Eckart's Equation For Wavelength Calculator

Eckart's Equation:

\[ \lambda = \left( \frac{[g] \cdot P^2}{2\pi} \right) \cdot \sqrt{\tanh\left( \frac{4\pi^2 d}{P^2 \cdot [g]} \right)} \]

Wavelength (λ):

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1. What is Eckart's Equation?

Eckart's Equation is used to calculate the wavelength of water waves, taking into account both deep and shallow water conditions. It provides a more accurate estimation than simplified equations by incorporating the hyperbolic tangent function.

2. How Does the Calculator Work?

The calculator uses Eckart's equation:

\[ \lambda = \left( \frac{[g] \cdot P^2}{2\pi} \right) \cdot \sqrt{\tanh\left( \frac{4\pi^2 d}{P^2 \cdot [g]} \right)} \]

Where:

\( \lambda \) — Wavelength (meters)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( P \) — Wave period (seconds)
\( d \) — Water depth (meters)
\( \pi \) — Pi constant (3.141592653589793)

Explanation: The equation accounts for the transition between deep water and shallow water wave behavior through the hyperbolic tangent function.

3. Importance of Wavelength Calculation

Details: Accurate wavelength calculation is crucial for coastal engineering, navigation, offshore operations, and understanding wave behavior in various water depth conditions.

4. Using the Calculator

Tips: Enter wave period in seconds and water depth in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between Eckart's equation and the deep water approximation?
A: The deep water approximation (λ = gP²/2π) only works for deep water conditions, while Eckart's equation provides accurate results for both deep and shallow water.

Q2: How does water depth affect wavelength?
A: In deep water, wavelength is determined solely by wave period. In shallow water, wavelength decreases as water depth decreases.

Q3: What is considered "deep water" for wave calculations?
A: Typically, water depth greater than half the wavelength is considered deep water for wave calculations.

Q4: Can this equation be used for all types of water waves?
A: This equation is primarily used for surface gravity waves. It may not be appropriate for very short waves (capillary waves) or very long waves (tsunamis).

Q5: Why use the hyperbolic tangent function in this equation?
A: The tanh function provides a smooth transition between deep water and shallow water wave behavior, making the equation valid for all depth conditions.