Critical Depth Calculator

Critical Depth Formula

Worked Example

A rectangular channel carrying 2 m²/s per metre width:

1. y_c = (q²/g)^(1/3) = (2² ÷ 9.80665)^(1/3) = 0.7416171629 m
2. E_c = 1.5 y_c = 1.112425744 m
3. E = y + q²/(2gy²) = 1.341627252 m

Critical velocity √(g y_c): 2.696809217 m/s · Specific energy at y = 1.2 m: 1.341627252 m · Froude number at y: 0.4858450573 · Flow at y is: subcritical

GATE tip

For a broad-crested weir the flow is critical over the crest, so q = √g (2E/3)^(3/2): Q ≈ 1.705 B H^(3/2) in SI units with H the upstream head.

More Hydraulics and Groundwater Calculators

• 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 →

• 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 →

• Darcy's Law Calculator

  Q = K i A, i = Δh/L

  Darcy velocity q = Ki; seepage (linear) velocity = q/nₑ

  Example: An aquifer with K = 10 m/day, 2 m head drop over 100 m and 50 m² cross-section: Discharge Q = 10 m³/day.

  Open the darcy's law calculator →

• 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 →

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.