## The Flow of Liquid Through a Pipe

The rate at which liquid flows through a pipe – actually the volume flow rate- may depend on many factor. The most obvious are:

1. The viscosityof the liquid.

2. The cross sectionand lengthof the tube. We can simplify the analysis by assuming the pipe has a circular cross section of radiusas shown below.

3. The pressure differencebetween the ends of the tube.

An expression for the volume flow rate may be deduced by dimensional analysis. We assume thatwhereis 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 givesandhence

can be shown to behence