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13 calculators

Fluid Mechanics Calculators

Reynolds number, Bernoulli equation, pipe flow, pumps, open channel flow, and drag

Fluid Mechanics covers the behavior of liquids and gases at rest and in motion. The course provides the analytical foundation for designing pipes, pumps, turbines, aircraft, ships, and any system where fluid flow is a central concern.

The course begins with fluid statics — pressure distribution, buoyancy, and forces on submerged surfaces. Fluid kinematics describes velocity fields, streamlines, and flow patterns without regard to forces. The Reynolds number classifies flow as laminar or turbulent, which has profound implications for friction losses and mixing. Bernoulli's equation is a powerful energy conservation tool for inviscid flow along a streamline, used to analyze flow in nozzles, venturis, and around airfoils. The Darcy-Weisbach equation accounts for viscous friction losses in pipe flow, with the friction factor determined from the Moody chart. Pump and turbine analysis connects fluid mechanical power to shaft power. Open channel flow (Manning equation) addresses rivers, drainage canals, and culverts. Drag and lift forces on bodies in external flow round out the treatment of external aerodynamics and hydrodynamics.

Fluid Mechanics is essential for civil, mechanical, chemical, and aerospace engineers who design any system involving the flow of water, air, steam, oil, or other fluids.

Key Concepts

  • Fluid statics: pressure, buoyancy, manometry
  • Reynolds number and flow regime classification
  • Bernoulli's equation and its applications
  • Continuity equation and mass conservation
  • Darcy-Weisbach equation for pipe head loss
  • Moody chart and friction factor determination
  • Minor losses in pipe fittings and components
  • Pump and turbine analysis; head-capacity curves
  • Open channel flow and Manning equation
  • Boundary layer theory and drag coefficients

Prerequisites

Statics

Fluid statics — pressure distribution and forces on submerged surfaces — is a direct extension of solid body statics.

Calculus and Differential Equations

The Navier-Stokes equations are PDEs; even simplified analyses require integration and differential reasoning.

Thermodynamics (for compressible flow)

Analyzing high-speed gas flows requires thermodynamic state relations and isentropic process equations.

Fluids Calculators

Reynolds Number Calculator

Calculate Reynolds number and classify flow as laminar, transitional, or turbulent with common fluid presets

Bernoulli Equation Calculator

Solve for any unknown in the Bernoulli equation given pressure, velocity, and elevation at two points

Darcy-Weisbach Calculator

Calculate head loss and pressure drop in pipes using the Darcy-Weisbach equation with friction factor

Moody Chart Calculator

Calculate Darcy friction factor from Reynolds number and relative roughness using Colebrook-White and Swamee-Jain

Pump Power Calculator

Calculate hydraulic power, shaft power, and NPSH for centrifugal pumps from flow rate, head, and efficiency

Orifice Flow Calculator

Calculate volumetric flow rate through an orifice from discharge coefficient, area, and pressure drop

Manning Equation Calculator

Calculate open-channel flow rate and velocity for rectangular, trapezoidal, and circular cross-sections

Hydraulic Diameter Calculator

Calculate hydraulic diameter (D_h = 4A/P) for rectangular, circular, annular, and custom cross-sections

Drag Force Calculator

Calculate aerodynamic drag force and power from drag coefficient, fluid density, frontal area, and velocity

Buoyancy Calculator

Calculate buoyant force, submerged fraction, and whether an object floats or sinks in various fluids

Compressible Flow Calculator

Isentropic flow relations T/T₀, P/P₀, ρ/ρ₀, A/A* and normal shock M₂, P₂/P₁, T₂/T₁ from Mach number and γ, with isentropic flow table

Water Hammer Calculator

Wave speed a = √(K/ρ)/(1+KD/Et) and Joukowski pressure surge ΔP = ρaV for rapid and gradual valve closure

Pipe Network Calculator

Hardy-Cross iteration for a single-loop pipe network: flow rates, head losses, and convergence table over 5 iterations