Dc motor load increase as rpm increases?

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mabuchi
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I have a dc motor geared to a diaphragm pump, and all hardware are unchanged.

As i increase the supplied voltage, rpm increases, but so does the current (torque).

I thought rpm increase would lead to higher back emf, and thus lowers the current. So would the only reason for my increased current be that the mechanical load increases as rpm increases?
 
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Yes, the mechanical load doesn't care about electrons: if the rpm increases on a pump, the pressure and power increase too - by square and cube funtions, respectively.
 
so if i were to use a different motor (other pump components unchanged) to achieve the same rpm as the current motor, does it need to have the same torque?

In other words, are rpm and torque tie together, so that you would need the same torque to achieve the same rpm for any motor (other pump components unchanged)?