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Mass Density
The mass density ρ is the mass m of a substance divided by its volume V:


SI Unit: kg / m³

Mass Densities of Common Substances

Pressure in fluids (liquids and gases)

Pressure is scalar measure which indicates the ratio of force to the area over which that force is distributed.

SI Unit: Pascal (Pa)

P=ρ·g·h

Where P is pressure
ρ (rho) is density (kg·m^-3)
g is acceleration of free fall (On Earth 9.81 m·s^-2)
h is height of liquid column or depth within a substance (m)

-Filip

Buoyancy

an upward force exerted by a fluid that opposes the weight of an immersed object.

SI Unit: Newton (N)

B=ρ·g·V

Where ρ (Rho) is density of surrounding fluid. (kg·m^-3)
g is acceleration of free fall (On Earth 9.81 m·s^-2)
V is volume of submerged part of body (m³)

Pascal's Principle
Any change in the pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and the enclosing walls.


Archimedes' Principle
An object, wholly or partially immersed in a fluid, experiences an upward buoyant force with magnitude equal to the weight of the displaced fluid.





Fluids in motion
Laminar flow: steady

Fluid velocity is approximately constant (with time) and predictable at each point

Laminar flow: unsteady

Fluid velocity is rapidly varying with time (and unpredictably from point to point)

Non-viscous flow: Neighboring fluid layers move independently
Viscous flow: Neighboring fluid layers experience mutual friction
Compressible flow: True for most gases (volume can change)
Incompressible flow: True for most liquids (volume cannot change)

Equation of Continuity
The mass flow rate (ρAv) has the same value at every position along a tube that has a single entry and a single exit point for fluid flow. For two positions along such a tube





Bernoulli's Equation
In the steady flow of a nonviscous, incompressible fluid of density ρ, the pressure P, the fluid speed v, and the elevation y at any two points (1 and 2) are related by

The force needed to move a layer of viscous fluid is:




Poiseuille's law
A fluid whose viscosity is η, flowing through a pipe of radius R and length L, has a volume flow rate Q given by

Solving for P[sub]1[/sub]: