Partial Discharge In Sub-Area Between Two Verticals Given Resultant Velocity Calculator

Partial Discharge Formula:

\[ \Delta Qi = \frac{(yi + yi+1)}{2} \times V^2 \times \sin(\theta) \times \cos(\theta) \times \Delta t \]

Depth 'yi' of Flow in Sub-Area:

Depth 'i+1' of Flow in Sub-Area:

Resultant Velocity:

m/s

Angle:

rad

Time of Transit between Two Verticals:

min

Partial Discharges:

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1. What is Partial Discharge in Sub-Area?

Partial Discharge in Sub-Area between Two Verticals represents the flow rate in a specific section of a water body between two measurement points, calculated using depth measurements, resultant velocity, angle, and transit time.

2. How Does the Calculator Work?

The calculator uses the Partial Discharge formula:

\[ \Delta Qi = \frac{(yi + yi+1)}{2} \times V^2 \times \sin(\theta) \times \cos(\theta) \times \Delta t \]

Where:

\( yi \) — Depth of flow at first vertical (m)
\( yi+1 \) — Depth of flow at second vertical (m)
\( V \) — Resultant velocity (m/s)
\( \theta \) — Angle with flow direction (rad)
\( \Delta t \) — Time of transit between verticals (min)

Explanation: The formula calculates the discharge through a sub-area by considering the average depth, velocity squared, trigonometric components of the angle, and the time taken to transit between measurement points.

3. Importance of Partial Discharge Calculation

Details: Accurate partial discharge calculation is crucial for hydraulic engineering, water resource management, and environmental monitoring. It helps in understanding flow distribution, sediment transport, and overall water balance in natural and artificial channels.

4. Using the Calculator

Tips: Enter all depth measurements in meters, velocity in m/s, angle in radians, and transit time in minutes. All values must be non-negative and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: Why use this specific formula for partial discharge calculation?
A: This formula provides an accurate estimation of flow in sub-areas by accounting for depth variations, velocity distribution, and angular components of flow direction.

Q2: What are typical values for partial discharge?
A: Partial discharge values vary widely depending on channel characteristics, flow conditions, and measurement location. They can range from small fractions to significant portions of total discharge.

Q3: When should partial discharge measurements be taken?
A: Measurements should be taken during stable flow conditions, avoiding periods of rapid change due to rainfall, dam releases, or other disturbances that might affect measurement accuracy.

Q4: Are there limitations to this calculation method?
A: The method assumes relatively uniform flow conditions and may be less accurate in highly turbulent flows, rapidly changing channels, or where significant secondary currents are present.

Q5: How does this relate to total discharge calculation?
A: Partial discharges from multiple sub-areas are summed to obtain the total discharge across the entire cross-section of the water body.