor corresponding to the velocity V and Vq is the 

 final velocity at exit. The values of K and f depend upon the lieynolds 

 number. The ratio V /V equals the coefficient of contraction in the case 

 of an orifice. For I simple pipe connection, V,^ = V. Inserting the coef- 

 ficient of contraction and solving for 7, 



V = 



(12) 



Here S is the velocity head coefficient and Cq is the coefficient of con- 

 traction at discharge. 



The continuity equation is 



Ad (H - h) = a / 2gh 



dt V W (lb) 



Assuming that h is sinusoidal as before, 



^ [lio sin ex t - hg sin oC(t + e)]= ^^ a [2_%_ sin oL (t +6)12 (I3) 



_ 1 



The solution given by Chapman expresses [sin cx(t -> 6 )J^ as a Fourier 

 series which preserves the absolute value of th3 right hand number. 



1 

 sin2 X = a]_ sin x + 33 sin 3x + ar sin 5x + + b^ sin nx. 



the values of the constants are: 



a^ = 1.113 



33 = 1/7 ai 



a 5 = 5/77 ai 



The series becomes 



[sin o<.(t +£ )]* = 1.113 [sin oc (t ^6) + l/7 sin 3«(t +£) * 5/77 sin 



5 cx(t •■ £) + ] 



27 



