## [Centrifugal?] Fan [Pump] Laws

## [Centrifugal?] Fan [Pump] Laws

(OP)

Hey all,

For those like me who don't quickly/readily intuit the fan/pump laws just from looking at a formula, I here include a summary as found in Steam Power Stations, copyright 1937, 1940, 1946 by the McGraw-Hill Book Company, Inc., pg. 403.

If any of this is incorrect, I'm sure someone will say so...

1. Capacity varies directly as speed.

2. Head varies as speed squared.

3. Horsepower varies as speed cubed.

For constant pressure, density, and point of rating where fan size varies:

1. Capacity and horsepower vary as the square of the fan size.

2. Speed varies inversely as the fan size.

For constant capacity and speed where density of air varies:

1. Horsepower and pressure vary directly as the air density, i.e. directly as the barometric pressure and inversely as the absolute temperature.

For those like me who don't quickly/readily intuit the fan/pump laws just from looking at a formula, I here include a summary as found in Steam Power Stations, copyright 1937, 1940, 1946 by the McGraw-Hill Book Company, Inc., pg. 403.

If any of this is incorrect, I'm sure someone will say so...

1. Capacity varies directly as speed.

2. Head varies as speed squared.

3. Horsepower varies as speed cubed.

For constant pressure, density, and point of rating where fan size varies:

1. Capacity and horsepower vary as the square of the fan size.

2. Speed varies inversely as the fan size.

For constant capacity and speed where density of air varies:

1. Horsepower and pressure vary directly as the air density, i.e. directly as the barometric pressure and inversely as the absolute temperature.

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

## RE: [Centrifugal?] Fan [Pump] Laws

It is correct but "capacity" is vague and I prefer to substitute "volume flow rate" or Q

It is also easy to misapply. It is intended as a similarity transformation in which all variables are mapped. So let's say you have a curve of Head vs volume flow rate at a given speed, then you can transform it to a curve of head vs volume flow rate at another speed by mapping each point on the old curve (Q1,H1) to a point on the new curve (Q2,H2).

Where you can run into trouble in potentially misapplying the laws is trying to just change one of these varuables without changing or considering the others. An example of that is trying to figure out what happens to a fixed-resistance system volume flow rate if you increase centrifugal pump speed by 10%. You may be tempted to say that it increases by 10%, but the answer is that it depends on the system characteristic. We only know what happens to the pump curve and to know what happens operating point, we have to look at change in the interesection of pump curve and system characteristic curve. It turns out (easy to see with a little thought) that flow rate at operating point of a fixed system would change proportionally to speed if and only if the system characteristic obeys head proportional to volume flow rate squared. A closed loop system dominated by turbulent flow resistance would match this required system characteristic, an open system or laminar flow or oddball choked flow would generally not meet the required system characteristic.

By the way this is more a pump forum question than a motor forum question.

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(2B)+(2B)' ?

## RE: [Centrifugal?] Fan [Pump] Laws

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

## RE: [Centrifugal?] Fan [Pump] Laws

With Pete's permission, your post and Pete's response will make a great FAQ.

You may wish to point out that the pump laws are limits for a linear system, operating within the mostly linear portion of the pump curves.

Performance may be degraded if a change moves any parameter outside of the range of linearity of either the pump curve or of the system characteristics.

Anecdote on:

I had a problem with some pumps when the discharge was moved further up the mountain to a point that almost equalled the maximum head of the pumps.

With one 15 HP pump running, the discharge was a trickle.

With both pumps running, the flow through each pump was further reduced due to increased dynamic friction.

The flow through the pumps with both pumps running was so little that churning was generating enough heat to boil the sewage in the pumps. If the priming vents were opened they blew steam and the paint was burning off of the pumps.

Solution #1: A pump shop assembled a belt driven pump with a 30 HP motor. The belt drive increased the available head of the pump so as to get back into the mostly linear portion of the pump curve.

Issue and solution #2: We still needed a backup system. The organization was out of money but had competent volunteer labour available. The original two 15 HP pumps were plumbed in series. This put them back into the mostly linear portion of the pump curves and the performance (as judged by the pump-down time) was similar to the new 30 HP pump.

In support of Pete's comments;

This is a good example of the pump laws failing when the operation was moved outside of the region of linearity but again becoming valid when the operation was moved back into the region of linearity.

Bill

--------------------

"Why not the best?"

Jimmy Carter

## RE: [Centrifugal?] Fan [Pump] Laws

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]