Equations in Fluid Mechanics
Equations used in fluid mechanics - like Bernoulli, conservation of energy, conservation of mass, pressure, Navier-Stokes, ideal gas law, Euler equations, Laplace equations, Darcy-Weisbach Equation and more.
| Equation Name | Category | Description | Key Principle |
|---|---|---|---|
| Bernoulli Equation | Conservation Laws | A statement of the conservation of energy in a form useful for solving problems involving fluids. | For a non-viscous, incompressible fluid in steady flow, the sum of pressure, potential and kinetic energies per unit volume is constant at any point. |
| Conservation of Energy | Conservation Laws | Energy is conserved in an isolated physical system. | Particular measurable properties of an isolated physical system does not change as the system evolves. |
| Conservation of Mass | Conservation Laws | Mass can neither be created nor destroyed. | The law of conservation of mass states that mass can neither be created or destroyed. |
| Continuity Equation | Conservation Laws | A statement that mass is conserved. | The Continuity Equation expresses conservation of mass in fluid flow. |
| Darcy-Weisbach Equation | Pressure Loss | Pressure loss and head loss due to friction in ducts and tubes. | Major loss - head loss or pressure loss - due to friction in pipes and ducts. |
| Euler Equations | Compressible Flow | Govern the motion of a compressible, inviscid fluid. | Corresponds to the Navier-Stokes equations with zero viscosity. Represents conservation of mass, momentum, and energy. |
| Laplace's Equation | Potential Flow | Describes the behavior of gravitational, electric, and fluid potentials. | Used for modeling potential flow in fluid mechanics. |
| Ideal Gas Law | Thermodynamics | For a perfect or ideal gas the change in density is directly related to the change in temperature and pressure. | PV = nRT or ρ = P/(RT) |
| Gas Mixture Properties | Thermodynamics | Special considerations for gas mixtures when using the ideal gas law. | Individual gas constants and mixture properties must be carefully calculated. |
| Individual and Universal Gas Constant | Thermodynamics | The Individual and Universal Gas Constant is common in fluid mechanics and thermodynamics. | R_universal = 8.314 J/(mol·K), R_individual varies by gas. |
| Navier-Stokes Equations | Viscous Flow | Govern the motion of a non-turbulent, Newtonian fluid. | Can be used to model turbulent flow where fluid parameters are interpreted as time-averaged values. |
| Mechanical Energy Equation | Energy | Energy per unit mass, per unit volume, and per unit weight involving heads. | Relates pressure head, velocity head, and elevation head. |
| Static Pressure and Pressure Head | Pressure | Pressure and pressure head in a static fluid. | Fundamental relationships for pressure analysis in fluids. |