Fluid Mechanics: Key Concepts, Laws, and Equations for Students

Fluid Mechanics

The study of fluids (liquids and gases) and the forces that act on them.

Fluid Statics (Fluids at Rest)

"The study of fluids that are stationary, where pressure and density are the main focus."

Fluid Dynamics

The more complex field that studies fluids in motion.

Density (ρ)

The mass of a material per unit volume (ρ=m/V).

Homogeneous Material

"A material, like steel or ice, that has the same density throughout."

SI Unit of Density

The kilogram per cubic meter (kg/m3).

Pressure (p)

"The force exerted by a fluid perpendicular to a surface, divided by the area (p=dF⊥​/dA)."

Pascal (Pa)

"The SI unit of pressure, equal to one Newton per square meter (1 N/m2)."

Pressure at Depth

The observation that pressure is greater deeper in a fluid than it is at the surface.

Pascal's Law

Pressure applied to an enclosed fluid is transmitted equally to every portion of the fluid and the container walls.

Atmospheric Pressure (patm​)

The pressure exerted by the Earth's atmosphere.

Absolute Pressure

"The total pressure, which is the gauge pressure plus atmospheric pressure."

Gauge Pressure

"The excess pressure above atmospheric pressure (e.g., the pressure reading on a car tire)."

Buoyancy

The phenomenon where an object immersed in a fluid appears to weigh less.

Buoyant Force

The upward force exerted by a fluid on an object immersed in it.

Archimedes's Principle

States that the buoyant force on an object equals the weight of the fluid that the object displaces.

Extensive Property

"A property that depends on the size or amount of the material (e.g., Mass, Volume, Weight, Length)."

Intensive Property

"A property that does not depend on the amount of material (e.g., Density, Boiling Point, Color, Temperature, Hardness)."

Flow Line

The path followed by a single particle in a moving fluid.

Steady Flow

"Flow where the overall pattern does not change with time, meaning all particles passing a point follow the same flow line."

Laminar Flow

A steady flow where adjacent fluid layers slide smoothly past each other.

Turbulent Flow

A non-steady flow at high flow rates where the flow pattern changes continuously and is chaotic.

Continuity Equation

The equation (A1​v1​=A2​v2​) stating that the volume flow rate (Av) is constant for an incompressible fluid.

Volume Flow Rate

The volume of fluid that passes a certain point per unit time (dV/dt).

Bernoulli's Equation

"An equation that relates the pressure (p), flow speed (v), and height (y) at two different points in a flowing fluid."

Ideal Flow

A theoretical type of flow that is non-viscous and non-turbulent.

Viscous Flow

Flow that involves internal friction and differs from ideal flow.