The Physics of Motion in a Liquid

As a whale or dolphin moves through liquid it creates turbulence.  This turbulence is overcome by streamlining the body.  Streamlining is tricking the liquid into following laminar flow.

The streamline is the path of the water around the body of the animal.  As it moves it may change the magnitude and direction of the velocity but its vector will always be tangent to the streamline of the body.  Streamlines never cross.

So if v = velocity, A = area and t = time then

DV = A1v1Dt

where v1Dt is a small distance.  This means that if the speed, v, is constant then the particle will pass any point on the animal such that

A1v1 = A2v2

This can be turned into a generalization for the volume flow rate, r, of the fluid and is called the equation of continuity for fluid flow.  It tells us that the flow is faster around linear body parts where the streamlines are closer to the streamlines of the body.

R = Av = a constant.

This is difficult, if not impossible to calculate for whales and dolphins as they move through water because they are not a closed system, like a pipe, but interact with an entire ocean.  This is why Rohr used bioluminescence and why scientists continue the study.

 

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