# P405

There are many everyday and industrial examples of non-ideal fluids forced to flow through tubes. Examples include the flow of water and oil through pipelines. A pressure difference ΔP is applied to a tube which causes the fluid to flow. Scientists study the flow of differing fluids through tubes to gain a better understanding of the flow.

At low flow speeds, the flow of a non-ideal fluid through a tube is laminar. The equation governing the flow is given by:

**Equation 1**

In Equation 1, r is the radius of the tube, η is the viscosity of the fluid, ΔP is the pressure difference between the ends of the tube, and l is the length of the tube. The volume flow rate is found by vA where v is the average speed of the fluid and A is the cross sectional area of the tube.

Consider an experiment in which 3 non-ideal fluids of differing viscosities, η_{1}, η_{2}, and η_{3}, are forced to flow through tubes of varying radius r, all with the same length l. In this experiment, the average speed of the fluid molecules is measured as a function of the cross sectional area of the tube when each tube is subjected to a given pressure difference ΔP. The results for fluid 1 are shown in the following figure.

**Figure 1.**Results from Fluid 1 experiment.

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