Flow is dependent on the system.
Both centrifugal and PDs have pump "curves", see attached, that can vary significantly with RPM. Of course the curve in a PD pump is more of a straight line with negative slope.
While it is true that a pd pump running at constant speed has relatively little variation in flow (when talking about a "normal" system curve), varying RPM affects flow in a centrifugal pump, a pd pump and the system.
The operating point depends on BOTH pump and system characteristics for either type of pump.
The only problem with a PD pump is there is no problem.
Draw the curves for variable speeds and you will see that you can get from 0 to runout flows in either type of pump.
Because of the relatively limited flow range with a fixed speed PD pump, a flow control valve on a fixed speed PD is virutally useless, which is why most drives for PDs are variable. A variable speed device combined with a control valve is belt and suspenders in most cases. Simply not needed. RPM can be varied to accomplish the same thing. jThey might be of use, if system head changes radically and fast, where a valve might be adjusted more quickly than the motor rpm, but I would think that circumstance is probably rare. A pressure control valve (used as a relief valve), does make sense.
It would also make little general sense to use a valve with a centrifugal pump with a VFD. Belt and suspenders again.
Flow control valves with a fixed speed centrifugal pump does make sense, due to the high flow variations possible, but used a a pressure control valve, probably is not necessary, as long as the system will tolerate the pump's shutoff pressure.
The secret to knowing what type of pump to use and what valve, if any, or if you need VFD or not, is to look at BOTH the system curve(s) and the pump curve(s), whether its a centrifugal or PD pump, the answer is there, right at the operating point(s) <where both curves intersect>.
If you look at the attachment of curves for a generic PD and centrifugal pump, combined with the flowrates you know that you must be able to run, everything becomes quite apparent.
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"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that
99% for pipeline companies)