Wire-to-Water Efficiency of Pumping Systems 2

[IBechir]

Greetings

Can anyone tell me how equation (2) was derived in the following article? The equation is regarding the wire-to-water efficiency of a multiple pump, constant speed pumping system. I am not sure how the pressure-head ratio fits in. The product of the pump and motor efficiency is obvious.

bookstore.ashrae.biz/journal/download.php?file=Rishel.pdf

The article is from the ASHRAE Journal so the application is for hot and chilled water circuits.

Thank you

 

[LittleInch]

Link doesn't work. Why not just type the equation out.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[bimr]

One thinks the point being made by the author is that if the pump fittings and pump header are included on multiple pump systems, the calculated pumping efficiencies will be lower in comparison to pump systems with a single pump. So, it would not be possible to compare pump efficiencies of multiple pump and single pump applications. Refer to Figure 9.

In the real world, the pump fitting and pump header friction losses should be a small fraction of the total pumping friction loss anyway, so it probably does not matter.

 

[IBechir]

The link works for me but here is the excerpt in question:

The wire-to-water efficiency of a multiple
pump, constant speed pumping system
is:​

WWE = ( H_s - H_pf ) / H_s x E_m x E_p

where,
Hs = Total friction loss of the water system
in feet of head
Hpf = Friction loss in feet of head of the
pump fittings including strainers, check
valve, shut-off valves, and the header
losses that direct the flow into and from
each pump.
Em = Motor Efficiency as a fraction
Ep = Pump Efficiency as a fraction​

 

[bimr]

If the link is cut and pasted, it works.

The formula was copied incorrectly. It should read:

WWE = (( Hs - Hpf ) / Hs) x Em x Ep