Water Depth Given Total Wave Energy Per Unit Crest Width Of Solitary Wave Calculator

Formula Used:

\[ D_w = \left( \frac{E}{\left( \frac{8}{3\sqrt{3}} \right) \times \rho_s \times [g] \times H_w^{3/2}} \right)^{2/3} \]

Water Depth from Bed:

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1. What is the Water Depth Calculation for Solitary Waves?

This calculator determines the water depth from the bed based on the total wave energy per unit crest width for solitary waves. It uses a specialized formula that considers wave energy, water density, and wave height to estimate the water depth.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ D_w = \left( \frac{E}{\left( \frac{8}{3\sqrt{3}} \right) \times \rho_s \times [g] \times H_w^{3/2}} \right)^{2/3} \]

Where:

\( D_w \) — Water Depth from Bed (m)
\( E \) — Total Wave Energy per Unit Crest Width (J/m)
\( \rho_s \) — Density of Salt Water (kg/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( H_w \) — Height of the Wave (m)

Explanation: The formula calculates water depth by relating wave energy to the physical properties of the wave and water medium, using the gravitational constant and mathematical constants.

3. Importance of Water Depth Calculation

Details: Accurate water depth estimation is crucial for coastal engineering, wave energy assessment, navigation safety, and understanding wave behavior in different water conditions.

4. Using the Calculator

Tips: Enter total wave energy in J/m, density of salt water in kg/m³, and wave height in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a solitary wave?
A: A solitary wave is a single hump of water that propagates without changing its shape, often observed in shallow water conditions.

Q2: Why is salt water density important in this calculation?
A: Salt water density affects wave energy propagation and is typically higher than fresh water density (around 1025 kg/m³ vs 1000 kg/m³).

Q3: What are typical values for wave energy per unit crest width?
A: Wave energy varies significantly but can range from thousands to millions of joules per meter depending on wave conditions.

Q4: How accurate is this calculation for real-world applications?
A: The formula provides a theoretical estimation. Real-world accuracy depends on how well conditions match the idealized solitary wave model.

Q5: Can this calculator be used for fresh water waves?
A: Yes, but you must use the appropriate density value for fresh water (approximately 1000 kg/m³) instead of salt water density.