ABSTRACT
The complex velocity presented in the above expression must be scaled so that the average velocity across the inlet of the ehysical domain is unity. This is achieved by dividing Equation (U) by the unsealed discharge, 0, and multiplying by the inlet width, L. The unsealed discharge through the reservoir is given by the difference in stream function values between the two inlet corner points at a" and b". Since a" and b" lie on the same equipotential line,
lb' Q-Y,b" - "'•"-.!. < rb" - r ... >-.!. dr ds I I a' ds (13) The limits of this integral lie on the real axis of the s-plane and so the integrand can be expressed entirely in terms of p. After rearrangement, the unsealed discharge becomes
Q-dp Ia' b' [(a'-p)(p-b')(p-c')(p-d')]i (14) The above equation is an incomplete elliptic integral of the first kind and may be rewritten accordmg to Byrd and Friedman [11) as Q-t F(>.,r) (15)
