Length Of Reach Calculator

Formula Used:

\[ L = \frac{0.13 \times B^2 \times C \times (0.7 \times C + 2 \times \sqrt{g})}{g \times d_{avg}} \]

Average Width of Stream (B):

Chézy's Coefficients (C):

Acceleration due to Gravity (g):

m/s²

Average Depth of Stream (d_avg):

Length of Reach (L):

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1. What is the Length of Reach Formula?

The Length of Reach formula calculates the mixing length in stream flow measurements using the dilution method. It incorporates stream width, Chézy's coefficient, gravitational acceleration, and average stream depth to determine the required reach length for effective mixing.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{0.13 \times B^2 \times C \times (0.7 \times C + 2 \times \sqrt{g})}{g \times d_{avg}} \]

Where:

\( L \) — Mixing Length (m)
\( B \) — Average Width of Stream (m)
\( C \) — Chézy's Coefficients (-)
\( g \) — Acceleration due to Gravity (m/s²)
\( d_{avg} \) — Average Depth of Stream (m)

Explanation: This formula accounts for the hydraulic characteristics of the stream to determine the minimum length required for complete mixing of tracers in dilution method flow measurements.

3. Importance of Length of Reach Calculation

Details: Accurate determination of mixing length is crucial for reliable stream flow measurements using the dilution method. It ensures complete mixing of tracers before measurement, which is essential for obtaining accurate flow rate calculations.

4. Using the Calculator

Tips: Enter average stream width in meters, Chézy's coefficient (dimensionless), acceleration due to gravity in m/s² (default is 9.8), and average stream depth in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is Chézy's coefficient?
A: Chézy's coefficient is a hydraulic parameter that relates the flow velocity to the hydraulic radius and slope of the channel. It depends on the flow Reynolds number and the relative roughness of the channel.

Q2: Why is the square root of gravity used in the formula?
A: The square root of gravity appears in the formula because it relates to the wave celerity and velocity distribution in open channel flow, which affects the mixing characteristics.

Q3: What are typical values for Chézy's coefficient?
A: Chézy's coefficient typically ranges from 30 m¹/²/s for rough channels to 90 m¹/²/s for smooth channels, though values can vary based on specific hydraulic conditions.

Q4: When is this formula most applicable?
A: This formula is specifically designed for determining mixing length in dilution method stream flow measurements, particularly in natural streams and rivers.

Q5: Are there limitations to this equation?
A: The formula assumes certain hydraulic conditions and may need adjustment for streams with unusual geometries, extreme turbulence, or non-uniform flow conditions.