# Confused about the pressure formula

In summary, there are two different formulae for pressure: p = p0 + rho*g*h and p = rho*g*d. The first formula includes the initial pressure (often atmospheric pressure) while the second one does not. They calculate the same thing, but the first formula gives the full pressure while the second only gives the pressure due to the fluid. When determining the maximum safe depth of a research submarine with a 20 cm diameter window, it is unclear whether the pressure inside the submarine is included in the maximum force it can withstand. Therefore, it is recommended to use the formula without the atmospheric pressure to be on the safe side.
Hi,

I've come across two different formulae for pressure:

p = p0 + rho*g*h (p0 = initial pressure)

OR

p = rho*g*d

My question is, why does one of the formulae includes the initial pressure (initial pressure is often the atmospheric pressure = 1.013*10^5 Pa) in the formula whereas the other one doesn't? Do they actual calculate the same thing?

Many thanks.

The second version just gives the pressure due to the fluid (density rho). If you want the full pressure, you need to add the pressure above the fluid, p0.

Doc Al said:
The second version just gives the pressure due to the fluid (density rho). If you want the full pressure, you need to add the pressure above the fluid, p0.

Having said that, then for the following question should I use the formula with or without the atmospheric pressure?

A research submarine has a 20 cm diameter window. It can withstand forces up to 1.0 x 10^6 N. What is the submarine's maxiumum safe depth in water?

Depends. Do they mean the inward force from the water or the net inward force? (Presumably, the pressure inside the submarine is atmospheric.) Lacking additional information, I would use the one without the atmospheric pressure.

Personally, I'd use the 'pessimistic' version. But I may be just a wimp.

## What is the pressure formula?

The pressure formula is defined as the force per unit area, represented by the equation P = F/A. In this formula, P stands for pressure, F stands for force, and A stands for area. This formula is used to calculate the amount of pressure exerted on a surface.

## What are the units of measurement for pressure?

The SI unit for pressure is the pascal (Pa), which is defined as 1 newton per square meter (N/m²). Other commonly used units include atmospheres (atm), bar (bar), and pounds per square inch (psi).

## How is pressure related to depth?

Pressure is directly proportional to depth, meaning that as depth increases, so does pressure. This is due to the weight of the fluid above an object increasing with depth, causing an increase in the force exerted on the object and therefore an increase in pressure.

## What is the difference between absolute pressure and gauge pressure?

Absolute pressure is the total pressure exerted by a fluid, including atmospheric pressure. Gauge pressure, on the other hand, only measures the pressure above atmospheric pressure. This means that absolute pressure will always be higher than gauge pressure.

## How does temperature affect pressure?

Temperature and pressure have a direct relationship, meaning that as temperature increases, so does pressure, and vice versa. This is known as Charles's Law and is due to the increase in the kinetic energy of gas particles with higher temperatures, causing them to exert more force on their surroundings.

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