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Superelevation due to Varying Entrance Channel Cross-Section Calculator

Superelevation Formula:

\[ S = a_o \times \left(1 - \frac{\left(\frac{a_B}{a_o}\right)^2}{4 \times \left(\frac{D_t}{a_o}\right)} - \frac{a_o}{m \times W} \times \left(0.5 - \frac{a_B}{a_o} \times \cos(k) - \frac{3}{2} \times \left(\frac{a_B}{a_o}\right)^2 + 4 \times \left(\frac{D_t}{a_o}\right)^2\right)\right) \]

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1. What is Superelevation due to Varying Entrance Channel Cross-Section?

Definition: This calculator estimates the superelevation (water surface elevation difference) caused by varying cross-sections in entrance channels, considering tidal amplitudes, channel geometry, and phase lag.

Purpose: It helps hydraulic engineers and coastal researchers predict water level variations in channels connecting bays to oceans.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ S = a_o \times \left(1 - \frac{\left(\frac{a_B}{a_o}\right)^2}{4 \times \left(\frac{D_t}{a_o}\right)} - \frac{a_o}{m \times W} \times \left(0.5 - \frac{a_B}{a_o} \times \cos(k) - \frac{3}{2} \times \left(\frac{a_B}{a_o}\right)^2 + 4 \times \left(\frac{D_t}{a_o}\right)^2\right)\right) \]

Where:

  • \( S \) — Superelevation (m)
  • \( a_o \) — Ocean tide amplitude (m)
  • \( a_B \) — Bay tide amplitude (m)
  • \( D_t \) — Channel depth (m)
  • \( m \) — Bank slope (±5%)
  • \( W \) — Channel width at mean water depth (m)
  • \( k \) — Phase lag (degrees)

Explanation: The formula accounts for tidal forcing, channel geometry effects, and phase differences between ocean and bay tides.

3. Importance of Superelevation Calculation

Details: Accurate superelevation prediction is crucial for flood risk assessment, navigation safety, and coastal infrastructure design.

4. Using the Calculator

Tips: Enter all required parameters. Bank slope typically has ±5% variation. Phase lag should be in degrees (0-360).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical bank slope value?
A: Natural channels typically have bank slopes between 1.5-3 (horizontal:vertical), but this can vary significantly.

Q2: How do I determine phase lag?
A: Phase lag can be measured from tidal gauge data as the time difference between high tides in the ocean and bay.

Q3: What if my channel has complex geometry?
A: This formula works best for relatively uniform channels. For complex geometries, numerical modeling may be needed.

Q4: Why is ocean tide amplitude typically larger than bay tide amplitude?
A: Bays often have reduced tidal ranges due to friction and resonance effects in the connecting channel.

Q5: Can this be used for river mouths?
A: Yes, but freshwater flow effects would need to be considered separately.

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