Analytical solutions for the Colebrook and White equation and for pressure drop in ideal gas flow in pipes

The friction factor, evaluated from the Colebrook and White equation, is traditionally computed iteratively. An analytical solution of the Colebrook and White equation for the friction factor can be obtained, using the Lambert W function. Also, the equation relating the outlet pressure to the inlet pressure of an ideal gas flowing through a straight pipe under isothermal, steady state conditions has been hitherto considered in literature to be implicit in these variables, probably due to its inherent non-linear nature. However, it can be shown that an analytical solution to the above equation for the pressure drop (or alternatively, outlet pressure) can also be obtained using the Lambert W function.