Major Horizontal Semi Axis For Shallow Water Condition Calculator

Horizontal Semi-axis Formula:

\[ A = \frac{H_w}{2} \times \frac{L}{2\pi d_s} \]

Height of the Wave (Hw):

Length of Water Wave (L):

Water Depth for Semi-Axis of Ellipse (ds):

Horizontal Semi-axis of Water Particle (A):

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1. What is Horizontal Semi-axis of Water Particle?

Horizontal Semi-axis of Water Particle refers to the horizontal component of the oscillation of water particles caused by waves or other hydrodynamic forces in coastal and engineering applications. It represents the maximum horizontal displacement of water particles in wave motion.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = \frac{H_w}{2} \times \frac{L}{2\pi d_s} \]

Where:

\( A \) — Horizontal Semi-axis of Water Particle (m)
\( H_w \) — Height of the Wave (m)
\( L \) — Length of Water Wave (m)
\( d_s \) — Water Depth for Semi-Axis of Ellipse (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the horizontal semi-axis for shallow water conditions where water depth affects wave particle motion.

3. Importance of Horizontal Semi-axis Calculation

Details: Calculating the horizontal semi-axis is crucial for understanding wave-induced sediment transport, coastal erosion patterns, and designing coastal structures that can withstand wave forces.

4. Using the Calculator

Tips: Enter wave height in meters, wave length in meters, and water depth in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between horizontal and vertical semi-axis?
A: Horizontal semi-axis represents the maximum horizontal displacement of water particles, while vertical semi-axis represents the maximum vertical displacement in wave motion.

Q2: How does water depth affect the horizontal semi-axis?
A: In shallow water conditions, decreased water depth increases the horizontal semi-axis as wave energy becomes more concentrated near the surface.

Q3: What are typical values for horizontal semi-axis?
A: Values vary significantly based on wave conditions, but typically range from a few centimeters for small waves to several meters for large storm waves.

Q4: Is this formula applicable for deep water conditions?
A: No, this specific formula is designed for shallow water conditions where water depth is less than half the wave length.

Q5: How is this calculation used in coastal engineering?
A: Engineers use horizontal semi-axis calculations to design breakwaters, sea walls, and other coastal protection structures that must withstand wave-induced forces.