Math equation for the pump diagram
Math equation for the pump diagram
(OP)
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.





RE: Math equation for the pump diagram
RE: Math equation for the pump diagram
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
RE: Math equation for the pump diagram
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.
RE: Math equation for the pump diagram
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.
RE: Math equation for the pump diagram
My email adress is:
ian.zuazo@caramail.com
RE: Math equation for the pump diagram
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
RE: Math equation for the pump diagram
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).
RE: Math equation for the pump diagram
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