Pressure Formula

The pressure is something that we apply to many objects in our daily life. For example, for opening tight jars and seal pack object we apply pressure on them to open them. In this topic, we are going to discuss pressure, pressure formula and solved examples.

Pressure

                                                                                                                                                             Pressure on walls of the container

We can define pressure as the physical force that we exert on an object. Also, the force applied to the object is perpendicular to the surface of the object per unit area. Moreover, the unit of pressure in Pascals (Pa).

Besides, there are different types of pressures such as atmospheric, absolute, gauge, and differential pressure. Moreover, when you sip out the beverage from a straw, you firstly suck out the air from the straw? Also, when you sip the beverage you actually apply ‘pressure’.

Meaning of Pressure

For understanding pressure in a more clear sense let’s discuss a situation. Suppose you take a bowling pin and try to hammer it into a wall. In doing so you find out that nothing will happen to the bowling pin but it can damage your wall.

But, if in place of the bowling pin you use a nail and try to hammer it with same force then the nail would likely to penetrate the wall. By this example, we came to know that just knowing the magnitude of the force is not enough you also need to know how that force will distribute on the surface of impact.

Moreover, for the nail the all the force amidst the wall and the nail was centered into the small area on the sharp tip of the nail. On the other hand, for the bowling pin, the area touching the wall was much larger in comparison to the nail and as a result, the force was less concentrated.

Pressure Formula

Simply the pressure formula is
P = F / A

Derivation
P = Pressure in Pascal
F = Force on the object
A = Area on which the force act

Besides, we often calculate pressure for gases and fluids. In those conditions, the pressure of liquid or gas is equal to the density of that fluid multiplied by the acceleration due to the gravity and the height (depth) of the fluid above a certain point.

Pressure = density of fluid × acceleration due to gravity × height of the fluid column
P = ρ ×g × h

Derivation of the Pressure Equation 

P = Pressure of the object (Pa)
ρ = is the density of the gas or fluid (kg/\(m^3\))
g = is the acceleration of the object due to gravity (9.80 m/\(s^2\))
h = is the height of the column of gas or fluid (m)

Solved Examples on Pressure Formula

Example 1

If the wreckage of the ship that sunk in the ocean is 3,800 m under the ocean water. Also, the density of cold saltwater above it is 1,050 Kg/\(m^3\). Then calculate the pressure at that depth?

Solution:

By using the pressure formula we can find the pressure on the sunk ship.
Now let’s apply pressure formula which is

P = ρ ×g × h
P = (1,050 kg/\(m^3\)) (9.80m/\(s^2\)) (3800 m)
P = 3,91,02,000 \(\frac{kg}{m\cdot s^2}\)
Or P = 3,91,02,000 Pa

For more simpler form we can convert it into Mega-Pascal that is 39.1 MPa.

Moreover, the pressure of the ocean water at the depth of the sunk ship is 3,91,02,000 Pa or 39.1 MPa.

Example 2

The pressure of the bottom of a cylinder that contains gas is P = 735.0 Pa. In addition, the height of the cylinder is 2.50 m, then calculate the density of the gas?

Solution: We can find the density of by rearranging the pressure formula:

P = ρ ×g × h \(\rightarrow\) \( \rho\) = \(\frac{P}{g × h}\)

\(\rho\) = \(\frac{(735.0 Pa)}{(9.80 m/s^2)(2.50m)}\)

\(\rho\) = rho = \(\frac{(735.0 \frac{kg}{m\cdot s^2})}{(9.80 m/s^2)(2.50m)}\)

\(\rho\) = 30.0 kg/\(m^3\)

So, the density of the gas cylinder is 30.0 kg/\(m^3\)