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Open Channel Hydraulic Critical Depth & Specific Energy Calculator

Open-channel waterways and hydraulic flumes transition between subcritical (tranquil) and supercritical (rapid) regimes at the critical depth state where specific energy is minimized.

Volumetric flow rate conveyed through the rectangular channel section.

Inside bed width of the rectangular flume or canal.

Measured or design water depth at the station.

Calculated Result
1.233 m

Hydraulic Critical Depth (yc)

Critical Depth (y_c)

1.233 m (4.05 ft)

Froude Number (Fr)

0.57

Flow Hydraulic Regime

SUBCRITICAL FLOW (Fr < 1: Tranquil, deep, gravity waves travel upstream)

Actual Specific Energy (E)

2.089 m

Minimum Specific Energy (E_min)

1.849 m

Critical Velocity (V_c)

3.48 m/s

Calculation Breakdown

  1. Unit Width Dischargeq = Q / b = 15 m³/s / 3.5 m = 4.29 m²/s
  2. Critical Depth Formulation (y_c = [q²/g]¹/³)y_c = [(4.29)² / 9.81]^(1/3) = 1.233 m
  3. Froude Number & Specific EnergyV = 15 / (3.5 × 1.8) = 2.38 m/s → Fr = 2.38 / √(9.81 × 1.8) = 0.57

Channel Energy & Depth States

Interactive visualization based on your current inputs

Value
0.00.51.01.62.1Critical Depth (yc)Min Specific EnergyActual Depth (y)Actual Energy (E)Velocity HeadParameterValue (m)

What Is the Open Channel Hydraulic Critical Depth & Specific Energy Calculator?

The Open Channel Hydraulic Critical Depth & Specific Energy Calculator evaluates flow regimes, specific energy curves, and critical transitions in open canals.

How Does the Open Channel Hydraulic Critical Depth & Specific Energy Calculator Work?

It computes unit discharge, critical depth, critical velocity, operating specific energy, and Froude number to classify the flow regime.

Open Channel Hydraulic Critical Depth & Specific Energy Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

y_c = \left( \frac{q^2}{g} \right)^{1/3}, \quad E = y + \frac{V^2}{2g}, \quad Fr = \frac{V}{\sqrt{g y}}

Bakhmeteff specific energy formulation where critical flow minimizes total head for a given discharge.

How to Use the Open Channel Hydraulic Critical Depth & Specific Energy Calculator

  1. Enter total discharge in m³/s.
  2. Specify channel base width in meters.
  3. Input operating depth to evaluate current state.

Step-by-Step Example Calculation

15 m³/s Rectangular Irrigation Canal

Input Values:

dischargeFlowRateM3s:15
bottomWidthM:3.5
actualWaterDepthM:1.8
Worked Steps: Critical depth is 1.23 m with minimum specific energy of 1.85 m. Actual depth (1.8 m) has Fr = 0.57 (subcritical flow).

Understanding Your Result

Critical Depth (y_c): Threshold water depth separating subcritical and supercritical states.

Minimum Specific Energy: Least energy needed to convey the discharge.

Froude Number: Dimensionless ratio classifying flow state (Fr < 1: subcritical; Fr > 1: supercritical).

Factors That Affect the Result

  • Increasing discharge raises critical depth with power of 2/3.
  • Constricting channel width increases unit discharge and elevates critical depth.

When Should You Use This Calculator?

  • Spillway chutes, weir crest design, canal drops, culvert transitions, and hydraulic jump stilling basin sizing.

Assumptions & Limitations

  • Assumes rectangular prismatic channel section and hydrostatic pressure distribution.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Conforms to Chow Open-Channel Hydraulics and standard fluid dynamics principles.

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