Chezy Formula for Slope of Dynamic Equation of Gradually Varied Flow Calculator

Chezy Formula:

\[ m = S_0 \times \frac{1 - \left(\frac{y}{d_f}\right)^3}{1 - \left(\frac{h_c}{d_f}\right)^3} \]

Bed Slope of Channel (S₀):

(dimensionless)

Normal Depth (y):

meters

Depth of Flow (d_f):

meters

Critical Depth of Weir (h_c):

meters

Slope of Line (m):

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1. What is the Chezy Formula for Slope of Dynamic Equation?

The Chezy Formula for Slope of Dynamic Equation of Gradually Varied Flow calculates the slope of the energy grade line in open channel flow. It relates the bed slope, normal depth, flow depth, and critical depth to determine the slope of the dynamic equation for gradually varied flow conditions.

2. How Does the Calculator Work?

The calculator uses the Chezy formula:

\[ m = S_0 \times \frac{1 - \left(\frac{y}{d_f}\right)^3}{1 - \left(\frac{h_c}{d_f}\right)^3} \]

Where:

\( m \) — Slope of Line (dimensionless)
\( S_0 \) — Bed Slope of Channel (dimensionless)
\( y \) — Normal Depth (meters)
\( d_f \) — Depth of Flow (meters)
\( h_c \) — Critical Depth of Weir (meters)

Explanation: The formula calculates the slope of the dynamic equation by comparing the ratios of normal depth and critical depth to the actual flow depth, scaled by the bed slope.

3. Importance of Slope Calculation

Details: Accurate slope calculation is crucial for designing open channel systems, predicting flow behavior, and ensuring proper water conveyance in hydraulic engineering projects.

4. Using the Calculator

Tips: Enter all values in appropriate units. Bed slope is dimensionless, while depth values should be in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is gradually varied flow?
A: Gradually varied flow occurs when the flow depth changes gradually along the channel length, unlike rapidly varied flow where depth changes abruptly.

Q2: When is this formula applicable?
A: This formula is used for open channel flow analysis where the flow is steady and the channel slope is relatively mild.

Q3: What does a negative slope indicate?
A: A negative slope typically indicates adverse flow conditions where the water surface slope opposes the bed slope.

Q4: How does critical depth affect the calculation?
A: Critical depth represents the depth at which flow energy is minimum for a given discharge, and it significantly influences the slope calculation.

Q5: Can this formula be used for all channel types?
A: While applicable to various channel types, the formula may need adjustments for extremely irregular cross-sections or complex flow conditions.