# Bernoulli

## Head, Pressure and Mr. Bernoulli 16-08

The term “pressure” can be a little confusing because the units we use to measure pressure change in various parts of the world. Here are a few units you could encounter in your travels:

- Psi.
- Bars
- kiloPascals
- Kilograms per square centimeter.
- Atmospheres

To clear up the confusion there are various charts available to help you make the conversion from an unfamiliar unit to a more familiar one. As an example: psi/14.7 = Atmospheres. Regardless of the units used, they all have one thing in common and that is that pressure is read with a gage of some type.

If you are new to centrifugal pumps, you must be confused by the industry’s referral to “head” instead of the more comfortable term “pressure”. The units for head are normally feet or meters, but any units of length could theoretically be used. And to compound the problem, there are no gages that read directly in units of head. So why do pump people stick with a term that makes little to no sense?

The simple answer is because they have to. They have no choice!

Put a weight on the end of a string, spin it around a let it go straight up into the air. It will rise to a certain height or head. The longer the string, and the faster you spin it, the further up it will go. That’s what a pump impeller does. It spins and gives speed or velocity to the fluid entering the pump. Pretend for a moment that the discharge of a centrifugal pump is pointing straight up into the air. The bigger the impeller and the faster the rpms, the higher it will throw the liquid. The maximum height an impeller will throw the liquid is called its shutoff head.

Please take a look at the following diagram:

This diagram describes a static head of fluid. The static head measures 100 feet from the top of the fluid to the center of the gage. Please note that the measurement is taken to the center of the gage not the base of the tank. The pressure gage will convert this head or height to a pressure using the following formula:

p = pressure in psi.

h = height in feet

sg .= specific gravity of the fluid

2.31 = a conversion factor. (2.31 feet of fresh water equals 1 psi.)

Now, take a look at the next diagram

The liquid is now flowing out of the tank, but an equal amount is entering the top. The head is the same, but you will notice that the gage is reading less pressure.

What happened?

Some of the head has been converted into fluid velocity. If you want to know how much head was converted you can use the following formula:

h=- head

V= velocity (feet per second)

G= 32.2 feet per second^{2}

This means that if you want to calculate the head in a pumping system, reading the gages and converting the pressure reading to head is not good enough. You must also add the velocity of the fluid, converted to head.

All of this discussion leads us to Mr. Bernoulli and his famous equation. Bernoulli simply stated that the head or pressure is equal everywhere in a piping system It is always a combination of both the dynamic and static head. There are several versions of this equation published so please note that in the following one the term specific gravity (sg) has been replaced with density (d).

In USCS units:

In SI or metric units

The individual terms mean:

144p/d= static pressure head or 0.102p/d= static pressure head

c^{2}/2g =dynamic head

y = elevation (feet or meters)

g = gravity (32.2 ft/sec^{2} or 9,8 meters/sec^{2})

c = velocity (feet or meters/ sec.)

p = pressure (lb/in^{2} or kPa)

d = density (lb/ft^{3} or kg/l)