The rate at which liquid flows through a pipe – actually the volume flow rate
- may depend on many factor. The most obvious are:
-
The viscosity
of the liquid. -
The cross section
and length
of the tube. We can simplify the analysis by assuming the pipe has a circular cross section of radius
as shown below. -
The pressure difference
between the ends of the tube.
An expression for the volume flow rate may be deduced by dimensional analysis. We assume that
where
is called the pressure gradient and k is a dimensionless constant.The dimensions of each quantity are:
hence
Equating powers for each of
Solving these three equations simultaneously gives
and
hence
can be shown to be
hence 