Basin Length along Axis for Closed Basin Calculator

Formula Used:

\[ L_{ba} = \frac{T_n \times N \times \sqrt{g \times d}}{2} \]

Natural Free Oscillating Period of a Basin (T_n):

Number of Nodes along the Axis of a Basin (N):

Water Depth at Harbor (d):

Length of Basin along Axis (L_ba):

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1. What is the Basin Length along Axis Formula?

The Basin Length along Axis formula calculates the length of a closed basin along its axis based on the natural free oscillating period, number of nodes, and water depth. This is important for understanding the resonant characteristics and wave behavior in enclosed water bodies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_{ba} = \frac{T_n \times N \times \sqrt{g \times d}}{2} \]

Where:

\( L_{ba} \) — Length of Basin along Axis (m)
\( T_n \) — Natural Free Oscillating Period of a Basin (s)
\( N \) — Number of Nodes along the Axis of a Basin
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( d \) — Water Depth at Harbor (m)

Explanation: The formula relates the basin length to its natural oscillation period, number of nodes, and water depth through the square root of gravity times depth.

3. Importance of Basin Length Calculation

Details: Calculating basin length is crucial for harbor design, understanding seiche phenomena, predicting wave resonance, and designing coastal structures that can withstand oscillatory wave forces.

4. Using the Calculator

Tips: Enter natural free oscillating period in seconds, number of nodes (dimensionless), and water depth in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a natural free oscillating period?
A: The natural free oscillating period is the time it takes for a wave to travel from one end of the basin to the other and back again, creating a standing wave pattern.

Q2: What are nodes in a basin context?
A: Nodes are points along the basin axis where there is minimal vertical water motion during oscillation, while antinodes are points with maximum vertical motion.

Q3: How does water depth affect basin length?
A: Deeper water increases wave speed (through √(g×d)), which means for the same oscillation period, a longer basin length is possible.

Q4: What types of basins does this formula apply to?
A: This formula applies to closed or semi-closed basins such as harbors, bays, lakes, and other enclosed water bodies where standing waves can form.

Q5: Are there limitations to this equation?
A: The formula assumes ideal conditions with uniform depth, rectangular basin shape, and neglects friction and Coriolis effects, which may limit accuracy in real-world applications.