Fluid Statics and Pressure Field Notes

Vocabulary flashcards covering concepts of fluid statics, pressure gradients, hydrostatic distribution, compressible/incompressible behavior, and atmospheric pressure measurements.

Body Force

A force that acts on the entire volume or mass of a fluid element, such as weight caused by gravity ($W = \gamma \delta x \delta y \delta z$).

Surface Force

A force acting directly on the boundaries or surface of a fluid element, such as pressure forces applied perpendicularly to the faces.

Gradient Operator

A vector operator denoted by $\nabla$, expressed in Cartesian coordinates as $\nabla = \frac{\partial}{\partial x}\hat{i} + \frac{\partial}{\partial y}\hat{j} + \frac{\partial}{\partial z}\hat{k}$.

Resultant Surface Force per Unit Volume

The net surface force per unit volume on a small fluid element in the absence of shearing stresses, equal to $-\nabla p$.

General Equation of Motion (Without Shearing Stresses)

The force balance equation $-\nabla p - \gamma \hat{k} = \rho \vec{a}$, which relates pressure gradient, fluid specific weight, density, and acceleration.

Hydrostatic Pressure Gradient

The vertical variation of pressure in a static fluid, defined by $\frac{dp}{dz} = -\gamma$, showing that pressure decreases as elevation $z$ increases.

Incompressible Fluid

A fluid characterized by a constant density ($\rho$), resulting in a linear relationship between pressure and depth when at rest.

Pressure Head

The height $h$ of a column of fluid of specific weight $\gamma$ required to generate a specific pressure difference $p_1 - p_2$, defined as $h = \frac{p_1 - p_2}{\gamma}$.

Hydrostatic Paradox

The phenomenon where pressure in a homogeneous, incompressible fluid at rest depends solely on vertical depth below the free surface ($p = \gamma h + p_0$), regardless of container size or shape.

Hydraulic Transmission of Pressure

The application of equal pressure at equal elevations in an enclosed fluid, enabling a small force $F_1$ on area $A_1$ to exert a larger force $F_2 = p A_2$ on area $A_2$.

Isothermal Pressure-Elevation Relation

The mathematical formula $p_2 = p_1 \exp\left(-\frac{g(z_2 - z_1)}{R T_0}\right)$, describing pressure variations in an ideal compressible gas under constant temperature $T_0$.

U.S. Standard Atmosphere

An idealized model of mid-latitude, year-round mean atmospheric conditions, specifying sea-level standards such as $T = 15\,^\circ \text{C}$ ($288.15\,\text{K}$) and $p = 101.33\,\text{kPa (abs)}$.

Absolute Pressure

Fluid pressure measured relative to a perfect vacuum (absolute zero pressure reference), which always maintains a non-negative value ($\ge 0$).

Gauge Pressure

Pressure measured relative to local atmospheric pressure, where zero gauge pressure corresponds directly to local atmospheric pressure.

Suction Pressure (Vacuum Pressure)

A negative gauge pressure value indicating that the measured pressure is below the local atmospheric pressure reference.

Mercury Barometer

An instrument designed to measure atmospheric pressure using a column of liquid mercury based on the equilibrium relation $p_{\text{atm}} = \gamma h + p_{\text{vapor}}$.