Master foundational physics, finance, calculus, and engineering equations with live evaluators, derivations, and worked examples.
Conservation of mechanical energy along a steady, incompressible, inviscid fluid streamline relating static pressure, dynamic velocity head, and elevation head.
Dimensionless ratio of inertial forces to viscous shear forces predicting laminar, transitional, or turbulent flow in pipes and boundary layers.
Universal hydraulic engineering equation calculating major frictional head loss and pressure drop along straight pressurized pipes.
Exact analytical solution of the Navier-Stokes equations for steady laminar volumetric flow through a cylindrical tube.
Structural mechanics formula determining the elastic axial compressive load at which a slender column undergoes sudden lateral buckling.
Fundamental solid mechanics relation linking internal bending moment M to longitudinal normal stress across a symmetric beam cross-section.
Calculates torsional shear stress and angle of twist in solid or hollow drive shafts transmitting mechanical torque.
Defines the −3 dB half-power corner frequency, phase shift, and exponential step-response time constant of first-order RC analog filters.