Math equation for the pump diagram 1

[Pucp]

Does anybody knows how to find the mathematical relations for the pumps diagrams. I want to find efficiency only with the information of pressure and flow rate, as an equation, but for that I have to introduce the diagrams as data for math equations. I can put the Pressure-flow rate curve in a math equation, but I will also like to do the same with the efficiency curve in order to have a equations that allows me to introduce two types of data (pressure and flowrate) and with that find the efficiency for every pump without having to read it from the diagram (less accurate). Thanks in advance.

 

[butelja]

The flow-head curve can be best fitted using a cubic least square's curve fitting algorithm. The power-flow curve can be best fit using either a linear or quadratic least square's curve fit of the data. Once these two curves are known, then efficiency is a simple calculation.

 

[MJCronin]

butelja,

Do you have a source or website for such (free I hope) curve fitting software ?

Any recommendations for the best programs to use ?

I have found your previous posts to be very informative and well thought out and I believe that you are an asset to this forum.......

Regards

MJC

 

[butelja]

MJC,

I have a Mathcad spreadsheet for extracting the curve fitting coefficients. If you have Mathcad, I can e-mail the file to you. For data input to that spreadsheet, I rely on output from pump vendor supplied pump selection software which gives tabular values for the performance curves, as well as graphic output.

If you have the cubic head-flow coefficients and use Crane Companion for fluid system modeling, then you can incorporate the pump into the fluid system model.

 

[gunnarhole]

The regression function in Excel (find it at Tools, Data Analysis, Regression) can handle these curves. Lotus 123 has a similar function. Excel does not load this function during a typical installation but it is available on the CD and can be easily installed.

Build a table with head/pressure in one column, efficiency in another, and capacity, capacity squared, capacity cubed and so on in additional columns as required. The regression function will return the constants necessary for computing the desired head or efficiency as a function of capacity, capacity squared and so on. I agree with butelja above that cubic functions will cover almost any pump you are interested in.

 

[Pucp]

Butelja, I will appreciate if you sent me those files in Mathcad format. I guess my answer is a lit bit late but better than never. Thanks in advance
My email adress is:
ian.zuazo@caramail.com

 

[PacificSteve]

I have used a program called Curvefit, free download 30 day shareware. Sorry, you have to find it on the web, I lost my link. Simple and intuitive.

I like the excel regression for a quick plot, but the coefficients do not show enough significant digits to allow you to plug these into other calculations. At the very least, test the exact coefficients you have developed by plotting them, as a reality check.

Aloha

 

[TD2K]

If you use Excel's regressions options, you can increase the number of digits to the right of the decimal place (I think the default is 2). Create the graph, for options ensure that you select 'show equation' and if you like 'regression coefficient'. Once the graph is finished, highlight the equation, 'format', 'cells' then pick 'number'. Enter in how many digits you want.

For most pump curves, I'll chose engineering notation with 3 or 4 digits to the right of the decimal point (you can add quite a few more if you want).

 

[tstead]

Here is what I do sometimes and it works out great in most instances...

Photocopy your curve and blow it up as much as possible.

Pick 5-6 *non-equally spaced* points on the curve and plug them into Excel in tabular format.

Plot the curve of the data points using the normal way of drawing a chart. Next, add a trendline to hte data series plot and adjust your function order appropriately.

Select the option, from within the trendline box, to display the function on the chart. Select the chart, right-click, change it's properties, and select "Scientific notation" with a good amount of decimal points to give you good accuracy.

Hide the original data plot by changing it's properties so that there is no line and there are no data markers.

Draw a nice-looking box aroun the curve you made, pretty it up a little and voila...you got yourself a cool looking curve. Best of all, all the functions you need are built into Excel.

Tim