Mesh Sizing
π Y+ Estimation
Estimates the first-cell wall distance (Ξy) needed to achieve a target y+ value, given flow conditions and geometry type.
Wall Distance for Target Y+
Estimates Ξy from flow conditions using skin friction coefficient correlation
$$y^+ = \frac{u_\tau \,\Delta y}{\nu}, \quad u_\tau = \sqrt{\frac{\tau_w}{\rho}}, \quad \tau_w = C_f \frac{\rho U^2}{2}, \quad \Delta y = \frac{y^+ \nu}{u_\tau}$$
CΖ = 0.079Β·Reβ»β°Β·Β²β΅ (Petukhov, turbulent pipe)
CΖ = 0.0592Β·Reβ»β°Β·Β² (Schlichting, turbulent flat plate)
CΖ = 0.074Β·Reβ»β°Β·Β² (approximate external body)
Free-stream velocity U
Reference length L
Density Ο
Dyn. viscosity ΞΌ
Target yβΊ
Results
Y* β Pressure-Velocity Wall Unit
Wall-distance scaling when pressure gradient dominates over friction
$$y^* = \frac{y\,u_p}{\nu},\quad u_p = \left(\nu\,\frac{|dp/dx|}{\rho}\right)^{1/3}$$
Used in low-Reynolds-number models with significant streamwise pressure gradient. y* β y+ in zero-pressure-gradient flow.
Wall distance y
Pressure gradient |dp/dx|
Density Ο
Dyn. viscosity ΞΌ
Results
Flow Classification
π Dimensionless Numbers
Reynolds, Mach, Strouhal, Dean, and PΓ©clet numbers with flow regime interpretation.
Reynolds Number
Re = ΟΒ·UΒ·L/ΞΌ β inertial vs viscous forces
$$\mathrm{Re} = \frac{\rho U L}{\mu} = \frac{U L}{\nu}, \qquad D_h = \frac{4A}{P_w}$$
Velocity U
Length/Diameter L
Density Ο
Dyn. viscosity ΞΌ
Results
Mach Number
Ma = U/a β compressibility effects
$$a = \sqrt{\gamma RT},\quad \mathrm{Ma}=U/a$$
Flow velocity U
Temperature T
Ratio Ξ³ (Cp/Cv)
Results
Strouhal Number
St = fΒ·L/U β oscillation vs convection
$$\mathrm{St}=fL/U$$
Frequency f
Char. length L
Velocity U
Results
Dean Number
De = ReΒ·β(r/R) β curved pipe secondary flow
$$\mathrm{De}=\mathrm{Re}\sqrt{r/R}$$
Reynolds number
Pipe radius r
Curvature radius R
Results
PΓ©clet Number
Pe = UΒ·L/D β advection vs diffusion
$$\mathrm{Pe}=UL/D=\mathrm{Re}\cdot\mathrm{Sc},\quad \mathrm{Sc}=\nu/D$$
Velocity U
Length L
Diffusivity D
Results
Turbulence Modeling
πͺ Turbulence Properties & Boundary Conditions
Compute k, Ξ΅, Ο, and Ξ½β from turbulence intensity and length scale for k-Ξ΅ and k-Ο SST solvers.
Turbulence Inlet BCs β k, Ξ΅, Ο, Ξ½β
For k-Ξ΅, k-Ο SST, and Spalart-Allmaras solvers from I and β
$$k=\tfrac{3}{2}(UI)^2,\quad \varepsilon=\frac{C_\mu^{3/4}k^{3/2}}{L_t},\quad \omega=\frac{\varepsilon}{C_\mu k}$$
Velocity U
Intensity I (%)
Length scale β
Ξ½ (kin. visc.)
Results β Paste into solver inlet
Turbulence Intensity Estimate
From Reynolds number (pipe / free-stream)
$$I_\mathrm{pipe}=0.16\,Re^{-1/8},\quad I_\mathrm{ext}=0.16\,Re^{-1/8}$$
Reynolds number
Results
Turbulent Length Scale Estimate
From geometry type and characteristic dimension
$$\ell_\mathrm{pipe}=0.07D,\quad \ell_\mathrm{ext}=0.07D$$
Geometry type
Char. dimension
Results
Boundary Layer
π Boundary Layer Thickness
Flat-plate laminar and turbulent boundary layer properties, plus pipe hydrodynamic entry length.
