Fluid Mechanics Formulas

Bernoulli's Equation

Bernoulli's equation relates pressure, velocity, and height in fluid flow. Learn the formula with practical worked examples.

Continuity Equation (Mass Conservation)

The continuity equation expresses conservation of mass in fluid flow. For incompressible flow, the product of cross-sectional area and velocity is constant.

Grashof Number — Definition, Formula, and Calculator (Gr)

Reference for the Grashof number (Gr) — buoyancy vs viscous forces in natural convection. Includes the formula, variable definitions, and a worked example.

Manning's Equation — Open Channel Flow Velocity

Manning's Equation calculates flow velocity in open channels such as rivers, drainage canals, and culverts. Used in civil and hydraulic engineering.

Prandtl Number Formula

The Prandtl number relates momentum diffusivity to thermal diffusivity. It determines whether heat transfer or momentum transfer dominates in a fluid.

Schmidt Number — Definition, Formula, and Calculator (Sc)

Reference for the Schmidt number (Sc) — ratio of momentum to mass diffusivity. Includes the formula, worked example, and typical values for common fluids.

Venturi Meter Flow Rate Formula

Calculate volumetric flow rate through a Venturi meter from the pressure difference between the throat and inlet. Used in industrial flow measurement.

Bernoulli's Equation

Bernoulli's equation P + ½ρv² + ρgh = constant relates pressure, velocity, and elevation in fluid flow. Essential for fluid dynamics.

Capillary Rise Formula (Surface Tension)

Calculate capillary rise height using h = 2 gamma cos(theta) / (rho g r). Explains meniscus, wicking, and liquid behavior in narrow tubes.

Froude Number Formula

Calculate the Froude number using Fr = v / sqrt(gL). Dimensionless ratio of flow inertia to gravity, used in ship design and open-channel hydraulics.

Reynolds Number

Reference for the Reynolds number formula Re = rho*v*D/mu. Predicts laminar flow below 2,300 and turbulent above 4,000 in pipes and open channels.

Weber Number Formula

Calculate the Weber number using We = rho v squared L / sigma. Ratio of inertia to surface tension for droplets, sprays, and atomization.

Buoyancy Force (Archimedes' Principle)

Reference for the Archimedes buoyancy principle: F = rho x g x V. Explains why objects float or sink with examples for water, seawater, and oil.

Drag Force Formula

Reference for drag force F_D = 0.5 × C_D × ρ × A × v². Covers drag coefficients for cars, spheres, and airfoils with Reynolds number and vehicle examples.

Flow Rate Formula

Calculate fluid flow rate Q = A × v (area × velocity). Returns volume per time in L/s, m³/s, and GPM for pipes, channels, and orifice applications.

Mach Number Formula

Calculate Mach number from speed and altitude. Classify flight as subsonic, transonic, supersonic, or hypersonic using the speed of sound at altitude.

Poiseuille's Law

Calculate fluid flow rate through a pipe based on pressure, viscosity, and pipe dimensions. Used in medical and engineering applications.