Fluid Mechanics Calculators
Bernoulli Theorem
P + ½ρv² + ρgh = const
Conservation of energy along a streamline — pressure, velocity, and elevation head.
Calculate →Chezy Equation
V = C · √(R · S)
Open-channel flow velocity from Chezy coefficient, hydraulic radius, and slope.
Calculate →Colebrook Equation
1/√f = −2·log₁₀(ε/(3.7D) + 2.51/(Re·√f))
Implicit Darcy friction factor for turbulent pipe flow from roughness and Reynolds number.
Calculate →Continuity
A₁ · v₁ = A₂ · v₂
Conservation of mass for incompressible flow — area-velocity continuity equation.
Calculate →Darcy Weisbach
hf = f · (L/D) · (v² / 2g)
Head loss in a pipe from friction factor, length, diameter, and velocity.
Calculate →Darcy's Law Equations
Q = −K · A · dh/dL
Groundwater flow rate through porous media from hydraulic conductivity and gradient.
Calculate →Fluid Pressure
P = ρ · g · h · K = ΔP / ΔV/V
Hydrostatic pressure, absolute pressure, bulk modulus, and compressibility for fluids.
Calculate →French Drain Design
Q = K · A · i
Subsurface drain seepage rate from area, hydraulic gradient, and soil conductivity.
Design →Gutter Design
Q = (0.56/n) · Sx^(5/3) · S^(1/2) · T^(8/3)
Curb-and-gutter flow rate, spread, and capture efficiency for stormwater drainage design.
Design →Hazen Williams
V = 0.849 · C · R^0.63 · S^0.54
Pipe flow velocity from Hazen-Williams coefficient, hydraulic radius, and energy slope.
Calculate →Hydraulic Radius
R = A / P (wetted)
Hydraulic radius, mean depth, and Froude number for open-channel flow.
Calculate →Manning
V = (1/n) · R^(2/3) · S^(1/2)
Open-channel flow velocity from Manning roughness, hydraulic radius, and energy slope.
Calculate →Minor Losses
hl = K · v² / 2g
Head loss from pipe fittings, valves, bends, and entrances via loss coefficients.
Calculate →Orifice Flow Design
Q = Cd · A · √(2gh)
Flow rate through an orifice from discharge coefficient, area, and centerline head.
Design →Parshall Flume Design
Q = K · Hₐⁿ
Open-channel flow rate through a Parshall flume from upstream head and throat size.
Design →Pipe Flow
Q = A · v
Volumetric flow rate, velocity, and pipe area for full-pipe flow.
Calculate →Pump
BHP = (Q · H · γ) / (3960 · η)
Pump brake horsepower, water horsepower, NPSH, and discharge.
Calculate →Time Of Concentration
tc (Kirpich · Bransby-Williams · …)
Storm-water travel time via Kirpich, Bransby-Williams, Kerby, Izzard, and watershed-lag methods.
Calculate →Venturi Meter
Q = Cd · A₂ · √(2(P₁−P₂) / ρ(1 − β⁴))
Pipe flow rate from venturi meter pressure differential and throat-to-pipe diameter ratio.
Calculate →Reynolds Number
Re = ρ · v · L / μ
Inertia vs viscous force ratio for pipe and channel flow regime classification.
Calculate →Water Hammer
ΔP = ρ · c · ΔV
Maximum pressure surge from sudden valve closure or pipe flow change (Joukowsky).
Calculate →Fluid mechanics calculators: Bernoulli's equation, continuity, Reynolds number, hydraulic radius, Stokes' law, pipe flow, orifice flow, wing lift, and the Manning equation for open-channel flow.
When to use these calculators
Used for engineering coursework and field calculations in civil, mechanical, and aerospace contexts. Each calculator handles the standard textbook form of the equation with unit conversions where needed.
Frequently Asked Questions
- How does the calculator show its work?
- Each calculator displays the substituted arithmetic step-by-step below the solution, so the user can verify the math by hand if needed. The 'Copy result' button captures the full formula → substitution → answer block.
- Are the formulas cross-verified?
- Every calculator's math has been cross-verified against textbook references and round-trip consistency tests (solve A from B, then solve B from A — the result must match the input). Spot-checks against Wolfram Alpha confirm the precision.
- How do I switch between solving for different variables?
- Most calculators in this category support multiple solve-for modes. Pick the unknown variable from the pill-toggle (or equation-card group) above the input fields, then enter the known values. The calculator auto-computes as you type.