Fluid Mechanics - Chapter 8

Practice flashcards covering definitions and core principles of density, buoyant force, pressure, Pascal's Principle, and fluid dynamics based on Chapter 8 lecture notes.

Density ($\rho$)

Mass per unit volume, which is dependent on temperature and pressure; calculated using $\rho = \frac{m}{V}$ and measured in $kg\,m^{-3}$.

Buoyant Force ($F_B$)

The upward force exerted by a liquid on an object immersed in or floating on the liquid, which is equal to the weight of the fluid displaced ($F_B = F_g(\text{displaced fluid}) = m_f g$).

Archimedes’ principle

The principle stating that any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object.

Sinking Condition

The state that occurs when the weight of the object F_g > F_B, resulting in a net force F_{net} < 0.

Rising Condition

The state that occurs when the weight of the object $F_g < F_B$, resulting in a net force $F_{net} > 0$.

Neutrally Buoyant

The state where the weight of the object $F_g = F_B$, resulting in a net force $F_{net} = 0$.

Density Ratio Formula

An equation for a submerged object with density $\rho_o$ in a fluid of density $\rho_f$ relating force to density: $\frac{F_g(\text{object})}{F_B} = \frac{\rho_o}{\rho_f}$.

Apparent Weight

The reduced weight of an object measured in a fluid because the buoyant force lessens the weight; calculated as $F_{apparent} = F_g - F_B$.

Pressure ($P$)

The magnitude of the force on a surface per unit area, defined as $P = \frac{F}{A}$.

Pascal ($Pa$)

The SI unit of pressure, equal to $1\,N\,m^{-2}$.

Atmospheric Pressure at Sea Level

The standard value defined as $1.01 \times 10^5\,Pa$, or $1\,atm$.

Pascal’s Principle

The principle stating that pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of the container ($\frac{F_1}{A_1} = \frac{F_2}{A_2}$).

Hydraulic Press

An application of Pascal’s Principle where the pressure inside the system is constant throughout the fluid ($P_{inc} = \frac{F_1}{A_1} = \frac{F_2}{A_2}$).

Continuity Equation

The principle stating that the cross-sectional area of a stream multiplied by its speed is constant ($A_1 v_1 = A_2 v_2$), meaning speed increases as cross-sectional area decreases.

Flow Rate

The product of cross-sectional area ($A$) and velocity ($v$), with units of volume per unit time.

Bernoulli's principle

The principle stating that the pressure in a fluid decreases as the fluid's velocity increases.