**Pressure measurement**

Force (F) is equal to Pressure (P) multiplied by the Area (A):

F = P x A.

Pressure is equal to the Force divided by the Area:

P = F/A

If we apply pressure to the surface of a liquid, the pressure is transmitted uniformly in all directions across the surface and even through the liquid to the walls and bottom of the vessel containing the liquid (Pascal’s Law). This is expressed as pounds per square inch (lbs/in2, or psi), or kilograms per square centimeter (k/cm2).

**Atmospheric pressure (ATM)**

Atmospheric pressure (ATM) is the force exerted by the weight of the atmosphere on a unit of area. ATM = 14.7 psia at sea level. As elevation rises above sea level, the atmospheric pressure is less.

**Absolute pressure (psia)**

Absolute pressure is the pressure measured from a zero pressure reference. Absolute pressure is 14.7 psia at sea level. Compound pressure gauges record absolute pressure.

**Gauge pressure (psig)**

Gauge pressure is the pressure indicated on a simple pressure gauge. Simple pressure gauges establish an artificial zero reference at atmospheric pressure. The formula is: psig = psia - ATM.

**Vacuum**

The term vacuum is used to express pressures less than atmospheric pressure (sometimes represented as a negative psi on pressure gauges). Another scale frequently used is ‘inches of mercury’. The conversion is:

14.7 psia = 29.92” Hg. Another scale gaining in popularity is the kilopascal (Kp) scale. 14.7 psia = 100 Kp

Note that there are many ways to express vacuum. Simple gauges record vacuum as a negative psig. Compound gauges record vacuum as a positive psia. The weatherman uses inches of mercury in the daily forecast, and millibars (1000 millibars is atmospheric pressure) to express the low-pressure zone in the eye of a hurricane. Boiler operators use water column inches and millimeters of mercury to express vacuum.

Pump manufacturers express vacuum in aspirated feet of water in a vertical column (0 psia = -33.9 feet of water). The pharmaceutical and chemical industry uses ‘Pascals’ (100,000 Pascals = atmospheric pressure) and the term TORR. This conglomeration of values and conversion rates causes confusion. In order to understand pumps, it‘s best to think of vacuum as a positive number less than 14.7 psi. In our experience, we’ve found that considering vacuum in this form aids the understanding of net positive suction head (NPSH), cavitation, suction specific speed (Nss), and the ability of pumps to suck-up (actually pumps don’t suck, but this will do for now) fluid from below. Remember that vacuum is the absence of atmospheric pressure, but it is not a negative number.

**Pump head**

The term ‘pump head’ represents the net work performed on the liquid by the pump. It is composed of four parts. They are: the static head (Hs), or elevation; the pressure head (Hp) or the pressures to be overcome; the friction head (Hf) and velocity head (Hf), which are frictions and other resistances in the piping system. The head formula is the following:

H= P/D

Where: H = head P = psi d = density

Pressure can be converted into head with the following equation:

Head ft = (2.31 x Pressure psi)/sp.gr.

Where:

H = head in feet

2.31= conversion factor

psi = pressure in pounds per square inch

sp. gr. = specific gravity

Head converts to pressure with the following formula:

Pressure psi = (Head ft x sp.gr.)/2.31

**Specific gravity**

Specific gravity is the comparison of the density of a liquid with the density of water. With pumps, it is used to convert head into pressure. The specific gravity formula is:

Sp.Gr = Density Liquid/Density Water

The standard for water is 60°F at sea level.

Water is designated a specific gravity of 1.0. Another liquid is either heavier (denser) or lighter than water. The volume is not important as long as we compare equal volumes. The specific gravity affects the pressure in relation to the head, and it affects the horsepower consumed by the pump with respect to pressure and flow.

