Discharge Given Total Energy Calculator

Formula Used:

\[ Q_f = \sqrt{(E_t - d_f) \times 2 \times g \times S^2} \]

Total Energy in Open Channel (E_t):

Joule

Depth of Flow (d_f):

Meter

Wetted Surface Area (S):

m²

Discharge for GVF Flow (Q_f):

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1. What is the Discharge Given Total Energy Formula?

The discharge formula calculates the flow rate in an open channel based on the total energy, depth of flow, and wetted surface area. This equation is particularly useful in gradually varied flow (GVF) calculations in hydraulic engineering.

2. How Does the Calculator Work?

The calculator uses the discharge formula:

\[ Q_f = \sqrt{(E_t - d_f) \times 2 \times g \times S^2} \]

Where:

\( Q_f \) — Discharge for GVF Flow (m³/s)
\( E_t \) — Total Energy in Open Channel (Joule)
\( d_f \) — Depth of Flow (Meter)
\( S \) — Wetted Surface Area (m²)
\( g \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The formula calculates discharge by considering the energy difference and the wetted surface area, incorporating gravitational acceleration.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is essential for designing hydraulic structures, flood forecasting, water resource management, and environmental flow assessments.

4. Using the Calculator

Tips: Enter total energy in joules, depth of flow in meters, and wetted surface area in square meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is gradually varied flow (GVF)?
A: GVF refers to flow in open channels where the depth changes gradually along the channel length, typically occurring when the channel slope changes.

Q2: How is total energy defined in open channel flow?
A: Total energy is the sum of potential energy, pressure energy, and kinetic energy at a particular section of the channel.

Q3: What factors affect discharge calculations?
A: Channel geometry, roughness, slope, and water depth significantly influence discharge calculations in open channels.

Q4: When is this formula most applicable?
A: This formula is particularly useful for gradually varied flow conditions in prismatic channels with uniform cross-sections.

Q5: Are there limitations to this equation?
A: The formula assumes steady flow conditions and may not be accurate for rapidly varied flow or non-prismatic channels.