Mechanical Properties of Fluids and Fluid Dynamics

Vocabulary flashcards covering key definitions, principles, and equations in fluid statics and dynamics, including pressure, Pascal's law, buoyancy, continuity, and Bernoulli's theorem.

Fluid mechanics

The branch of physics that deals with fluids either at rest or in motion.

Fluid dynamics

The branch of mechanics that deals with fluids in motion.

Pressure

The ratio of force acting per unit surface area ($P = \frac{F}{A}$); a scalar quantity with the SI unit of $\text{N}\,\text{m}^{-2}$ or $\text{Pa}$, where $1\,\text{atm} = 1.013 \times 10^5\,\text{Pa}$.

Density of a liquid ($S$)

The ratio of mass to volume ($S = \frac{m}{V}$); a scalar quantity with the SI unit of $\text{kg}\,\text{m}^{-3}$ and CGS unit of $\text{g}\,\text{cm}^{-3}$, where $1\,\text{kg}\,\text{m}^{-3} = 10^{-3}\,\text{g}\,\text{cm}^{-3}$.

Relative density (Specific gravity)

The ratio of the density of a substance to the density of water at $4^\circ\text{C}$ ($S_g = \frac{S_{\text{substance}}}{S_{\text{water at } 4^\circ\text{C}}}$); a dimensionless and unitless quantity.

Pascal's law

A fluid principle stating that the pressure is the same at all points at the same level in a fluid at rest ($P_A = P_B = P_C = \text{constant}$).

Barometer

A device used to measure atmospheric pressure using the hydrostatic formula $P_0 = Sgh$, equaling $1.013 \times 10^5\,\text{Pa}$ for a $76\,\text{cm}$ column of mercury ($S = 13.6 \times 10^3\,\text{kg}\,\text{m}^{-3}$).

Manometer

A device filled with mercury ($\text{Hg}$) used to measure the pressure of any gas contained within a closed vessel ($P = P_0 \pm Sgh$).

Gauge pressure

The excess pressure of a system above atmospheric pressure, represented as $P - P_0 = Sgh$.

Force of Buoyancy

The resultant upward force exerted by fluid pressure acting on an immersed body.

Apparent weight of a body in liquid

The true weight minus the loss of weight of the body in a liquid, formulated as $A_{p_w} = mg\left(1 - \frac{S}{\sigma}\right)$, where $\sigma$ is the density of the body and $S$ is the density of the liquid.

Ideal fluid

A fluid whose flow is steady (constant velocity at a point), irrotational (non-rotatory), incompressible (constant density), and non-viscous (no frictional force between liquid layers).

Equation of continuity

The relation stating that the rate of mass flow of an ideal fluid across every cross section remains constant ($A_1 V_1 = A_2 V_2$), representing the law of conservation of mass.

Pressure-Energy

The energy possessed by a body or fluid by virtue of its pressure, where the incremental work done is given by $dW = P\,dv$.

Bernoulli's theorem

The principle stating that when an incompressible, non-viscous fluid flows in a steady streamline, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along the flow path ($P + \frac{1}{2}Sv^2 + Sgh = \text{constant}$).

Efflux

The outflow of a liquid from an orifice or hole in a container.

Torricelli's law

An application of Bernoulli's theorem stating that the speed of efflux of a liquid through a small hole at depth $h$ from the free surface of a tank open to the atmosphere is $v = \sqrt{2gh}$.

Horizontal Range ($R$)

The horizontal distance traveled by an exiting stream of fluid before hitting the ground level, given by $R = 2\sqrt{h(H - h)}$, which attains its maximum value when the orifice is placed at $h = \frac{H}{2}$.