**Pressure measurement**

**Pressure exists in our daily lives. At sea level the atmospheric pressure is 14.7 psia. This is the pressure exerted on us by the air we breathe. If we should remove all the air, then the pressure would be zero.**

We’re more concerned with pressures above atmospheric pressure. For example, a flat tire on a car still has 14.7 pounds of pressure inside it. We would consider this to be a flat tire because the pressure outside the tire is equal to the pressure inside the tire. We would say the tire has no pressure because it would not be inflated and could not support the weight of the car.

What is more important to us is the differential pressure inside the tire compared to outside the tire (atmospheric pressure). For reasons such as these, the world has adopted a second and artificial zero, at atmospheric pressure as a reference point. This is why a simple pressure gauge will read zero at atmospheric pressure.

Because simple pressure gauges are made with an artificial zero at atmospheric pressure, this is why the term psig exists, meaning pounds per square inch gauge. As mentioned earlier, the psig is equal to the absolute pressure minus the atmospheric pressure.

Psig = Psia - ATM

Pressures less than atmospheric are recorded as negative pressures (-psi) on a simple pressure gauge.

Technically speaking, negative pressures don’t exist. Pressure is only a positive force and it is either present or absent.

**Pressures inside the pump**

__Suction pressure__

Suction pressure is the pressure at the pump’s suction nozzle as measured on a gauge. The suction pressure is probably the most important pressure inside the pump. All the pump’s production is based on the suction pressure. The pump takes suction pressure and converts it into discharge pressure. If the suction pressure is inadequate, it leads to cavitation. Because of this, all pumps need a gauge at the suction nozzle to measure the pressure entering the pump.

__Discharge pressure__

This is the pressure at the pump discharge nozzle as measured by a gauge. It is equal to the suction pressure plus the total pressure developed by the pump.

__Seal chamber pressure__

This is the pressure measured in the stuffing box or seal chamber. This is the pressure to be sealed by the mechanical seal or packing. The seal chamber pressure must be within the limits of the mechanical seal. This pressure is very important with double mechanical seals, because it governs the pressure setting of the barrier fluid.

**Head versus pressure**

Figures above show the relationship between head and pressure in a centrifugal pump moving liquids with different specific gravities.

The above graphic shows three identical pumps, each designed to develop 92.4 feet of head. When they pump liquids of different specific gravities, the heads remain the same, but the pressures vary in proportion to the specific gravity.

In the last graphic above, these three pumps are developing the same discharge pressure. In this case they develop different heads inversely proportional to the specific gravity of the fluids.

Given the following information:

sp. gr. of water = 1.0

sp. gr. of gasoline = 0.70

sp. gr. of concentrated sulfuric acid = 2.00

sp.gr. of sea water = 1.03

A pump capable of generating 125 feet of head would provide the

following pressures:

Pressure = (Head ft. x sp.gr.) / 2.31

P water = 54.1 psig

P gasoline = 37.8 psig

P concentrated sulfuric acid = 108.2 psig

P sea water = 55.3 psig

This pump (see Figure below) is raising the liquid from the level in the suction vessel to the level in the discharge vessel. This distance is called the Total Head.

The total head is:

- The work of the pump.
- The measure of the pump's ability to raise the liquid to a given height.
- The measure of the pump's ability to develop a given discharge pressure.
- The discharge elevation minus the suction elevation.
- The discharge head minus the suction head.
- The discharge head plus the suction lift.
- The discharge absolute pressure reading minus the suction absolute pressure reading.

__Suction head__

The suction head is the available head at the suction nozzle of the pump.

__Discharge head__

The discharge head is the vertical distance from the centerline of the pump (this would be the shaft on a horizontal pump) to the level in the discharge vessel.

__Suction lift__

Suction lift is negative suction head. It exists when the liquid level in the suction vessel is below the centerline of the pump. The pump must aspirate the liquid up from the suction vessel into the pump and then push the liquid up into the discharge vessel. This pump (See Figure below) is said to be in suction lift.

In this case, the pump must aspirate or lift the liquid up from the suction vessel into the pump and then push the liquid up into the discharge vessel. In this case the total head is the discharge head plus the suction lift. In all cases the total head is the work being performed by the pump.

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