Potential Energy Due To Deformation Of Free Surface Calculator

Formula Used:

\[ E_p = \frac{\rho \cdot [g] \cdot \eta^2 \cdot \lambda}{2} \]

Potential Energy of Wave (Eₚ):

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1. What is Potential Energy Due To Deformation Of Free Surface?

Potential Energy Due To Deformation Of Free Surface refers to the energy stored in a wave due to its height or amplitude above the surrounding water level. This energy is a result of the gravitational potential energy associated with the displacement of water from its equilibrium position.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E_p = \frac{\rho \cdot [g] \cdot \eta^2 \cdot \lambda}{2} \]

Where:

\( E_p \) — Potential Energy of Wave (J)
\( \rho \) — Density of Fluid (kg/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( \eta \) — Surface Elevation (m)
\( \lambda \) — Wavelength (m)

Explanation: The formula calculates the potential energy per unit width of wave crest, considering the density of the fluid, gravitational acceleration, square of the surface elevation, and the wavelength.

3. Importance of Potential Energy Calculation

Details: Calculating wave potential energy is crucial for understanding wave energy conversion, coastal engineering, oceanography, and predicting wave behavior in various marine environments.

4. Using the Calculator

Tips: Enter fluid density in kg/m³, surface elevation in meters, and wavelength in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of surface elevation in wave energy?
A: Surface elevation (wave height) is squared in the formula, making it the most significant factor affecting wave potential energy.

Q2: How does fluid density affect wave potential energy?
A: Higher density fluids (like saltwater) will have greater potential energy for the same wave characteristics compared to lower density fluids.

Q3: What are typical values for wave potential energy?
A: Values vary widely depending on wave conditions, ranging from small values for ripples to very large values for storm waves.

Q4: Can this formula be used for all types of waves?
A: This formula is primarily for linear wave theory and works best for small amplitude waves in deep water conditions.

Q5: How is this energy related to total wave energy?
A: In linear wave theory, potential energy equals kinetic energy, so total wave energy is twice the potential energy calculated.