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 ∆P 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
where r is the radius of the tube, η is the viscosity of the fluid, ∆P 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, η1, η2, η3, are forced to flow through tubes of varying radii 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 ∆P. The results for fluid 1 are shown in the following figure.
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