Pressure

Pressure formula

So how do we calculate the concentration of force in a given area? Simple, we know that pressure is nothing but the force acting per unit area which in mathematical terms give

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

or in words

id="2827891" role="math" $\mathrm{Pressure}=\frac{\mathrm{Force}\mathrm{normal}\mathrm{to}\mathrm{the}\mathrm{surface}}{\mathrm{Area}}$

Pressure is expressed in Pascals ($\mathrm{Pa}$),$F$is the force in$\mathrm{N}$, and the area is measured in units of${\mathrm{m}}^2$.

These knives have different contact areas with the surface, the sharper knife exerts more pressure for a given amount of force because the force is acting over a smaller surface area, StudySmarter Originals

A pressure of$1\mathrm{Pa}$can be defined as a force of$1\mathrm{N}$acting on an area of$1{\mathrm{m}}^2$(unit area). The above formula is only valid when the force acts at right angles to the surface. As you can see from the equation. Pressure is directly proportional to the force applied and inversely proportional to the area on which it acts. This means that to increase the pressure we can either

• Increase the force keeping the area constant or

• Decrease the area keeping the force at a constant.

As the area of contact decreases, the pressure increases provided the force remains the same, this allows the nail to be driven into the wall, StudySmarter Originals

Units of pressure

The SI unit of pressure is$\mathrm{Pa}\mathrm{or}\mathrm{N}/{\mathrm{mm}}^2$1 Pascal =$1\mathrm{N}/{\mathrm{mm}}^2$. For large quantities of pressure, we can use $1\mathrm{kPa}={10}^3\mathrm{Pa}$and$1\mathrm{MPa}={10}^6\mathrm{Pa}$. You may also see other units of pressure such as torr, $\mathrm{barr},\mathrm{atm},\mathrm{psi}\mathrm{and}\mathrm{mm}\mathrm{Hg}.$

Types of pressure

We can categorise types of pressure in terms of the states of matter that are exerting the pressure. In this section we'll have a look at each of the types of pressure and some examples of each type too.

Pressure can be exerted by solids, liquids, and gases. Solids exert pressure through their point of contact. Liquids and gases exert pressure on a solid due to the collision of their particles with the solid.

The pressure exerted by liquids

The pressure exerted by liquids is mainly due to the weight of the liquid. Imagine taking a dive at your local swimming pool. Let's say you dive into the deep end. Now due to the effects of gravity, all of the weight of the water above you will act to press the water molecules down onto your body and any other object submerged in the water. This pressing is what we mean by the pressure exerted due to a liquid. The number of water molecules that are present above you will increase as you keep going deeper. This is why the pressure exerted by liquids increases with increasing depth and it's why the pressure you feel increases as you dive deeper into a body of water. Another factor that comes into play is the density of the liquid. Since density measures the mass per unit volume of a liquid. Liquids with higher density will exert a larger pressure at the same depths due to their larger weights.

The pressure exerted at a particular depth on a base Area A can be calculated by considering the weight of the column of liquid directly above A, StudySmarter Originals.

Lets now consider how to calculate the pressure exerted by a liquid at a particular depth. We consider a rectangular column of water with a base area$A$and height$h$.

We already know that the formula for pressure is:

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

The weight of the liquid situated directly above the base area of consideration$A$is given by the following equation:

$F=mg$

Or in words

$\mathrm{Weight}=\mathrm{mass}\times \mathrm{gravitational}\mathrm{field}\mathrm{strength}$

The next step in our calculation was considered to consider the density of the liquid in order to calculate the mass of the column of water:

$\rho =\frac{m}{V}$,

or in words,

$\mathrm{Density}=\frac{\mathrm{mass}}{\mathrm{volume}}$.

Rearranging for mass we get:

$m=\rho V$.

The volume of a cuboid can be written as the product of its base area$A$and its height$h$:

$V=Ah$,

or in words,

$\mathrm{Volume}=\mathrm{Base}\mathrm{area}\times \mathrm{height}$.

We Substitute the formula for weight in terms of mass before substituting the formula for mass in terms of density and volume. Finally, we substitute the formula for volume in terms of base area and height into the equation for pressure:

$P=\frac{mg}{A}=\frac{\rho \times V\times g}{A}=\frac{\rho \times A\times h\times g}{A}$

After further rearrangement, we arrive at the formula for the pressure exerted by a column of liquid pressure in terms of the density of the liquid$\rho$, the height of the column of liquid$h$, and the base area of the column of liquid$A$:

$P=\rho hg$

$\mathrm{pressure}=\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{column}\times \mathrm{density}\mathrm{of}\mathrm{the}\mathrm{liquid}\times \mathrm{gravitational}\mathrm{field}\mathrm{strength}$

Next, let us look at a few examples where we use these formulas to calculate the pressure.

Atmospheric pressure

Atmospheric pressure is due to the air molecules in the atmosphere colliding with the earth or any other object contained within. The atmospheric pressure reduces as the altitude increases because the density of the air decreases at higher altitudes. At higher altitudes, there is less air, therefore the weight of the air pressing down on an object is reduced. This is the reason why some people experience ear pain during air travel that occurs due to quick changes in air pressure. The atmospheric pressure can be calculated using the same formula as the pressure due to liquids.

Atmospheric pressure is due to the weight of the air molecules directly above the surface of the Earth, StudySmarter originals

Examples of pressure