If I need to calculate the head coefficient using $c_h=\dfrac{gH}{N^2D^2}$ and the volume coefficient using $c_q= \dfrac{v}{ND^3}$ while keeping $N$ (impeller rotational speed in rpm), how can I make the units cancel out and have a dimensionless answer?

I am measuring $D$ (impeller diameter in meters), $g$ (gravity m/s^2), $H$ (total pressure head in meters), $V$ (volumetric flow rate in m/s).

I made it dimensionless by changing RPM to 1/s, however I have been asked to keep RPM and change the other units, can someone plz help.


Volumetric flow rate is not m/s, it is m^3/s...

But if you want rpm in minutes then have the volumtric flow rate in m^3/minute.

This is just balancing units.

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  • $\begingroup$ Yes sorry my mistake, volumetric flow rate was measured in Liters/second. So if I convert l/s to m^3/min, do the units cancel out? $\endgroup$ – Shahad Feb 24 '19 at 9:28
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    $\begingroup$ What is the difference between minutes and seconds? You should be able to cancel units... This is dimensional analysis 101... $\endgroup$ – Solar Mike Feb 24 '19 at 9:33
  • $\begingroup$ I mean will 1/rpm cancel with minutes? Since I'm confused about the concept of rpm . I know its #of revolutions per minute. r/min. but do revolutions have units? $\endgroup$ – Shahad Feb 24 '19 at 10:17
  • $\begingroup$ Think of rpm is (1/min) $\endgroup$ – Solar Mike Feb 24 '19 at 10:18
  • $\begingroup$ Why not put all the terms into the equation, replace each with their units (ie Mass, Length or Time) and show they cancel out... $\endgroup$ – Solar Mike Feb 24 '19 at 10:22

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