Fluid Mechanics

Fluid Mechanics

Fluid mechanics studies the behavior of fluids (liquids and gases) at rest (statics) and in motion (dynamics). It is essential for hydraulic engineering, water supply, and coastal engineering.

Density and Pressure

Density ($\rho$)

Mass per unit volume. $\rho = \frac{m}{V}$ Specific gravity ($SG$) is the ratio of a substance's density to that of water at $4^\circ$C ($\rho_{water} = 1000 \text{ kg/m}^3$).

Pressure ($P$)

Force per unit area exerted perpendicular to a surface. $P = \frac{F}{A}$ Unit: Pascal (Pa). 1 atm = 101,325 Pa.

Hydrostatic Pressure: Pressure increases with depth in a static fluid. $P = P_0 + \rho g h$ where $P_0$ is the surface pressure and $h$ is the depth.

Buoyancy (Archimedes' Principle)

Archimedes' Principle: An object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. $F_B = \rho_{fluid} V_{displaced} g$

• Floating Object: $F_B = W_{object}$. The object sinks until the displaced fluid weight equals its own weight.
• Sinking Object: $F_B < W_{object}$.

Fluid Dynamics (Bernoulli's Principle)

Continuity Equation

For an incompressible fluid in steady flow, the mass flow rate is constant. $A_1 v_1 = A_2 v_2$ where $A$ is the cross-sectional area and $v$ is the fluid velocity.

Bernoulli's Equation

Conservation of energy for a flowing fluid. $P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant}$ Along a streamline: $P_1 + \frac{1}{2} \rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2$

This principle explains lift on airfoils and flow through pipes.