Affinity Laws Affecting Gage Datum

[Pumpguy2000]

I have a question related to testing a vertical multi-stage pump when pumping clean water. The Hydraulic Institute calculates Total Head by adding gage pressure, gage datum, and velocity head. If the pump test is performed at 1200 rpm and we wish to know the calculated results for 1800 rpm, would you calculate the Total Head, and then apply the affinity laws? For example, (200' + 5' + 10')[(1800/1200)^2]= 483.75. That makes sense to me. However, I am being told that the gage datum and velocity head are not affected by changes in rpm and therefore should be added after the affinity laws are applied to the gage pressure. For example, (200')[(1800/1200)^2] + 5' + 10'= 465'. Can anyone show proof of the explanation please.

 

[Artisi]

Why would gauge datum be included, this is the gauge position in relation to the pump centreline, is it not?

If you have a pump test curve at 1200RPM and you are going to operate the pump at 1800RPM (assume this is / had been ok'd and confirmed by the manufacturer) the pump new performance is H = N2/N1^2, Q = N2/N1 and power P = N2/N1^3, gauge point and V are operational considerations and nothing to do with the pump hydraulic performance.
If BEP head is 200ft at 1200RPM then at 1800 it becomes 450ft, what you measure on a site test has to be accounted for and corrected back to the pump centreline.
For an accurate assessment you need to post the installation detail / drawing, a performance curve together with full operating conditions including system losses etc as you can not base the change to the pump operating only on head change.

You also need to bear in mind that power changes as the cube of the speed change.

Have you asked the pump manufacturer for a 1800RPM curve?

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

 

[Pumpguy2000]

Let me further explain the situation and it will make more sense. I am referring to data that is collected in a test lab and trying to calculate the 1800 rpm performance of a bowl assembly based on 1200 rpm test results. The equation being used is shown below along with a Figure copied from Pumps.org:

Note that the height of the gauge above the first stage impeller must be measured as well as the inside diameter of the column pipe. The total head with water can then be calculated as follows:

Hba = 2.31pgba + Zd – Zw + vd2/2g where:

Hba = bowl assembly head – feet of water

pgba = discharge gage pressure-psi

Zd = height of discharge pressure gage above first stage impeller datum – feet

Zw = height of water level above first stage impeller datum– feet

vd = liquid velocity in column pipe – feet/second