Exercise 11 Solution

  1. The assumptions of the equation are that the fluid is incompressible and Newtonian; the flow is laminar through a pipe of constant circular cross section that is substantially longer than its diameter; and there is no acceleration of fluid in the pipe.
  2. If µ increases, then the gradient increases in order to drive the same mean volumetric flow rate of a more viscous fluid through the same opening. That is, is the more viscous fluid presents more resistance to flow. This makes sense because a more viscous fluid is “thicker” like syrup compared to water, so the fluid does not flow as easily thus requiring more pressure to push the fluid through the pipe.
  3. The specific velocity is linearly proportional to the pressure gradient if the viscosity of the fluid is constant.

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Introduction to Karst Aquifers Copyright © 2022 by Eve L. Kuniansky, Charles J. Taylor, and Frederick Paillet. All Rights Reserved.