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# Pressure

Pressure is the amount of force that presses on a particular area. The bigger the force or the smaller the area, the bigger the pressure is. For example, the pressure on your toes is different when you are standing normally and when you are standing on tiptoe. When you are standing normally, your weight is spread over the whole bottom of your foot. This means that the pressure on each small area of your foot, such as the bottoms of your toes, is quite small. But if you stand on tiptoe, all your weight is on your toes. So the same force is spread over a much smaller area than before. The pressure is higher and it quickly begins to hurt.

## Definition

As always in physics, we want to measure the squeeze, to assign a number to it. We could use a device like the little can: The amount the spring is compressed is a direct measure of how much squeeze there is. But that is not so good, because, as we just saw, the observed result depends on how big the can is. A better measure is the ratio of the force to the area of the can cover. This will work because even though the force on the can and the amount of compression of the spring goes to zero as the area of the lid goes to zero, the ratio of force to area approaches a definite value. This is both conceptually and practically useful, and therefore, we define pressure $P$ to be the ratio of the force $F$ to the small area $A$ on which it acts perpendicularly,

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

Because of this definition, we use "force per unit area" as a measure of pressure.

## Units

Pressure is the normal force exerted by a system against unit area of the boundary surface. The unit $pf$ pressure depends on the units of force and area. In $SI$ system, the practical units of pressure are $N/mm^2$, $N/m^2$, $kN/m^2$, $MN/m^2$ etc.

A bigger unit of pressure known as bar, such that

$1\ bar$ = $1\ \times\ 105\ N/m^2$ = $0.1\ \times\ 106\ N/m^2$ = $0.1\ MN/m^2$
Other practical units of pressure are Pascal $(Pa)$, kilopascal $(kPa)$ and mega Pascal $(MPa)$, such that

$1\ Pa$ = $1\ N/m^2$

$1\ kPa$ = $1kN/m^2$ = $103\ N/m^2$

$1\ MPa$ = $1\ \times\ 105\ N/m^2$ = $103\ kPa$ = $1\ N/mm^2$

## Types

The pressure under your feet can compress soft ground so that your feet sink in. The pressure of the air can push mercury up an evacuated barometer tube or crush an evacuated can. The pressure of water can throw a fountain high in the air. The increased pressure inside a pressure cooker makes the food cook more quickly at a higher temperature and the high air pressure inside a bicycle or car tire helps it support a heavy load. In these examples the word pressure is being used correctly, but in everyday language it is often used more freely and incorrectly to mean force. Many techniques are available for the measurement of pressure. The more common pressure measuring instruments include liquid manometers, Bourdon tube pressure gauges and pressure transducers. These instruments, in general, measure the gauge pressure, which is the difference in pressure between a fluid and the surrounding atmosphere.

Vapor pressure

Vapor pressure is defined as the pressure exerted when a solid or liquid is in equilibrium with its own vapor at a specific temperature, that is, as many molecules of the solid or liquid are going into the vapor state as there are vapor molecules condensing into the solid or liquid state. If a solid or liquid is placed in a closed container and the container is evacuated, some of the solid or liquid vaporizes. As long as some of the solid or liquid is still present, the pressure in the container represents the vapor pressure of the compound at the temperature of the measurement. Vapor pressures vary with temperature but are independent of the external pressure.
Remember that the vapor pressure depends on:
• The kinetic energy of the molecules, and therefore is temperature dependent
• The intermolecular forces between the molecules

Vapor pressure is independent of external pressure because, for example, as the external pressure increases at a constant temperature, the number of moles in the vapor phase decreases as the volume decreases, so the vapor pressure remains the same.

Stagnation pressure

The stagnation pressure is an indication of the entropy level of the fluid. The change in stagnation pressure indicates increase in entropy due to irreversibility. The stagnation pressure is equal to the reservoir pressure, if the flow from the reservoir takes place isentropically. Then, the static pressure record of the fluid in the reservoir is the stagnation pressure of the flow, and hence can be easily measured. If, however, the flow is adiabatic due to frictional effect or shock wave effect, there will be entropy change and in such cases, the stagnation pressure will not be equal to the reservoir pressure. Stagnation pressure for such flows must be measured locally.
The stagnation pressure represents the pressure at a point where the fluid is brought to a complete stop isentropically. The sum of the static and dynamic pressures is called the stagnation pressure, and it is expressed as,

$P_{stag}$ = $P\ +\ \rho$ $\frac{V^{2}}{2}$

Fluid pressure

Swimmers know that the deeper an object is submerged in a fluid, the greater the pressure on the object. Pressure is defined as the force per unit of area over the surface of a body. For example, because a column of water that is 10 feet in height and 1 inch square weighs 4.3 pounds, the fluid pressure at a depth of 10 feet of water is 4.3 pounds per square inch. At 20 feet, this would increase to 8.6 pounds per square inch, and in general the pressure is proportional to the depth of the object in the fluid.
The pressure on an object at depth h in a liquid is
$P$ = $wh$
Where $w$ is the weight density of the liquid per unit of volume.

Liquid pressure

The thrust exerted by a liquid per unit area of the surface is called the pressure of the liquid or hydrostatic pressure.

Laws of liquid pressure

The five laws of liquid pressure are as follows:
• Pressure is same in all directions, about a given point within the liquid.
• Pressure at a point inside the liquid at a given depth increases with the increase in the density of the liquid.
• Pressure at a point inside the liquid increases with the depth from the free surface of the liquid.
• Pressure is the same at all points in a horizontal plane at a given depth in a stationary liquid.
• A liquid seeks its own level.

Negative pressures

If the area enclosed has high pressure than the surroundings, the air will blow from enclosed area to surroundings. This is the positive pressure. Whereas the negative pressure is just opposite to the positive pressure. If the pressure of the enclosed area is lower than the surroundings, the air will blow inside the enclosed area. This is because of the negative pressure.