Pressure

Pfluid = ρgh
Pfluid is pressure in Pa or N/m²
ρ is the density of the fluid in kg/m³
density of water at 20C = 0.998 g/cm³ = 998 kg/m³
density of seawater = 1.025 g/cm³ = 1025 kg/m³
g is the acceleration of gravity 9.8 m/s²
h is the height of the fluid above the object in m
Ptotal = Patmosphere + Pfluid
Patmos = 1.01e5 N/m² or 101 kPa
One bar is 100 kPa

Buoyancy, Archimedes' principle
Buoyancy force is equal to the weight of the displaced fluid.

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object

For a sunken object the volume of displaced fluid is the volume of the object, and for a floating object on a liquid, the weight of the displaced liquid is the weight of the object

apparent immersed weight = weight – weight of displaced fluid

density of object / density of fluid = weight / weight of displaced fluid

density of object / density of fluid = weight / (weight – apparent immersed weight)

Pascal's law or the Principle of transmission of fluid-pressure states that "pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure ratio (initial difference) remains the same.

ΔP = ρg(Δh)

ΔP is the hydrostatic pressure (given in pascals in the SI system), or the difference in pressure at two points within a fluid column, due to the weight of the fluid;
ρ is the fluid density (in kilograms per cubic meter in the SI system);
g is acceleration due to gravity (normally using the sea level acceleration due to Earth's gravity in metres per second squared);
Δh is the height of fluid above the point of measurement, or the difference in elevation between the two points within the fluid column (in metres in SI).

Air pressure versus altitude.

P = Po [ 1 – (Lh/To) ]^(gM/RL)

P is pressure in Pa
Po sea level standard atmospheric pressure 101325 Pa
h altitude in meters
L temperature lapse rate 0.0065 K/m
To sea level standard temperature 288 K
g Earth-surface gravitational acceleration 9.81 m/s²
M molar mass of dry air 0.0290 kg/mol
R universal gas constant 8.31 J/(mol•K)