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For a given pump moving water out of a container, how does the diameter of the pipe leaving the pump affect the mass or volume of water transferred in a given unit of time? We can make simplifications and assume that frictional losses are negligible.

My instinct is that more cross sectional area allows more water to flow though, but the speed at which the water flows will drop correspondingly, and the volumetric flow rate would be unaffected. After all, the pump does a given amount of work on the water, and that remains unchanged in these scenarios.

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  • $\begingroup$ Backpressure impacts pump performance in the real world. $\endgroup$
    – Jon Custer
    Commented Jan 6, 2023 at 19:35
  • $\begingroup$ What kind of pump? $\endgroup$
    – David White
    Commented Jan 6, 2023 at 19:55

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In steady state, at a given speed the pump operates at a point determined by the intersection of the pump head curve (pump head as function of volumetric flow rate) and the system head curve (elevation and friction loss in the system served by the pump). For a frictionless outlet pipe the system head curve is not changed so the pump flow rate is not changed, but the velocity in the pipe increases.

In reality, the greater velocity through the smaller pipe causes more friction loss which changes the operating point and more power must be supplied to maintain constant flow rate.

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