Slope of Dynamic Equation of Gradually Varied Flow Given Energy Gradient Calculator

Formula Used:

\[ Slope of Line = \frac{Hydraulic Gradient to Head Loss}{1 - \frac{Discharge by Energy Gradient^2 \times Top Width}{[g] \times Wetted Surface Area^3}} \] \[ m = \frac{i}{1 - \frac{Q_{eg}^2 \times T}{[g] \times S^3}} \]

Hydraulic Gradient to Head Loss (i):

Discharge by Energy Gradient (Q_eg):

m³/s

Top Width (T):

Wetted Surface Area (S):

m²

Slope of Line (m):

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1. What is the Slope of Dynamic Equation of Gradually Varied Flow?

The Slope of Dynamic Equation of Gradually Varied Flow Given Energy Gradient represents the rate of change of water surface profile in open channel flow. It is a crucial parameter in hydraulic engineering for analyzing and designing water conveyance systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ m = \frac{i}{1 - \frac{Q_{eg}^2 \times T}{[g] \times S^3}} \]

Where:

\( m \) — Slope of Line
\( i \) — Hydraulic Gradient to Head Loss
\( Q_{eg} \) — Discharge by Energy Gradient (m³/s)
\( T \) — Top Width (m)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( S \) — Wetted Surface Area (m²)

Explanation: The formula calculates the slope of the energy gradient line in gradually varied flow conditions, accounting for the relationship between discharge, channel geometry, and gravitational effects.

3. Importance of Slope Calculation

Details: Accurate slope calculation is essential for designing efficient hydraulic structures, predicting water surface profiles, and ensuring proper flow conditions in open channels and rivers.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure values are positive and within reasonable ranges for hydraulic calculations.

5. Frequently Asked Questions (FAQ)

Q1: What is gradually varied flow?
A: Gradually varied flow occurs when the depth of flow changes gradually along the channel length, with the water surface forming a smooth curve.

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

Q3: What are typical values for slope of line?
A: Slope values vary significantly depending on channel characteristics, but typically range from 0.001 to 0.01 for most natural and artificial channels.

Q4: What factors affect the slope calculation?
A: Channel geometry, discharge rate, roughness coefficient, and gravitational effects all influence the slope calculation.

Q5: How accurate is this calculation?
A: The calculation provides a theoretical estimate based on the given parameters. Actual field conditions may vary due to factors not accounted for in the formula.