Opposition

    Fish experience significant opposition in their movement through water.  One of the main opposing forces (acting in a direction opposite motion) is the drag force.  All fluids have a certain viscosity, which is a description of  the friction between nearby regions of the fluid moving at different velocities.  Viscosity is responsible for the conversion of some kinetic energy to internal energy which makes it act in a frictional manner.  Viscosity can be expressed by

 Viscosity=(pressure)x(time)
or
Viscosity=(mass)/(length)x(time)

    With the SI unit of viscosity being 1 (Pascal)x(second).  Water and solutions that are mostly water have a viscosity around
0.001 (Pascal)x(second).  The viscosity of a fluid is used to find a dimension less quantity known as the Reynolds number to help determine the drag coefficient.  The Reynolds number can be expressed by

 Reynolds number={(velocity)x(length)x(mass density)}/(viscosity)

    Although this number is necessary for determining drag coefficients, the calculations only seem to  be well understood for Reynolds numbers much less than one.  For this case the drag force can be expressed by

 f_drag=(viscosity)x(longest dimension of object)x(velocity of object)

    For fish, the Reynolds number can be on the order of 10⁶ which leads to turbulent flow with complicated eddies and vortices that make drag coefficient calculations difficult.  This information doesn't provide a method for quantitatively determining opposing forces, but it does illustrate qualitatively the increased difficulty fish experience by traveling through a substance more viscous than air.

                         
       

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