On the uncertainties stemming from use of the Colebrook-White equation

Abstract

The Darcy-Weisbach and Colebrook-White equations are considered to be the most accurate formulae available for calculating head losses in pipes. Because of the implicit nature of the latter equation, various graphical methods and analytic approximations for explicitly determining the friction factor have been developed. Detailed comparisons among these approximations have revealed that they exhibit varying levels of accuracy depending upon the complexity of their functional forms. However, none of these comparisons has taken into account the crucial fact that the input quantities needed to compute the friction factor are obtained from measurements, and consequently those quantities are subject to experimental uncertainties. The present paper proposes a procedure for evaluating the impact these uncertainties have on the dispersion of the values that can be attributed to the friction factor and other relevant quantities computed from the Colebrook-White equation. The procedure, which accords with current international recommendations, is based on the assumption that this equation is “exact”.