Darcy's Law Calculator

Darcy's Law Formula

Worked Example

An aquifer with K = 10 m/day, 2 m head drop over 100 m and 50 m² cross-section:

1. i = Δh ÷ L = 2 ÷ 100 = 0.02
2. Q = K i A = 0.0001157407407 m/s × 0.02 × 50 m² = 10 m³/day
3. Seepage velocity = q ÷ nₑ = 0.8 m/day

Darcy velocity q = Ki: 0.2 m/day · Seepage (average linear) velocity q/nₑ: 0.8 m/day · Travel time over L: 125 days

GATE tip

Transmissivity T = Kb for a confined aquifer of thickness b. Questions often give T, so Q = T i W for a strip of width W.

More Hydraulics and Groundwater Calculators

• Well Yield Calculator

  Confined: Q = 2πKb(h₂ − h₁)/ln(r₂/r₁)

  unconfined: Q = πK(h₂² − h₁²)/ln(r₂/r₁)

  Example: A confined aquifer, K = 20 m/day, 30 m thick, with heads 40 m at the 0.15 m well and 45 m at 300 m: Well discharge Q = 2479.91 m³/day.

  Open the well yield calculator →

• Manning's Equation Calculator

  V = (1/n) R^(2/3) S^(1/2), Q = VA

  R = A/P hydraulic radius; SI units (multiply by 1.49 in US units)

  Example: A 2 m wide concrete rectangular channel flowing 0.5 m deep at a slope of 0.001: Discharge Q = 1.01351 m³/s.

  Open the manning's equation calculator →

• Critical Depth Calculator

  y_c = (q²/g)^(1/3), E_c = 1.5 y_c

  specific energy E = y + q²/(2gy²); V_c = √(g y_c)

  Example: A rectangular channel carrying 2 m²/s per metre width: Critical depth y_c = 0.741617 m.

  Open the critical depth calculator →

• Hydraulic Jump Calculator

  y₂/y₁ = ½(√(1 + 8F₁²) − 1)

  F₁ = V₁/√(gy₁); head loss h_L = (y₂ − y₁)³/(4y₁y₂)

  Example: Flow 0.3 m deep at 6 m/s entering a 3 m wide stilling basin: Sequent depth y₂ = 1.34167 m.

  Open the hydraulic jump calculator →

Frequently asked questions

Sources

• The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.