Chezy Formula for Normal Depth of Wide Rectangular Channel Calculator

Chezy Formula:

\[ Y_n = \left( \frac{C^3 \times g}{C_{VF}^2 \times S_0} \right)^{1/3} \]

Critical Depth of Channel (C):

Chézy's Coefficients for Varied Flow (CVF):

Bed Slope of Channel (S₀):

Normal Depth of Varied Flow (Yₙ):

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1. What is the Chezy Formula for Normal Depth?

The Chezy Formula for Normal Depth of Wide Rectangular Channel calculates the depth of flow in a channel when the water surface slope equals the channel bed slope, and the depth remains constant. It's derived from the Chezy equation for uniform flow in open channels.

2. How Does the Calculator Work?

The calculator uses the Chezy formula:

\[ Y_n = \left( \frac{C^3 \times g}{C_{VF}^2 \times S_0} \right)^{1/3} \]

Where:

\( Y_n \) — Normal Depth of Varied Flow (m)
\( C \) — Critical Depth of Channel (m)
\( C_{VF} \) — Chézy's Coefficients for Varied Flow
\( S_0 \) — Bed Slope of Channel
\( g \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The formula calculates the normal depth by considering the balance between gravitational forces driving the flow and frictional forces resisting it.

3. Importance of Normal Depth Calculation

Details: Calculating normal depth is essential for hydraulic engineering design, including channel sizing, flood control, irrigation systems, and drainage design. It helps determine the expected water depth under uniform flow conditions.

4. Using the Calculator

Tips: Enter critical depth in meters, Chézy's coefficient (dimensionless), and bed slope (dimensionless). All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of typical Chézy coefficients?
A: Chézy coefficients typically range from 30 m¹/²/s for rough channels to 90 m¹/²/s for smooth concrete channels.

Q2: When is this formula most accurate?
A: The formula is most accurate for wide rectangular channels with uniform flow conditions and constant channel properties.

Q3: How does bed slope affect normal depth?
A: Steeper slopes generally result in shallower normal depths for the same discharge, while flatter slopes result in deeper normal depths.

Q4: What are the limitations of this formula?
A: The formula assumes wide rectangular channels, uniform flow, and constant roughness. It may be less accurate for irregular channels or non-uniform flow conditions.

Q5: How is critical depth different from normal depth?
A: Critical depth occurs at minimum specific energy for a given discharge, while normal depth occurs when gravitational forces exactly balance frictional forces in uniform flow.