As is shown by Eq. 6.143 the pressure gradient for laminar flow through a tube of consta...

As is shown by Eq. 6.143 the pressure gradient for laminar flow through a tube of constant radius is given by the expression

For a tube whose radius is changing very gradually, such as the one illustrated in Fig. P6.83, it is expected that this equation can be used to approximate the pressure change along the tube if the actual radius, R(z), is used at each cross section. The following measurements were obtained along a particular tube.

Compare the pressure drop over the length l for this nonuniform tube with one having the constant radius R₀. Hint: To solve this problem you will need to numerically integrate the equation for the pressure gradient given previously.