Theory
It is a natural phenomenon for a fluid to lose head as it flows through a pipe due to its viscosity. For smooth pipes one can analyze its head loss with the length of the pipe for a given flow condition. A simple apparatus to study this behavior may constitute of a pipe of a certain diameter and a fixed length that has a smooth inner surface. Lets design and conduct analysis on one such apparatus. To start off, lets choose a pipe. Pipes commonly range in diameter from 0.5 inches to 2 inches and for a realistic lab experiment a pipe ranges in length on a few meters.
J.T. Fanning proposed that the head loss in a pipe can be expressed as,
where
h = head loss in pipe
f = Fanning friction factor
l = length of pipe
v = superficial velocity of fluid in pipe
ρ = density of fluid
g = gravitational constant
d = diameter of pipe