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 fu
nction of the flow rate is based on Manning's equations. This method requir
es 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 re
lationship and its practical use are presented. Comparisons of the now velo
cities calculated using the proposed relationship and flow velocities rigor
ously calculated using the iterative process show that a great degree of pr
ecision is obtained even when the now rate is very small compared to the ma
ximum 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 appli
cations (such as pipes used in leakage collection systems beneath a landfil
l liner) where liquid flows in a pipe that is almost empty. The proposed me
thod is explicitly analytical and can easily be programmed on a pocket calc
ulator.