I'm new to to pump selection and engineering (as well as the forum).  I have heard and read the term "pump run back" and am looking for an explanation of the term.  A specific instance of use is "When the recirculation valve closes the pump will initially run back on its curve to provide the required flow rate".  I understand as the valve closes the system head will increase but it seems this would cause the flow to decrease, not increase.  Is the statement incorrect or is there something I'm missing?  What exactly is meant by the term "run back"?

As 10p states, I also believe your description of the scenario was written by someone that made the logical assumption that, when running with the recirculation valve open, you were doing that because the system curve would not allow you to run into the system with that flowrate, so therefore you HAD to be recirculating.  Why recirculate otherwise.  If you could flow into the system, you should be doing that.  If you were recirculating for the fun of it, its costing you money.  

Thus the flowrate you were at during recirculation was higher than what you could do as you open the discharge valve and close the recirculation valve.

A typical scenario would be starting a diesel driven pump against a very high system head; pumping up the face of a steep slope to a city with a 1500 ft msl elevation.  The pump would probably have a discharge check valve to prevent backflow from the higher elevations whenever the pump was turned off.  Therefore, when starting the pump, no flow would be discharged until the pump discharge pressure reached the pressure on the check valve.  Something that would probably take most of the diesel's rpm to achieve.   During diesel rpm runup when below normal operating speeds, you couldn't flow into the system until you reached check valve backpressure and you would have to be recirculating during that time.  The second that the check valve opens, the system is at zero flow and the pump momentarily moves to zero flow too, until it can accelerate the system flow from zero flow and reach its new flowrate.  I would never want to disappoint Patricia, so here's the pump curve diagram.  The blue dots move from lower left to top right, deviating to the left when rpm reaches check valve opening pressure.  I should make one of those animated .gif pictures of this some day... soon.

In your example, 'run back on its curve' means exactly what vpl said, closing the valve means a higher head to overcome, so the operating point moves to the left on the pump curve, in order to meet the higher head requirement, and therefore the flow is less, exactly as you said.

Nothing in that sentence you quoted suggests that the flow will increase, the use of the phrase 'provide the required flow rate' suggests that closing the valve is being done to DECREASE the flow rate as required.

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