Physics calculators

Fluid Mechanics Calculators

66 tools

Internal pipe, open channel, flow meters, pumps, and dimensionless numbers. Tools may appear in more than one topic.

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Reynolds Number Calculator Compute Re = ρvL/μ (or vL/ν) with laminar/turbulent guidance for pipes. Runs locally in your browser.
Bernoulli Equation Calculator Incompressible Bernoulli along a streamline: solve P2, v2, or h2. Runs locally in your browser.
Darcy–Weisbach Calculator Compute pipe head loss hf = f L v²/(2 g D) and Δp = ρ g hf from a given Darcy friction factor. Runs locally. Does not solve Colebrook for f.
Manning Formula Calculator Compute SI Manning discharge Q = (1/n) A R^{2/3} S^{1/2}. Runs locally. Not Q=Av, not Darcy–Weisbach, and not a weir.

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Alternate Depth Calculator Compute both rectangular depths at the same specific energy from E, Q, and width b. Runs locally. Not specific energy from y+v; not specific force M; not hydraulic jump y2; not critical depth yc as the product.
Bernoulli Equation Calculator Incompressible Bernoulli along a streamline: solve P2, v2, or h2. Runs locally in your browser.
Broad-Crested Weir Calculator Compute rectangular broad-crested weir discharge Q = C_d (2/3)^{3/2} b √g H^{3/2}. Default C_d=0.85. Runs locally. Not a thin-plate weir, not Manning, not Q=Av, and not an orifice.
Cavitation Number Calculator Compute the cavitation number σ = (p − p_v) / (½ ρ v²). Runs locally. Not NPSH, not Thoma NPSH/H, not Weber, and not Euler Eu=Δp/(ρ v²).
Chezy Formula Calculator Compute open-channel mean velocity V = C √(R S). Runs locally. Not Manning n, not Q=Av, not Hazen–Williams, and not Darcy.
Colebrook Friction Factor Calculator Solve the Colebrook–White equation for Darcy friction factor f from Re and ε/D. Turbulent pipes Re≥4000. Runs locally. Not laminar 64/Re and not a Moody-chart lookup.
Concentric Reducer Calculator Compute concentric-reducer loss h = K v₂² / (2g) with K = 0.5 (1 − A₂/A₁) referenced to the downstream speed. Runs locally. Not sudden expansion, not gradual contraction α, not vena-contracta C_c, not catalog K, and not Q=Av.
Critical Depth Calculator Compute rectangular critical depth yc = (q²/g)^{1/3}. Runs locally. Not a Froude wrap, not specific energy, not a hydraulic jump, and not Q=Av.
Critical Slope Calculator Compute rectangular critical bed slope Sc such that yn=yc using SI Manning at y=yc. Runs locally. Not Manning A,R; not normal-depth yn; not critical-depth yc as the product; not Chezy; not Q=Av.
Cutthroat Flume Calculator Compute Skogerboe cutthroat flume free-flow discharge from throat width W, independent flume length L_f, and gage head Ha. Runs locally. Not a Parshall flume, not a thin-plate weir, not a broad-crested weir, not Manning, not Q=Av, and not an orifice.
Darcy–Weisbach Calculator Compute pipe head loss hf = f L v²/(2 g D) and Δp = ρ g hf from a given Darcy friction factor. Runs locally. Does not solve Colebrook for f.
Drag Force Calculator Fd = ½ ρ v² Cd A. Runs locally in your browser.
Drowned Sluice Calculator Compute Swamee 1992 drowned undershot sluice discharge from opening a, width b, upstream depth y1, and downstream depth y2. Runs locally. C_d is reported, not an input. Not free-flow sluice, not a Villemonte weir, not a tank orifice, not Manning, and not Q=Av.
Elbow Flow Meter Calculator Compute 90° elbow-tap discharge from inner/outer Δp. C=√((R/D)/2). Runs locally. Not pipe-bend K, not Pitot C=1, not venturi, not ISO 5167-6 wedge, not given C_d.
Flow Rate Calculator Volumetric flow Q=A·v (or from pipe diameter). Runs locally in your browser.
