# HEAD V PRESSURE - TECHNICAL BRIEFING

12th Nov 2020

#### A History Lesson

Around 400 years BC the Greek Philosopher Aristotle proposed a theory that, if dropped from the same height, a 10 kg rock would fall twice as fast as a 5 kg rock or, indeed, 10 times faster than a 1 kg rock. Seems logical? Well, he had no real way of proving his theory but some 2,000 years later (in 1589) Galileo strove to disprove the theory and carried two objects of differing weights to the top of the leaning tower of Pisa (almost 200 ft high) and dropped them to find that both objects struck the ground at the same time. Thus, disproving Aristotle and, more importantly, proving that gravity is a constant force not related in any way to the mass of an object. Galileo continued experimenting and went on to prove that the acceleration of gravity is also a constant at 9.8m/sec2.

#### In Practice

So how does that help us in selecting pumps? Well, it naturally follows that if gravity is a constant then elevating an object against gravity must also be a constant when lifting 1 litre of water to 10 metres, or 1 litre of sulphuric acid or, indeed a litre of mercury. So, when a pump performance curve is marked in metres (or feet) head then that applies to all liquids, regardless of their density. However, when pressure in the form of psi (pounds per square inch) or bar, etc. is discussed then this factor includes the density (Specific Gravity) of the liquid in the equation:

#### Pressure = Head x Density (SG)

Going back to Galileo, think about him carry two objects, say a cannon ball and a musket ball, to the top of the tower. Did it take the same effort to carry the musket ball as it did the cannon ball? Obviously not, so it follows that density has a lot to do with the effort required which means that in fluid handling it will take more power to lift Sodium Hydroxide (SG: 1.5) than it does to elevate water (SG:1), precisely; if it takes 2kW to lift water then it will take 3kW (2kW x 1.5) to lift Sodium Hydroxide to the same height.

Every pump manufacturer worldwide produces performance curve reading in metres (or feet) head because it is impossible to know all the possible parameters for every liquid, or combination of liquids, so we need to convert all readings back to head, not pressure.

So, as we have determined that:                    Pressure = Head x SG

Then:                                                               Head = Pressure / SG

But so many people confuse head v pressure so it is always important to determine how they have made their calculation, particularly with liquids with a higher SG.

#### Worked Example

Say that we need to pump Sulphuric Acid with an SG of 1.25 to a storage tank 30 metres above the pump at a flow rate of 20 m3/hr. The discharge pipework has a series of elbows and valves resulting in friction loss of 1.25 m for water. We will not go over the specific calculation for friction loss here but please refer to our other Technical Briefings if you need more information.

Total Head = Static head (30m) + Pipework Losses (1.25m) = 31.25m

Pressure = Head (31.25) x SG (1.25) = 39.06

But what units is this in? Well, 1 bar = 10.2m so 39.06 / 10.2 = 3.83 bar pressure required.

To read from the pump curve we need to convert back to Head in metres so if a customer quotes that he needs a certain pressure from the pump we need to know the SG of the liquid. In this case we know it is 1.25 so:

Head = Pressure (3.83) x 10.2 / SG (1.25) = 31.25 m

To read from the pump curve we take a flowrate of 20m3/hr and read up to 31.25m to determine the impeller size, then read down to the power curve to find the absorbed power at the duty point. Remembering that Galileo exerted more force to carry his cannon ball up to the top of the tower, we then need to multiply the power absorbed by the SG.

`N.B All pump manufacturers performance curves are for clean cold water simply because it is impossible to produce curves covering all the possible liquids with their individual Specific Gravities.`

We often post articles and other news on our LinkedIn page like this head v pressure article, so please go and follow to keep up to date.