Water Surface above Bottom Calculator

Water Surface Ordinate Formula:

\[ y_s' = D_w + H_w \times \left( \text{sech}\left( \sqrt{\frac{3}{4} \times \frac{H_w}{D_w^3}} \times (x - C \times t) \right) \right)^2 \]

Water Depth from Bed (D_w):

Height of the Wave (H_w):

Spatial (Progressive Wave) (x):

Celerity of the Wave (C):

m/s

Temporal (Progressive Wave) (t):

Water Surface Ordinate (y_s'):

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1. What is Water Surface Ordinate?

Water Surface Ordinate is defined as the vertical distance between two points on the water plane. It represents the height of the water surface above the bottom bed, accounting for wave effects and other hydrodynamic factors.

2. How Does the Calculator Work?

The calculator uses the Water Surface Ordinate formula:

\[ y_s' = D_w + H_w \times \left( \text{sech}\left( \sqrt{\frac{3}{4} \times \frac{H_w}{D_w^3}} \times (x - C \times t) \right) \right)^2 \]

Where:

\( y_s' \) — Water Surface Ordinate (m)
\( D_w \) — Water Depth from Bed (m)
\( H_w \) — Height of the Wave (m)
\( x \) — Spatial (Progressive Wave) (m)
\( C \) — Celerity of the Wave (m/s)
\( t \) — Temporal (Progressive Wave) (s)

Explanation: The formula calculates the water surface elevation above the bottom by considering wave characteristics and propagation parameters.

3. Importance of Water Surface Calculation

Details: Accurate water surface ordinate calculation is crucial for coastal engineering, flood prediction, navigation safety, and understanding wave behavior in various water bodies.

4. Using the Calculator

Tips: Enter all values in appropriate units. Water depth and wave height must be positive values. Ensure temporal and spatial values are consistent with wave celerity.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of water surface ordinate?
A: It represents the actual water level at a specific point, accounting for wave effects, which is essential for determining water depth for navigation and construction.

Q2: How does wave height affect the water surface ordinate?
A: Higher wave heights generally result in greater variations in water surface ordinate, with higher crests and deeper troughs.

Q3: What is the role of the sech function in this formula?
A: The hyperbolic secant function describes the shape of solitary waves, which are used to model certain types of water wave propagation.

Q4: When is this formula most applicable?
A: This formula is particularly useful for modeling solitary waves in relatively shallow water conditions.

Q5: What are the limitations of this calculation?
A: The formula assumes ideal wave conditions and may not account for complex interactions like wave breaking, refraction, or nonlinear effects in extreme conditions.