Discharge Given Energy Gradient Calculator

Formula Used:

\[ Q_{eg} = \sqrt{\frac{(1 - \frac{i}{m}) \cdot (g \cdot S^3)}{T}} \]

Hydraulic Gradient to Head Loss (i):

Slope of Line (m):

Wetted Surface Area (S):

m²

Top Width (T):

Discharge by Energy Gradient (Q_eg):

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1. What is the Energy Gradient Formula?

The Energy Gradient Formula calculates the discharge rate in open channel flow based on hydraulic gradient, slope, wetted surface area, and top width. It provides an accurate assessment of flow rate considering energy losses in the system.

2. How Does the Calculator Work?

The calculator uses the energy gradient formula:

\[ Q_{eg} = \sqrt{\frac{(1 - \frac{i}{m}) \cdot (g \cdot S^3)}{T}} \]

Where:

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

Explanation: The equation accounts for the relationship between energy gradient, channel geometry, and flow characteristics to determine discharge rate.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for hydraulic engineering, flood forecasting, irrigation system design, and environmental flow assessments in open channels.

4. Using the Calculator

Tips: Enter hydraulic gradient, slope, wetted surface area in m², and top width in meters. All values must be positive numbers with slope, wetted area, and top width greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is hydraulic gradient to head loss?
A: Hydraulic gradient represents the rate of energy loss per unit length along the flow path, indicating the slope of the energy line.

Q2: How is wetted surface area different from cross-sectional area?
A: Wetted surface area refers to the total area in contact with water, while cross-sectional area is the area perpendicular to flow direction at a specific section.

Q3: What are typical values for energy gradient discharge?
A: Values vary widely depending on channel size and slope, ranging from small streams (0.1-10 m³/s) to major rivers (100-10,000+ m³/s).

Q4: When is this formula most accurate?
A: The formula works best for uniform flow conditions in prismatic channels with steady discharge and constant slope.

Q5: Are there limitations to this equation?
A: The formula may be less accurate for rapidly varied flow, non-prismatic channels, or when sediment transport significantly affects flow characteristics.