Water distribution

Home Continuity Bernoulli Interpretation Pumps Siphons

Assume you have created an indoor water fountain.  You have connected pieces of pipe with different diameters into a path along which the water will flow.  You also have inserted a pump into the circuit.  A very simple circuit is shown in the figure below.

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Running the pump for a while will accelerate the water and start it flowing.  The pump creates a pressure gradient.  If we look at a volume V of water in a straight section of pipe while the water is accelerating, then the pressure on side 1 of this volume is different than the pressure on side 2.  This results in a net force on the volume of water in that section, and the volume of water accelerates.  

Once the water is flowing at the chosen speed, the pump has to do much less work.  If the pressure were the same on both sides of the volume V, then the net force would be zero, and the volume of water would continue to move with constant velocity.  However, there will still be a small pressure gradient due to frictional forces.  The pump now only has to do work against frictional forces.  In a frictionless environment the pump would be no longer needed to keep the water flowing.  Such a frictionless environment can actually be created.  While most liquids freeze at near zero absolute temperature, liquid helium becomes a superfluid.  It flows without friction. You do not need a pump to keep a superfluid liquid Helium fountain operating.