Flat Plate BL Thickness
Laminar (Blasius) and turbulent Schlichting correlations
$$\delta_\mathrm{lam}=\frac{5x}{\sqrt{Re_x}},\quad \delta^*=\frac{1.72x}{\sqrt{Re_x}},\quad \theta=\frac{0.664x}{\sqrt{Re_x}}$$
Distance x
Velocity U
Kin. viscosity Ξ½
Results
Pipe Entry / Development Length
Hydrodynamic and thermal entry lengths
$$L_{e,\mathrm{lam}}=0.06\,Re\,D,\quad L_{e,\mathrm{turb}}=4.4\,Re^{1/6}D,\quad L_t=0.05\,Re\,Pr\,D$$
Pipe diameter D
Reynolds number
Prandtl number Pr
Results
Internal Flow
π΅ Pipe & Channel Flow
Hagen-Poiseuille laminar flow, Darcy-Weisbach pressure drop with Moody friction factor.
Hagen-Poiseuille (Laminar)
Q = ΟRβ΄ΞP / (8ΞΌL) β assumes Re < 2300
$$Q=\frac{\pi R^4\Delta P}{8\mu L},\quad \bar{U}=\frac{R^2\Delta P}{4\mu L},\quad U_\mathrm{max}=2\bar{U}$$
Pressure drop ΞP
Flow rate Q
Pipe radius R
Pipe length L
Dyn. viscosity ΞΌ
Results
Darcy-Weisbach Pressure Drop
ΞP = fΒ·(L/D)Β·(ΟUΒ²/2) with Moody friction factor
$$\Delta P=f\frac{L}{D}\frac{\rho U^2}{2},\quad f_\mathrm{lam}=\frac{64}{Re},\quad \frac{1}{\sqrt{f}}=-2\log_{10}\!\left(\frac{\varepsilon}{3.7D}+\frac{2.51}{Re\sqrt{f}}\right)$$
Velocity U
Pipe diameter D
Pipe length L
Density Ο
Dyn. viscosity ΞΌ
Roughness Ξ΅
Results
Hydraulic Diameter
D_h = 4A/P for non-circular channels
$$D_h=4A/P_w$$
Width w
Height h
Outer D_o
Inner D_i
Base b
Height h_t
Results
Biomedical CFD
π©Έ Non-Newtonian Viscosity Models
Effective viscosity from Power Law, Carreau, and Quemada models. Particularly relevant for blood flow simulation.
Power Law (Ostwald-de Waele)
ΞΌ_eff = KΒ·Ξ³ΜβΏβ»ΒΉ
$$\tau=K\dot\gamma^n,\quad \mu_\mathrm{eff}=K\dot\gamma^{n-1}$$
Consistency K
Power index n
Shear rate Ξ³Μ
Results
Carreau Model (Blood Default)
ΞΌ_eff = ΞΌ_β + (ΞΌββΞΌ_β)Β·[1+(λγΜ)Β²]^((nβ1)/2)
$$\mu(\dot\gamma)=\mu_\infty+(\mu_0-\mu_\infty)\bigl[1+(\lambda\dot\gamma)^2\bigr]^{(n-1)/2}$$
ΞΌβ (zero-rate)
ΞΌ_β (inf-rate)
Ξ» (time const.)
n (power index)
Shear rate Ξ³Μ
Results
Newtonian Validity Check
Identifies regions where non-Newtonian models are needed
$$\dot\gamma>100\ \mathrm{s}^{-1}:\ \text{Newtonian OK};\quad \dot\gamma<100\ \mathrm{s}^{-1}:\ \text{non-Newtonian}$$
Mean velocity U
Vessel radius R
Results
Biomedical CFD
π Pulsatile Flow & Wall Metrics
Womersley number, wall shear stress, and oscillatory shear index for cardiovascular flow simulations.
Womersley Number
Ξ± = RΒ·β(2Οf/Ξ½) β pulsatile flow inertia
$$\alpha=R\sqrt{\omega/\nu},\quad \alpha<2:\ \text{quasi-steady},\quad \alpha\gg10:\ \text{inertia-dominated}$$
Vessel radius R
Heart rate / freq.