Froude Number Calculator Compute the open-channel Froude number Fr = v / √(g L). Default g=9.80665 m/s². Runs locally. Not Reynolds, not Manning, not Chezy, and not Q=Av.
Gradual Contraction Calculator Compute conical-contraction loss h = K v2² / (2g) with K = 0.5 sin(α) (1 − v1/v2). α is the wall half-angle. Runs locally. Not sudden contraction, not gradual expansion, not minor-loss K as an input, and not Q=Av.
Gradual Expansion Calculator Compute conical-diffuser loss h = k (v1 − v2)² / (2g) with k = 2.6 sin(α). α is the wall half-angle. Runs locally. Not sudden expansion, not minor-loss K as an input, and not Q=Av.
Hagen–Poiseuille Calculator Compute laminar circular-pipe flow Q = π Δp D⁴ / (128 μ L). Runs locally. Not Darcy f, not Colebrook, and not Q=Av.
Hazen–Williams Calculator Compute SI Hazen–Williams head loss hf = 10.67 L Q^{1.852} / (C^{1.852} D^{4.87}) for a circular water pipe. Runs locally. Not Darcy–Weisbach, not Colebrook, and not Manning.
Hydraulic Diameter Calculator Compute hydraulic diameter D_h=4A/P_w for a general section, a full circular pipe, a closed rectangular duct, or an annulus. Runs locally. Not Q=Av, not Manning, and not Darcy.
Hydraulic Jump Calculator Compute rectangular sequent depths y₂/y₁ = (√(1+8 Fr₁²) − 1)/2. Fr₁ > 1. Runs locally. Not a Froude wrap, not Manning, not a weir, and not Q=Av.
ISO 5167 Cone Meter Calculator Compute ISO 5167-5 uncalibrated cone-meter discharge. β=√(1−(d_c/D)²). Runs locally. Not ISA 1932, not RHG orifice, not ISO 5167-4 type C, not long-radius, not given C_d.
ISO 5167 Long-Radius Nozzle Calculator Compute ISO 5167-3 long-radius nozzle discharge with C from β. Runs locally. Not ISA 1932, not given C_d=0.98, not RHG orifice, not ISO 5167-4 type C, not Q=Av.
ISO 5167 Nozzle Calculator Compute ISO 5167-3 ISA 1932 nozzle discharge with C from β and Re_D, not a given C_d. Runs locally. Not a venturi wrap with C_d=0.98, not orifice C_d=0.61, not Q=Av, and not Darcy.
ISO 5167 Orifice Plate Calculator Compute ISO 5167-2 orifice-plate discharge with Reader–Harris/Gallagher C from β, Re_D, and tapping. Runs locally. Not tank orifice C_d A √(2gH), not given C_d=0.61, not ISA 1932 nozzle, not venturi C_d=0.98.
ISO 5167 Venturi Tube Calculator Compute ISO 5167-4 classical Venturi-tube discharge with C from convergent type. Runs locally. Not given C_d=0.98, not ISA 1932 nozzle, not RHG orifice, not Q=Av.
ISO 5167 Wedge Meter Calculator Compute ISO 5167-6 uncalibrated wedge-meter discharge. β from circular-segment h/D. Runs locally. Not cone C=0.82, not ISA 1932, not RHG orifice, not ISO 5167-4 type C, not given C_d.
Manning Formula Calculator Compute SI Manning discharge Q = (1/n) A R^{2/3} S^{1/2}. Runs locally. Not Q=Av, not Darcy–Weisbach, and not a weir.
Minor Loss Calculator Compute fitting minor loss h_m = K v²/(2g). Optional Δp = ρ g h_m. Runs locally. Not Darcy–Weisbach, not Hazen–Williams, and not an orifice.
Mitered Bend Calculator Compute sharp mitered-elbow loss h = K v² / (2g) with K = n [sin²(δ/2) + 2 sin⁴(δ/2)], δ = θ/n. Runs locally. Not circular-arc R/D, not minor-loss K as an input, not Crane f_T, and not Q=Av.
Normal Depth Calculator Compute rectangular uniform-flow normal depth yn from SI Manning with A=b yn and R=b yn/(b+2 yn). Runs locally. Not Manning A,R; not critical depth; not specific energy; not Chezy; not Q=Av.
