Pump Head and Flow: What Equation?

I once did a curve fitting using H = H0 - mQ^c for a short range of the curves .

The results were rather good.

If you're fitting an equation by known points, you could do it by try, it's just that simple.

In excell, pay close attention to number formats found in the regression. It tends to hide significant digits, and the result may not be so good as you expect.

Instead of excell, have you tried curvexpert ? Try it...

However, I'd expect at a minimum a power of two, because flow in respect to head loss is not linear over the entire pump curve. It's more like an inverted quadratic or so...

You can sometimes get a reasonable fit by the general equation:

H=A x n^2 + B x n x Q + C x Q^2

H= Head

Q = Flow Rate

n = Speed

A, B and C are constants determined by solving 3 simultaneous equations from your data.

Otherwise as already suggested, use Excell curvefit, picking one of the options given in the menu. Dont forget to show the equation and the R squared value on the graph (from the options tab on the curvefit menu). Ideally R squared should be 1 for an exact fit, but I have never come across as good a fit as this.However, the R squared value gives you a good idea how good the fit is.

Sorry,

I might have confused you with saying Excell curvefit. In actual fact I was referring to the 'add trendline' option when you have plotted your curve in Excell

yes, I use add trendline function in excel by choosing polynomial. But I wonder that what order is suitable in this case.

I think that your best bet would be to keep trying different orders (I think trendline goes up 6) or different equation types from the menu. As well as looking, pick the one with an R squared value closest to 1. Use the equation given by trendline to calculate the values and see if they are accurate enough. You need to remember to tick the 'display equation' and 'show R squared' on the options tab in 'add trendline' (I usually forget the first time)

Head in feet x Gallons per Minute / 3960 = Hp @ 100% Efficiency.

That Hp (55) / the pump efficeincy (75)% , 55hp/.75= 73.33 = Pump Shaft Hp