Kin. viscosity Ξ½
Results
Wall Shear Stress (Pipe)
Laminar: Ο_w = 4ΞΌQ/(ΟRΒ³) or from ΞP
$$\tau_w=\frac{4\mu Q}{\pi R^3},\quad \mathrm{TAWSS}=\frac{1}{T}\int_0^T|\tau_w|\,dt$$
Flow rate Q
Pressure drop ΞP
Pipe length L
Radius R
Dyn. viscosity ΞΌ
Results
Oscillatory Shear Index (OSI)
Quantifies WSS directionality over a cardiac cycle
$$\mathrm{OSI}=\frac{1}{2}\!\left(1-\frac{|\int\tau_w\,dt|}{\int|\tau_w|\,dt}\right)$$
Enter time-series of WSS values (space or comma separated):
Results
Structural FEA
π© Elastic Constants Conversion
Convert between Young's modulus E, Poisson's ratio Ξ½, shear modulus G, bulk modulus K, and LamΓ© constants.
Isotropic Elastic Constants
Given any two independent constants, compute all others
$$E=2G(1+\nu)=3K(1-2\nu),\quad G=\frac{E}{2(1+\nu)},\quad K=\frac{E}{3(1-2\nu)}$$
Provide two of these
Young's E
Poisson's Ξ½
Shear G
Bulk K
LamΓ© Ξ»
Results
Structural FEA
β‘ Stress Analysis & Failure Criteria
Von Mises equivalent stress, principal stresses, Tresca criterion, and safety factors.
Von Mises Stress (2D / 3D)
Distortion energy failure criterion
$$\sigma_\mathrm{VM}=\sqrt{\sigma_x^2-\sigma_x\sigma_y+\sigma_y^2+3\tau_{xy}^2}\quad(2\mathrm{D})$$
Ο_x
Ο_y
Ο_xy
Οβ
Οβ
Οβ
Yield strength Ο_y
Results
Pressure Vessel / Cylinder
LamΓ© equations for thick/thin-walled vessels
$$\sigma_h=pr/t\ (\text{thin}),\quad \sigma_h(r)=\frac{pr_i^2}{r_o^2-r_i^2}\!\left(1+\frac{r_o^2}{r^2}\right)\ (\text{Lam\'{e}})$$
Internal pressure P
Inner radius r_i
Outer radius r_o
Yield strength Ο_y
Results
Structural FEA
π Beam Deflection & Second Moment of Area
Classical beam deflection formulas and moment of inertia for common cross-sections.
Beam Deflection
Cantilever, simply supported, UDL cases
$$\delta_\mathrm{cant}=\frac{PL^3}{3EI},\quad \sigma_\mathrm{max}=\frac{PLc}{I}$$
$$\delta_\mathrm{SS}=\frac{PL^3}{48EI},\quad \sigma_\mathrm{max}=\frac{PLc}{4I}$$
$$\delta_\mathrm{UDL}=\frac{5wL^4}{384EI}$$
Load F (or w)
Length L
Young's E
2nd moment I
Neutral axis c
Results
Second Moment of Area
I for rectangle, circle, hollow circle, I-beam
$$I=\frac{bh^3}{12},\quad A=bh$$
Width b
Height h
$$I=\frac{\pi D^4}{64},\quad A=\frac{\pi D^2}{4}$$
Diameter D
$$I=\frac{\pi(D_o^4-D_i^4)}{64}$$
Outer D_o
Inner D_i
Results
All Engineers
π Geometry
Areas, volumes, moments of inertia, centroids, surface areas β circles, rectangles, triangles, ellipses, spheres, cylinders, cones, and more.
2D Shape Properties
Area, perimeter, centroid, second moment of area
$$A_\mathrm{circle}=\pi r^2,\quad I_x=\frac{\pi r^4}{4},\quad A_\mathrm{rect}=bh,\quad I_x=\frac{bh^3}{12}$$
Radius r
Results
Width b
Height h
Results
Base b
Height h
Side c (optional)
Results
Semi-major a
Semi-minor b
Results
Outer radius R
Inner radius r
Results
3D Shape Properties
Volume, surface area, centroid height
$$V_\mathrm{sphere}=\tfrac{4}{3}\pi r^3,\quad V_\mathrm{cyl}=\pi r^2 h,\quad V_\mathrm{cone}=\tfrac{1}{3}\pi r^2 h$$
Radius r
Results
Radius r
Height h
Results
Base radius r
Height h
Results
Length a
Width b
Height c
Results
Major radius R
Tube radius r
Results
Triangle Solver Auto-solve β Law of Cosines / Sines
Enter any 3 known values (side or angle) β all others computed
$$c^2=a^2+b^2-2ab\cos C,\qquad \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$
Leave one field blank. Angles in degrees. At least one side must be known.
