Fluid mechanics

Pressure

$p = \displaystyle\frac {F}{S}$

where

$p$ is the value of pressure, $[Pa]$;
$F$ is the value of force, $[N]$;
$S$ is the value of surface area $[m^2]$.

Continuity equation

$q = V/t=A·v$

where

$q$ is the volumetric flow rate, $[m^3/s]$
$V$ is then volume of fluid, $[m^3]$;
$t$ is the unit of time, $[s]$;
$A$ is the cross-sectin area, $[m^2]$;
$v$ is the speed of fluid, $[m/s]$.

Air friction (air drag force)

$F_{drag}=\displaystyle -\frac {1}{2}·C_d\left( ρ·v^2 \right)·A$

where

$F_{drag}$ if the drag force, $[N]$;
$C_d$ is the drag coefficient;
$ρ$ is the the density of the fluid, $[kg/m^3]$;
$v$ is the speed of the object relative to the fluid, $[m/s]$;
$A$ is the cross sectional area, $[m^2]$.

Viscous resistance (falling sphere through a liquid)

$F_{drag} = -6\pi·\left(a·\eta\right)·v$

where

$F_{drag}$ if the drag force, $[N]$;
$a$ is the sphere radius, $[m]$;
$\eta$ is the dynamic viscosity, $[Pa·s]$;
$v$ is the particle velocity, $[m/s]$.

Kinematic viscosity

$\nu = \eta/ρ$

where

$\nu$ is the kinematic viscosity of the fluid, $\displaystyle[\frac{m^2}{s}]$;
$\eta$ is the dynamic viscosity of the fluid, $[Pa⋅s]$;
$ρ$ is the the density of the fluid, $[kg/m^3]$.

Viscous friction (laminar flow)

$μ = \displaystyle \left(\frac {F}{A} \right)⋅ \left(\frac {\Delta y}{\Delta v}\right)$

where

$μ$ is the dynamic viscosity of the fluid, $[Pa⋅s]$;
$F$ is the is the constant force applied to the plate, $[N]$;
$A$ is the area of each plate, $[m^2]$;
$\Delta y$ is the height of a fluid layer, $[m]$;
$\Delta v$ is the difference in flow velocity between adjacent fluid layers, $[m/s]$.

Stevino's law

$p = p_0 + ρ·g·h$

where

$p_0$ is the initial pressure, $[Pa]$;
$ρ$ is the density of the flow, $[kg/m^3]$;
$g$ is the acceleration due to gravity, $[m/s^2]$;
$h$ where h is the height $(z − z_0)$ of the liquid column between the test volume and the zero reference point of the pressure, $[m]$.

Archimede's principle

$F_a = (ρ·g)·V$

where

$F_a$ denotes the buoyant force applied onto the submerged object, $[N]$;
$ρ$ is the the density of the fluid, $[kg/m^3]$;
$g$ is the acceleration due to gravity, $[m/s^2]$;
$V$ represents the volume of the displaced fluid, $[m^3]$.

Bernoulli's law

$p + (ρ·g)·h + 1/2·ρ·v² = costant$

where

$p$ is the pressure at the chosen point, $[Pa]$;
$ρ$ is the density of the fluid at all points in the fluid, $[kg/m^3]$;
$g$ is the acceleration due to gravity, $[m/s^2]$;
$h$ is the mean potential elevation of the section, $[m]$;
$v$ is the fluid flow speed at a point, $[m/s]$.