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.

4 Answers

  • Favorite Answer

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

    p = F/A


    p is the pressure,

    F is the normal force,

    A is the area of the surface on contact.

    For liquids,

    p = \rho g h


    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.


  • Ecko
    Lv 7
    8 years ago

    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.


    Pressure_pascals = (m_kg * g_acceleration) / area_m^2




    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.


    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


    Look up density or molar mass of your gas.


    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

  • 6 years ago

    pressure = (mass x rho x g)/A


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

    = rho x g x h

    = pgh

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