The velocity profile of a Power-law fluid is given by this equation.

where

- r is the radial position i.e. distance from the center line (m)
- R is the pipe radius (m)
- u(r) is the axial velocity (m s
^{-1}) - dp/dz is the axial pressure gradient (Pa m
^{-1}) - K is the flow consistency index (Pa s
^{n}) - n is the flow behavior index

The value of n determines the relationship between the axial velocity and radial distance. If

- n = 1, the fluid is Newtonian
- n < 1, the fluid is pseudoplastic
- n > 1, the fluid is dilatant

The spreadsheet is simple to use. Simply enter the parameters

Excel will then plot the velocity profile from the centerline to the surface of the pipe. As expected, the velocity profile is symmetrical.

The transient velocity profile in laminar flow is more difficult to calculate; this requires the numerical solution of a partial differential equation via a finite difference scheme. This will be the subject of another spreadsheet.

**Download Spreadsheet to Calculate the Velocity Profile in a Circular Pipe**