In the following discussion, we define volumetric flow rate V̇ (i.e. volume of fluid flowing per time) as 
where
: r = radius of the pipe (for a pipe of circular section, the internal radius of the pipe).
: v = mean velocity of fluid flowing through the pipe.
: A = cross sectional area of the pipe.
In long pipes, the loss in pressure (assuming the pipe is level) is proportional to the length of pipe involved.
Friction loss is then the change in pressure Δp per unit length of pipe L
When the pressure is expressed in terms of the equivalent height of a column of that fluid, as is common with water, the friction loss is expressed as S, the "head loss" per length of pipe, a dimensionless quantity also known as the hydraulic slope. 
where
: ρ = density of the fluid, (SI kg / m)
: g = the local acceleration due to gravity;