NPSH Calculator Compute NPSH available from an open tank or a suction flange, and compare with manufacturer NPSHr. Runs locally. Not pump power, not an orifice, not a weir, not Q=Av, and not Darcy.
Ogee Spillway Calculator Compute USBR high-overflow ogee spillway discharge from crest length L, head H, and design head Hd. Runs locally. C is 3.98 (H/Hd)^{0.12}, not an input. Not a thin-plate weir, not broad-crested, not a sluice, not Manning, and not Q=Av.
Orifice Discharge Calculator Compute sharp-edged orifice discharge. Tank Q=C_d A √(2gH). Meter Q=C_d E A_t √(2Δp/ρ) with E=1/√(1−β⁴). Runs locally. Not a weir, not Q=Av, not Darcy, and not Manning.
Parshall Flume Calculator Compute USBR 1–8 ft Parshall flume free-flow discharge from throat width W and gage head Ha. Runs locally. Not a thin-plate weir, not a broad-crested weir, not Manning, not Q=Av, and not an orifice.
Pipe Bend Calculator Compute circular-arc bend loss h = K v² / (2g) with K = 0.21 (θ/90)/√(R/D). Runs locally. Not minor-loss K as an input, not mitered, not Darcy, and not Q=Av.
Pipe Cross Calculator Compute equal-area sharp 90° four-way cross loss h = K v_c² / (2g) from dividing or combining flow and branch or through split with equal opposite laterals. Runs locally. Not a 90° tee, not a wye, not catalog K, and not Q=Av.
Pipe Entrance Calculator Compute pipe-inlet loss h = K v² / (2g) from geometry: flush K=0.5, reentrant K=0.8, rounded K=0.5/[1+36(rᵢ/D)^1.2]. Runs locally. Not catalog K, not circular-arc R/D, not mitered n, and not Q=Av.
Pipe Exit Calculator Compute pipe-exit loss h = K v² / (2g) with K=1 into a large reservoir. Runs locally. Not catalog K, not inlet geometry, not sudden expansion (v1−v2)², and not Q=Av.
Pipe Period Calculator Compute the water-hammer pipe period T = 2L/c. Runs locally. Not Joukowsky Δp, not Korteweg–Hall c from K/D/e/E, and not Darcy f.
Pipe Tee Calculator Compute equal-area sharp 90° T loss h = K v_c² / (2g) from dividing or combining flow and branch or run split. Runs locally. Not catalog K, not a bend, not pipe-entrance, not pipe-exit, and not Q=Av.
Pipe Wye Calculator Compute equal-area sharp wye loss h = K v_c² / (2g) from branch angle α in (0, 90°), dividing or combining flow, and branch or run split. Runs locally. Not a 90° tee, not catalog K, not a bend, and not Q=Av.
Pitot Tube Calculator Compute incompressible pitot-static speed v = C √(2 Δp / ρ). Default C=1. Runs locally. Not a venturi, not an orifice, not Q=Av, and not two-station Bernoulli.
Pump Power Calculator Compute incompressible pump power P=ρgQH/η and affinity-law scaling Q∝ND, H∝N²D², P∝N³D³. Runs locally. Not an orifice, not a weir, not Q=Av, and not Darcy.
Reynolds Number Calculator Compute Re = ρvL/μ (or vL/ν) with laminar/turbulent guidance for pipes. Runs locally in your browser.
Side Weir Calculator Compute Borghei 1999 sharp-crested rectangular side-weir discharge from channel width B, weir length L, upstream depth y1, sill p, and approach Q1. Runs locally. C_d is 0.71−0.41 Fr₁−0.22(p/y1), not an input. Not a frontal thin-plate weir, not an ogee, not a sluice, not Manning, and not Q=Av.
Sluice Gate Calculator Compute free-flow undershot sluice discharge from gate opening a, width b, and upstream depth y1. Runs locally. C_d is Swamee 1992, not an input. Not a tank orifice, not a weir, not a flume, not Manning, and not Q=Av.
Specific Energy Calculator Compute open-channel specific energy E = y + v²/(2g). Runs locally. Not a Froude wrap, not a hydraulic jump, and not Q=Av.
