# Derivation of pressure formula?

How is the formula : P = (mg(delta)h)/V derived? I can't seem to find anything specific about it in my book, I don't understand how it works.

Relevance

That eqn looks odd, it is not homogenous. Mathematically:

p = F/A

where:

p is the pressure,

F is the normal force,

A is the area of the surface on contact.

For liquids,

p = \rho g h

where:

p is the pressure,

\rho is the density of the liquid,

g \approx 9.8 N/kg (the value is equal to the gravitational acceleration),

h is the depth of the liquid in metres.

.

• This is for pressure in a cylinder of gas as the volume changes, e.g a piston reduces the volume. You could have mentioned the context.

First some basic basics:

F = ma

A newton is the force to accelerate 1kg mass at 1m/s/s, thus m * g where gravity is 9.81m/s/s.

A pascal (pressure unit) is one newton per square meter.

Therefore:

Pressure_pascals = (m_kg * g_acceleration) / area_m^2

Next:

p1v1=p2v2

Where:

The 1s are initial pressure and volume, and the 2s are after the change in pressure and volume. If the volume changes, the pressure changes to keep it balanced.

Next:

Introduce the height change and volume into the pressure formula instead of area.

Area = volume / height (depending on shape, but this works for a vertical cylinder with a piston in it, for example)

Related stuff...

(Working out the mass of the gas in the initial state)

To get the density of a gas:

It is at standard temperature and pressure (STP)

Convert the volume and pressure and temperature to what it would be at STP

Volume of 1 mol of any gas at STP = 22.4 liters

e.g. Molar mass of oxygen, O2, is 2 * 16 = 32g/mol

Density = mass / volume = 32 / 22.4 = 1.4286g / L

Or

Look up density or molar mass of your gas.

Or

PV= nRT

(look up ideal gas law which relates pressure, temperature, volume and moles)

• Anonymous
4 years ago

Hmm...easily relies upon on what "V" stands for: if P = rigidity then its person-friendly Unit in terms of M)***, L)ength and T)ime are: P = F/A = ML/T² ÷ L² = ML/T²(a million/L²) = M/T²L <= P instruments mgh = ML/T²(L) = ML²/T² V = assuming velocity = L/T mgh/V = ML²/T² ÷ L/T = ML²/T²(T/L) = ML/T {analyze with P instruments above} if V represents "quantity" then its instruments could be L³ and mgh/V = ML²/T² ÷ L³ = ML²/T²(L³) = M/T²L <= that's P (rigidity instruments) so rigidity that's rigidity in line with unit section = capability in line with unit quantity rigidity/section = F/A = E/V {capability/quantity} if we multiply the two numerator and denominator of rigidity = F/A by skill of distance = d F•d/A•d = capability/quantity

• pressure = (mass x rho x g)/A

=force/area

= (h x A x rho x g)/A.......Area, A canceling each other in equation

= rho x g x h

= pgh