Side a
Side b
Side c
Angle AΒ°
Angle BΒ°
Angle CΒ°
Results
Coordinate Geometry
Distance, midpoint, line equations, angle between lines, circle equation
$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2},\quad \text{slope}=\frac{y_2-y_1}{x_2-x_1}$$
xβ
yβ
xβ
yβ
Results
Enter slope and one point, or two points.
Slope m
Point (xβ, yβ)
Results
Centre (h, k)
Radius r
Results
All Engineers
β« Calculus Tools
Numerical differentiation, numerical integration (Simpson / Gauss), Taylor series, gradient / divergence / curl in Cartesian coordinates, and common engineering transforms.
Numerical Differentiation
Forward, backward, central difference β enter f(xΒ±h) values
$$f'(x)\approx\frac{f(x+h)-f(x-h)}{2h},\quad f''(x)\approx\frac{f(x+h)-2f(x)+f(x-h)}{h^2}$$
f(x β h)
f(x)
f(x + h)
Step size h
Results
Numerical Integration
Trapezoidal rule, Simpson's 1/3, Simpson's 3/8 β up to 9 equally-spaced points
$$\int_a^b f\,dx \approx \frac{h}{3}(f_0+4f_1+2f_2+\cdots+4f_{n-1}+f_n)\quad \text{(Simpson)}$$
Enter equally-spaced y-values (at least 3). For Simpson's: use 3, 5, 7, or 9 points (n+1 odd).
x start (a)
x end (b)
y values (comma separated)
Results
Taylor Series Approximation
sin, cos, eΛ£, ln(1+x), (1+x)βΏ β value and error estimate
$$f(x)=\sum_{n=0}^N \frac{f^{(n)}(a)}{n!}(x-a)^n$$
Function
x (radians for trig)
Terms to use (1β12)
Results
Vector Calculus β Gradient, Divergence, Curl
Numerical evaluation at a point from finite-difference stencils
$$\nabla f=\left(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z}\right),\quad \nabla\cdot\mathbf{F}=\frac{\partial F_x}{\partial x}+\frac{\partial F_y}{\partial y}+\frac{\partial F_z}{\partial z}$$
Enter scalar f at 6 neighbouring points (central difference). All h = step size.
f(x+h,y,z)
f(x-h,y,z)
f(x,y+h,z)
f(x,y-h,z)
f(x,y,z+h)
f(x,y,z-h)
Step size h
Results
Enter vector field components F=(Fx,Fy,Fz) at neighbouring points.
Fx(x+h)
Fx(x-h)
Fy(y+h)
Fy(y-h)
Fz(z+h)
Fz(z-h)
Step size h
Results
βΓF = (βFz/βyββFy/βz, βFx/βzββFz/βx, βFy/βxββFx/βy)
Fz(y+h)
Fz(y-h)
Fy(z+h)
Fy(z-h)
Fx(z+h)
Fx(z-h)
Fz(x+h)
Fz(x-h)
Fy(x+h)
Fy(x-h)
Fx(y+h)
Fx(y-h)
Step size h
Results
Unit Converters
π All Unit Converters
Live unit conversion β type a value to see all equivalents instantly.
MME / ChE / EE
π‘οΈ Heat Transfer
Conduction, convection, radiation, thermal resistance, and Fourier / Newton / Stefan-Boltzmann laws.
Fourier Conduction / Thermal Resistance
Flat wall, cylindrical, and composite wall
$$q=\frac{kA\,\Delta T}{L},\quad R_{th}=\frac{L}{kA},\quad q_\mathrm{cyl}=\frac{2\pi kL\,\Delta T}{\ln(r_2/r_1)}$$
Conductivity k
Area A
Thickness L
ΞT
Results
Conductivity k
Length L
Inner radius rβ
Outer radius rβ
ΞT
Results
Forced Convection β Nusselt / h
Dittus-Boelter (pipe), Churchill-Bernstein (cylinder), flat plate
$$\mathrm{Nu}=hL/k,\quad \mathrm{Nu}_\mathrm{pipe}=0.023\,Re^{0.8}Pr^n,\quad \mathrm{Nu}_\mathrm{plate}=0.664\,Re^{0.5}Pr^{1/3}$$
Dittus-Boelter: n=0.4 heating, n=0.3 cooling. Valid Re>10,000, 0.6<Pr<160.
