## What is Pressure?

Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.

## Absolute Pressure

When there are many forces acting on a body the total pressure on the body is called absolute pressure is defined with respect to perfect vacuum which is assumed to be at zero pressure. The vacuum is defined to be absolute zero, so the absolute pressure cannot be negative.

## Gauge Pressure (Overpressure)

Gauge in English means measurement (up to linear order) according to some standard system. So Gauge pressure is the pressure measured relative to atmospheric pressure (or any other finite value other than a vacuum that has zero pressure). Since it is a relative quantity, it can be either positive or negative depending upon the absolute pressure being measured is lesser or greater than the atmospheric (ambient air) pressure. So, the absolute pressure can be defined as the

sum of gauge pressure and atmospheric pressure, i.e. ${P}_{abs}={P}_{gauge}+{P}_{atm}$

Usually denoted by P, the pressure exerted is given by the formula,

$P=\frac{F}{A}$

Where F is the total force and A is the surface area. It is a scalar quantity with dimensions ML^{-1}T^{-}^{2} and has SI units **Pascal. **One Pascal is one Newton per square meter acting perpendicular on the surface. Other commonly used units of pressure are,

- 1 torr=133.3 Pa
- 1 psi=6900 Pa
- 1 atom=101325 Pa

In these units, a postfix (a for absolute, g for gauge) can be added to describe the kind of pressure being mentioned. For example, psia stands for absolute pressure in units psi, whereas psig would mean gauge pressure in units psi.

If the fluid is at rest, it exerts a uniform pressure in all directions on the walls of container known as **Hydrostatic Pressure**, this makes static pressure measurement independent of direction at a point, the origin of hydrostatic pressure lies in the gravitational pull on each volume element of the fluid, so as one goes deep into the fluid the pressure increases as there are more and more fluid molecules are piling up and contributing to the net force on a given point. The pressure exerted at a point which is at a distance of h below the surface in a fluid with density ρ is given by P=ρ gh

However, in the case of flowing fluid, there is an additional contribution to pressure in the direction parallel to the flow due to the flow of fluid which is known as **Dynamic Pressure**. Dimensionally it is equal to Kinetic Energy density and is given by the formula,

${P}_{dynamic}=\frac{1}{2}\rho {v}^{2}$

v is the velocity of flowing fluid.

As the dynamic pressure is proportional to velocity, faster the flow higher the pressure.

## Pressure Measurement

The device used to pressure measurement is known as a **pressure gauge**. The pressure gauge works on the principle that when a system which can interact with surroundings with pressure takes on different states when the gauge pressure (or equivalently absolute pressure) varies. Some pressure measurement equipment's are discussed below:

### Manometer

One of the simplest pressure gauge is a manometer, which is essentially a U-shaped glass tube partially filled with liquid, one of the characteristics of a manometer is its inherent accuracy and simplicity of operation as it has no moving parts and requires no calibration. This comes in handy when there is a referential pressure value available (0 for vacuum)

When both the legs of the U-Tube are open to the atmosphere, the height of liquid in both legs are equal, as the atmospheric pressure is the same for both, this establishes zero references (this is just zero references of the referential scale, not the vacuum zero).

To measure the gauge pressure, one of the legs of the U-tube is connected to the region of where pressure is to be measured and other is left open to the atmosphere (if one side is towards vacuum, then observed pressure is absolute pressure), in this setup the difference in heights of the columns are measured towards pressure measurement.

For instance, if one leg is in higher pressure region than atmospheric pressure, this will result in lowering of the liquid level in that leg and an equal rise in the leg connected to the atmosphere,

The pressure exerted by liquid column is given by,

$P=\rho g({h}_{2}-{h}_{1})$

- ρ is the density of fluid
- g is the gravitational acceleration
- h is the height of the liquid column.

### Aneroid Gauges

Aneroid basically means “without fluid”, these pressure gauges are based on metallic pressure-sensors that can flex elastically when there is a pressure difference across, they are independent of the type of gas whose pressure is being measured and are less contaminating than other hydrostatic gauges.

### Diaphragm Sensor

Another pressure gauge uses a diaphragm sensor (pressure sensor), where one side is exposed to a pressure medium to be measured and another side exposed to ambient atmospheric pressure.

### Bourdon Tube

The most prevalent pressure measuring device today is **Bourdon Tube, **which measures Gauge pressure from 0.6 to 7000 bar. Bourdon tubes are radial tubes with a cross-section that is oval in shape. This tube produces a motion in the non-clamped end of the tube.

For low-pressure measurement of about 60 bar a C-shaped Bourdon tube with angle about 250° can be used but for higher pressure range, the bourdon tubes with many windings with the same angular diameter or a spiral coil in one the plane is used.

