Basin Length Along Axis Given Maximum Oscillation Period Corresponding To Fundamental Mode Calculator

Formula Used:

\[ L_{ba} = \frac{T_1 \times \sqrt{g \times D}}{2} \]

Length of Basin along Axis (Lₐ):

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1. What is the Basin Length along Axis Formula?

The formula calculates the length of a basin along its axis based on the maximum oscillation period corresponding to the fundamental mode and the water depth. This is particularly useful in coastal engineering and oceanography for designing harbors and understanding basin resonance.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_{ba} = \frac{T_1 \times \sqrt{g \times D}}{2} \]

Where:

\( L_{ba} \) — Length of Basin along Axis (m)
\( T_1 \) — Maximum Oscillation Period (s)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( D \) — Water Depth (m)

Explanation: The formula relates the basin length to the oscillation period and water depth through the square root of gravitational acceleration times depth.

3. Importance of Basin Length Calculation

Details: Accurate calculation of basin length is crucial for designing harbor basins, predicting seiche periods, and understanding resonance phenomena in enclosed water bodies.

4. Using the Calculator

Tips: Enter maximum oscillation period in seconds and water depth in meters. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is maximum oscillation period?
A: The maximum oscillation period refers to the longest time it takes for a water body to complete one full cycle of oscillation in its fundamental mode.

Q2: Why is gravitational acceleration constant used?
A: Gravitational acceleration (g) is a fundamental constant that affects wave propagation and water oscillation in basins.

Q3: What applications does this calculation have?
A: This calculation is used in harbor design, coastal engineering, and the study of seiche phenomena in lakes and enclosed basins.

Q4: Are there limitations to this formula?
A: The formula assumes ideal conditions and may need adjustments for complex basin geometries, friction effects, or non-uniform depth distributions.

Q5: How accurate is this calculation?
A: The calculation provides a good estimate for simple rectangular basins but may require more complex modeling for irregular shapes.