Re
Pr
Fluid k
Diameter D
Mode
Results
Laminar: Nu=0.664Β·Re^0.5Β·Pr^(1/3). Turbulent: Nu=0.037Β·Re^0.8Β·Pr^(1/3).
Re_L
Pr
Fluid k
Length L
Results
Thermal Radiation β Stefan-Boltzmann
Blackbody, greybody, and net exchange between surfaces
$$q=\varepsilon\sigma A(T_1^4-T_2^4),\quad \sigma=5.67\times10^{-8}\ \mathrm{W/(m^2 K^4)}$$
Emissivity Ξ΅
Surface area A
Surface temp Tβ
Surroundings Tβ
Results
Extended Surface (Fin) Efficiency
Rectangular, spine, and annular fins
$$m=\sqrt{hP/(kA_c)},\quad \eta=\tanh(mL)/(mL),\quad q=\eta hPL\,\Delta T$$
Conv. coeff h
Conductivity k
Fin width w
Fin thickness t
Fin length L
T_base β T_β
Results
MME / Civil / Aerospace
π§ Material & Fracture Mechanics
Stress intensity factors, fatigue life (S-N), torsion, thick-wall pressure vessels, and buckling.
Stress Intensity Factor β Mode I
Through-crack in infinite plate; Irwin K_I = Οβ(Οa)
$$K_\mathrm{I}=Y\sigma\sqrt{\pi a},\quad a_\mathrm{cr}=\frac{1}{\pi}\!\left(\frac{K_\mathrm{IC}}{Y\sigma}\right)^2$$
Remote stress Ο
Half crack length a
Geometry factor Y
Fracture toughness K_IC
Results
Fatigue Life β Basquin S-N
Cycles to failure from stress amplitude and material constants
$$\sigma_a=\sigma_{f}^{\prime}(2N_f)^b,\quad N_f=\tfrac{1}{2}\!\left(\sigma_a/\sigma_{f}^{\prime}\right)^{1/b},\quad \sigma_a/S_e+\sigma_m/S_u=1$$
Stress amplitude Ο_a
Fatigue strength coeff Ο_fβ²
Fatigue strength exponent b
Mean stress Ο_m
Ultimate strength S_u
Results
Torsion of Circular Shaft
Shear stress, angle of twist, polar moment of inertia
$$\tau_\mathrm{max}=Tr/J,\quad \phi=TL/(GJ),\quad J_\mathrm{solid}=\pi d^4/32$$
Torque T
Diameter d
Length L
Shear modulus G
Results
Torque T
Outer diam d_o
Inner diam d_i
Length L
Shear modulus G
Results
Thick-Wall Pressure Vessel & Column Buckling
LamΓ© hoop/radial stress; Euler critical load
$$\sigma_\theta=\frac{pr_i^2(r_o^2+r^2)}{r^2(r_o^2-r_i^2)},\qquad P_\mathrm{cr}=\frac{\pi^2 EI}{(KL)^2}$$
Internal pressure p
Inner radius r_i
Outer radius r_o
Results
K: 0.5=fixed-fixed, 0.7=fixed-pinned, 1.0=pinned-pinned, 2.0=fixed-free
Elastic modulus E
2nd moment I
Column length L
End condition K
Results
EE / BME
β‘ Electrical Engineering
RC/RL/RLC circuits, filter design, Ohm's law, power, dB, and signal encoding.
Ohm's Law & DC Power
Solve any two of V, I, R, P
$$V=IR,\quad P=VI=I^2R=V^2/R$$
Enter any two fields β the others are computed.
Voltage V
Current I
Resistance R
Power P
Results
RC / RL / RLC Circuits
Time constants, cutoff frequency, resonance, Q-factor
$$\tau_{RC}=RC,\;\; f_c=\frac{1}{2\pi RC},\;\; f_0=\frac{1}{2\pi\sqrt{LC}},\;\; Q=\frac{\omega_0 L}{R}$$
β‘ Auto-solve: leave R or C blank β enter Ο or fc below to back-calculate.