Standard Bourdon tube pressure gauges are suitable for a gaseous medium that is not crystallizing and have low viscosity, as long as they don’t corrode the material of the tube. Stainless steel is the material of choice when it comes to manufacturing corrosion-resistant Bourdon tubes which can read Gauge pressures up to 7000 bar, the condition of low viscosity and non-crystallizing media remains the same.

## Atmospheric Pressure in Units of Mercury Column Length

Mercury being liquid metal at room temperature, it has high density which makes it fluid of choice for measuring high pressures (like atmospheric pressure) within reasonable column height.

The density of mercury is 13600 kgm^{3}, 1 atom=101325 Pa (14.7 psi) and g=9.8 ms^{2}, which gives 1 atom in terms of mercury column height as,

$\begin{array}{c}h=\frac{101325}{13600\times 980}\\ =76\text{cm}\end{array}$

Which means 76cm of mercury exerts a pressure (with respect to vacuum) equal to that of atmospheric pressure i.e. 1 atom, which is a nominal height range for the column for a rather large value of pressure 1atm=101325 Pa=14.6 psig.

## Formulas

$\begin{array}{c}{P}_{abs}={P}_{gauge}+{P}_{atm}\\ {P}_{hydrostatic}=\rho gh\\ {P}_{dynamic}=\frac{1}{2}\rho {v}^{2}\end{array}$

## Common Mistakes

- One of the things to be paid attention to is that Gauge pressure should not be used in ideal gas law calculation as it is not the true pressure, it is just a reference pressure.
- When measuring gauge pressure, note that the measured gauge pressure value varies with changes in weather pattern unless the measuring point is left open and measures the atmospheric pressure.

## Context and Applications

- The common way of measuring blood pressure is in terms of mercury column height, normal blood pressure is 80mm Hg to 120 mm Hg, meanwhile, measurement of central venous pressure and lung pressures in centimeters of water is still common in many parts of the world.
- Air brake systems on trucks are inspected via Pressure gauge.
- Water jet cutting and high-pressure cleaning use a Bourdon tube pressure gauge.
- The oil pressure gauge is one of the essential instruments in car and other vehicles, it indicates the overall engine’s health and as an early-warning system giving notice of any problems in advance, the oil pressure in the engine is monitored by a pressure gauge in one of the main oilway that is near to the pump.

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

- Bachelors in Technology (Mechanical Engineering)
- Masters in Technology (Mechanical Engineering)
- Bachelors in Technology (Civil Engineering)
- Masters in Technology (Civil Engineering)
- Bachelors in Science (Physics)
- Masters in Science (Physics)
- Bachelors in Technology (Automobile Engineering)
- Masters in Technology (Automobile Engineering).

## Related Concepts

- Gauge
- Vacuum Engineering
- Piezometer
- Tire-Pressure Gauge
- Force Gauge

## Practice Problems

Q 1.Find the gauge pressure and absolute pressure on a diver who is 10 meters below the surface of the ocean. Assume standard atmospheric conditions. Use the density of seawater = 1000kg/m^{3} and the atmospheric pressure of 101.325 kPa.

Solution: The gauge pressure due to water in ocean is given by,

$\begin{array}{c}{P}_{gauge}=1000\times 9.8\times 10\\ =98\times {10}^{3}\text{Pa}\end{array}$

The atmospheric pressure is $101.325\text{kPa}(101.325\text{}x{10}^{3}\text{Pa})$so the absolute pressure is

$\begin{array}{c}{P}_{abs}={P}_{atm}+{P}_{gauge}\\ =(98+101.325)\times {10}^{3}\\ =199.325\times {10}^{3}\text{Pa}\end{array}$

Q 2.Intravenous administration is usually done with the help of the gravitational force. If the density of the fluid being administered is 1g/ml, what should be the height of IV bag be if fluid just enters the vein if the blood pressure in the vein is 18 mm Hg above atmospheric pressure? Assume that the IV bag is collapsible.

Solution: If the fluid has to just enter the vein, the pressure exerted at the entry point must exceed the blood pressure, therefore the height of the IV bag needs to adjusted such that the absolute pressure of the fluid is greater than the absolute pressure of the blood or in other words the gauge pressure must be positive.

Firstly, the pressure of 18 mm Hg column in SI units is, $1\text{mmHg=133Pa}$

$\begin{array}{c}{P}_{18mm}=\frac{18\text{mm}\times 133\text{Pa}}{1\text{mm}}\\ =2400\text{Pa}\end{array}$

So the height of IV bag required such that the pressure the gauge would register a positive value is (i.e. the fluid pressure would be greater than blood pressure)

$\begin{array}{c}h=\frac{2400\text{Pa}}{9.8{\text{m/s}}^{\text{2}}\times 1\times {10}^{3}{\text{kg/m}}^{\text{3}}}\\ =0.24\text{m}\end{array}$

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