Use of Exponential Equations in the Analysis of Flow in Channels

Exponential equations have been in use for the solution of channel problems since long. Their choice of adoption is based on simplicity and case of computation. However, the chief drawback is that for the desired accuracy, they have very limited range of applicability. Also the equations generally in vogue are of empirical nature. Hence the logarithmic equations, like the one advanced in the recent past by Keulagan, are preferred these days because of their reliability over a wide range of flow conditions and also because they are dimensionally correct. But such equations are often found to be very cumbersome for practical application. Hence based on rational approach as suggested by Pal, suitable exponential equations which are dimensionally homogeneous, have been derived covering the entire range of applicability of logarithmic equation.