Specific Force Calculator Compute rectangular specific force M = Q²/(gA) + A ȳ with ȳ = y/2. Runs locally. Not hydraulic jump y2; not specific energy E; not Froude as the product; not Manning; not Q=Av.
Submerged Weir Calculator Compute Villemonte rectangular submerged-weir discharge from crest L, upstream head H1, and downstream head H2. Qs=Qf [1−(H2/H1)^{1.5}]^{0.385}. Runs locally. Not free-flow thin-plate H only, not an ogee, not a side weir, not Manning, and not Q=Av.
Sudden Contraction Calculator Compute vena-contracta sudden-contraction loss h = (1/C_c − 1)² v2² / (2g). Default C_c=0.62. Runs locally. Not sudden expansion, not minor-loss K as an input, not an orifice, and not Q=Av.
Sudden Expansion Calculator Compute Borda–Carnot sudden-expansion loss h = (v1 − v2)² / (2g). Runs locally. Not minor-loss K as an input, not Darcy, not an orifice, and not Q=Av.
Trapezoidal Alternate Depth Calculator Compute both trapezoid depths at the same specific energy from E, Q, b, and z with A=(b+z y)y. Runs locally. Not rectangular alternate depth; not trapezoid E; not trapezoid yc; not trapezoid yn.
Trapezoidal Critical Depth Calculator Compute trapezoid critical depth from Q, bottom width b, and side slope z. Runs locally. Not rectangular yc=(q²/g)^{1/3}, not normal depth, and not Q=Av.
Trapezoidal Hydraulic Jump Calculator Compute trapezoid sequent depths from specific force on A=(b+z y)y. Runs locally. Not rectangular Bélanger y2/y1=(√(1+8Fr₁²)−1)/2; not trapezoid alternate E-pair; not trapezoid yc; not trapezoid yn.
Trapezoidal Normal Depth Calculator Compute trapezoid uniform-flow yn from SI Manning with A=(b+z y)y and P=b+2 y √(1+z²). Runs locally. Not rectangular yn, not trapezoid yc, not Manning A,R, not Chezy, not Q=Av.
Trapezoidal Specific Energy Calculator Compute trapezoid specific energy E=y+Q²/(2gA²) with A=(b+z y)y. Runs locally. Not rectangular E=y+v²/(2g), not trapezoid yc, not trapezoid yn, not Manning A,R, not Q=Av.
Trapezoidal Specific Force Calculator Compute trapezoid specific force M = Q²/(gA) + A ȳ on A=(b+z y)y. Runs locally. Not rectangular ȳ=y/2; not sequent y2; not specific energy E; not Manning; not Q=Av.
Valve Flow Coefficient Calculator Compute incompressible liquid valve flow from Kv or Cv. Q_m³/h = Kv √(Δp_bar/SG). Kv = 0.865 Cv. Runs locally. Not a venturi, not an orifice, not Q=Av, and not Darcy.
Venturi Meter Calculator Compute incompressible venturi flow Q = C_d A2 √(2Δp/(ρ(1−β⁴))) with β = D2/D1. Default C_d = 0.98. Runs locally. Not an orifice plate, not Q=Av, not Darcy, and not valve Cv/Kv.
Viscosity Calculator τ = η du/dy. Runs locally in your browser.
Water Hammer Calculator Compute Joukowsky water-hammer Δp = ρ c Δv. Runs locally. Not Darcy f, not minor-loss K, and not Q=Av.
Wave Celerity Calculator Compute pipe-wave celerity c = √[(K/ρ)/(1+(K D)/(E e))]. Runs locally. Not Joukowsky Δp, not Darcy f, and not minor-loss K.
Weber Number Calculator Compute the Weber number We = ρ v² L / σ. Runs locally. Not Reynolds, not Froude, not Manning, not Q=Av, and not capillary Ca=μv/σ.
Weir Discharge Calculator Compute thin-plate weir discharge. Rectangular Q=(2/3) C_d L √(2g) H^{3/2}. V-notch Q=(8/15) C_d √(2g) tan(θ/2) H^{5/2}. Runs locally. Not Manning, not Q=Av, not Darcy, and not an orifice.