# head coefficient and volume coefficient for centrifugal pump

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.

• 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? – Shahad Feb 24 at 9:28
• What is the difference between minutes and seconds? You should be able to cancel units... This is dimensional analysis 101... – Solar Mike Feb 24 at 9:33
• 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? – Shahad Feb 24 at 10:17
• Think of rpm is (1/min) – Solar Mike Feb 24 at 10:18
• Why not put all the terms into the equation, replace each with their units (ie Mass, Length or Time) and show they cancel out... – Solar Mike Feb 24 at 10:22