Fluid Mechanics Lecture Notes

Vocabulary flashcards covering the fundamental concepts of fluid mechanics, including states of matter, density, pressure, buoyancy, and fluid dynamics principles.

Fluid Statics

The study of fluids at rest.

Fluid Dynamics

The study of fluids in motion.

Fluid

Any material that flows with low viscosity, including liquids, gases, and plasmas.

Solid

A state of matter where atoms or molecules are rigidly fixed with respect to each other, maintaining a definite volume and shape, and remaining essentially incompressible.

Liquid

A state of matter where atoms or molecules are free to move with respect to each other; it has a definite volume but an indefinite shape and is essentially incompressible.

Gas

A state of matter where atoms or molecules move at high speeds with little interaction, possessing indefinite volume and shape, and being highly compressible.

Plasma

A highly energetic gaseous state consisting of a mix of electrons and positive ions that gives off light.

Density ($\rho$)

The ratio of mass per unit volume, represented by the formula $\rho = \frac{m}{V}$.

Density of water

Constant value defined as $1000\text{\,kg/m}^3$ or $1\text{\,g/cm}^3$.

Specific gravity

A unitless value defined as the ratio of the density of a material to the density of water ($s.g. = \frac{\rho_{\text{material}}}{\rho_{\text{water}}}$).

Pressure ($P$)

The force ($F$) applied over an area ($A$), represented by the formula $P = \frac{F}{A}$.

Pascal ($\text{Pa}$)

The unit of pressure equivalent to one Newton per square meter ($1\text{\,N/m}^2$).

Atmospheric pressure ($P_{\text{atm}}$)

The pressure due to the atmosphere at sea level under standard conditions, equal to $1.013 \times 10^5\text{\,Pa}$, $760\text{\,torr}$, or $14.7\text{\,psi}$.

Absolute pressure

Pressure measured with respect to a perfect vacuum ($P = 0$).

Gauge pressure

Pressure measured with respect to atmospheric pressure, often read by pressure gauges.

Buoyant force ($F_B$)

A net upward force experienced by an object completely or partially submerged within a fluid.

Archimedes’s Principle

The principle stating that the buoyant force experienced by an object is equal in magnitude to the weight of the fluid displaced by the object ($F_B = \rho_{\text{fluid}} V_{\text{disp}} g$).

Pascal’s Principle

The principle stating that pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid and exerted on the walls of its container.

Laminar flow

A characteristic of ideal fluid flow where all particles passing through a point have the same velocity.

Non-viscous flow

A characteristic of ideal fluid flow where internal friction is neglected.

Flow rate

The volume of fluid passing a point per unit time, calculated as the product of cross-sectional area and fluid speed ($A v$), with units in $\text{m}^3\text{/s}$.

Equation of continuity

The expression $A_1 v_1 = A_2 v_2$, which indicates that for an incompressible fluid, the flow rate is constant throughout a pipe.

Bernoulli’s Equation

The equation relating pressure, speed, and height in fluid flow: $P_1 + \frac{1}{2}\rho v_1^2 + \rho gy_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho gy_2$.

The Bernoulli Effect

The principle that as the speed of a fluid increases, the internal pressure of that fluid decreases.