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

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  • Favorite Answer

    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.

    .

  • 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.

    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

  • 6 years ago

    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

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