Calculation of Flow Velocity in Pipes as a Function of Flow Rate

Abstract

There are many design situations where the rate of flow in a pipe is known and the average velocity of the liquid in the pipe must be calculated. The classical method to determine the average velocity of flow in pipes as a function of the flow rate is based on Manning's equations. This method requires an iterative process or the use of cumbersome tables or graphs. A direct relationship between the average velocity of flow and the rate of flow in pipes is proposed. To the best of the authors' knowledge, this is the first time that such a direct relationship is proposed. The derivation of the relationship and its practical use are presented. Comparisons of the flow velocities calculated using the proposed relationship and flow velocities rigorously calculated using the iterative process show that a great degree of precision is obtained even when the flow rate is very small compared to the maximum flow capacity of the pipe. This is important because the traditional method is not precise when the flow rate is small, and there are many applications (such as pipes used in leakage collection systems beneath a landfill liner) where liquid flows in a pipe that is almost empty. The proposed method is explicitly analytical and can easily be programmed on a pocket calculator.