Resistance R
Capacitance C
Results
Resistance R
Inductance L
Results
Resistance R
Inductance L
Capacitance C
Results
Decibels & Signal Levels
Voltage gain, power gain, dBm, SNR, and noise figure
$$G_\mathrm{dB}=20\log_{10}(V_2/V_1)\ \text{(voltage)},\quad G_\mathrm{dB}=10\log_{10}(P_2/P_1)\ \text{(power)}$$
Type
Input value
Output value
Results
Power (mW)
Power (dBm)
Results
Op-Amp Configurations
Inverting, non-inverting, difference, integrator, differentiator
$$A_v^\mathrm{inv}=-R_f/R_{in},\quad A_v^\mathrm{non-inv}=1+R_f/R_1,\quad V_o=\frac{R_f}{R_{in}}(V_+-V_-)$$
R_in
R_f
V_in
Results
Rβ (to ground)
R_f
V_in
Results
R_in
R_f
V+ (non-inv input)
Vβ (inv input)
Results
BME / Clinical
π« Biomedical Engineering
Cardiac output, vascular resistance, Poiseuille flow, Windkessel model, Nernst potential, and electrode impedance.
Cardiovascular Hemodynamics
Cardiac output, stroke volume, vascular resistance, Poiseuille
$$\mathrm{CO}=\mathrm{SV}\times\mathrm{HR},\quad \mathrm{SVR}=\mathrm{MAP}/\mathrm{CO},\quad Q=\pi R^4\Delta P/(8\mu L)$$
Stroke volume SV
Heart rate HR
MAP
Results
Hagen-Poiseuille: Q = ΟΞPΒ·rβ΄/(8ΞΌL) β valid laminar, Newtonian, fully developed flow.
Pressure drop ΞP
Vessel radius r
Length L
Viscosity ΞΌ
Results
Nernst & Goldman Equations
Equilibrium potential, Goldman membrane voltage
$$E_X=\frac{RT}{zF}\ln\frac{[X]_o}{[X]_i},\quad V_m=\frac{RT}{F}\ln\frac{P_K[K]_o+P_{Na}[Na]_o+P_{Cl}[Cl]_i}{P_K[K]_i+P_{Na}[Na]_i+P_{Cl}[Cl]_o}$$
Ion charge z
Outside conc [X]_o
Inside conc [X]_i
Temperature T
Results
Goldman-Hodgkin-Katz for KβΊ, NaβΊ, Clβ». Permeabilities relative to P_K.
[KβΊ]_out / [KβΊ]_in (mM)
[NaβΊ]_out / [NaβΊ]_in
[Clβ»]_out / [Clβ»]_in
P_K : P_Na : P_Cl
Results
MME / EE / Aerospace
ποΈ Dynamics & Control
Mass-spring-damper, natural frequency, damping ratio, PID tuning, and projectile motion.
Mass-Spring-Damper System
Natural frequency, damping ratio, response classification
$$\omega_n=\sqrt{k/m},\quad \zeta=c/(2\sqrt{km}),\quad \omega_d=\omega_n\sqrt{1-\zeta^2}$$
Mass m
Spring constant k
Damping coefficient c
Results
Projectile Motion
Range, max height, time of flight β vacuum and with drag
$$R=v_0^2\sin2\theta/g,\quad H=v_0^2\sin^2\!\theta/(2g),\quad t_f=2v_0\sin\theta/g$$
Initial speed vβ
Launch angle ΞΈ
Initial height hβ
Gravity g
Results
Civil / Environmental
ποΈ Civil & Geotechnical
Manning's equation, Darcy seepage, soil bearing capacity, hydraulic jump, and retaining wall stability.
Manning's Open-Channel Flow
Discharge, velocity, and channel design for uniform flow
$$Q=\frac{1}{n}A\,R_h^{2/3}S^{1/2},\quad R_h=A/P_w$$
Manning's n
Channel width b
Flow depth y
Slope S
Results
Full circular pipe (D = diameter, R_h = D/4).
Manning's n
Diameter D
Slope S
Results
Darcy's Law β Groundwater Seepage
Flow through porous media and soil permeability
$$Q=kiA,\quad i=\Delta h/L,\quad v=ki$$
Hydraulic conductivity k
Head difference Ξh
Flow path length L
Cross-section area A
Results