Ordinate of Water Surface given Pressure under Cnoidal Wave in Hydrostatic Form Calculator

Formula Used:

\[ y_s = \frac{p}{\rho_s \cdot g} + y \]

Pressure Under Wave (p):

Density of Salt Water (ρs):

kg/m³

Elevation above the Bottom (y):

Ordinate of the Water Surface (ys):

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1. What is the Ordinate of Water Surface?

The Ordinate of the Water Surface is defined as the vertical distance between two points on the water plane. In hydrostatic form, it represents the height of the water surface above a reference point, accounting for pressure variations under wave conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ y_s = \frac{p}{\rho_s \cdot g} + y \]

Where:

\( y_s \) — Ordinate of the Water Surface (m)
\( p \) — Pressure Under Wave (Pa)
\( \rho_s \) — Density of Salt Water (kg/m³)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( y \) — Elevation above the Bottom (m)

Explanation: The formula calculates the water surface elevation by converting pressure to an equivalent water height and adding the bottom elevation.

3. Importance of Water Surface Calculation

Details: Accurate calculation of water surface ordinate is crucial for coastal engineering, wave analysis, flood prediction, and offshore structure design. It helps in understanding wave behavior and its impact on marine structures.

4. Using the Calculator

Tips: Enter pressure in Pascals, density in kg/m³, and elevation in meters. All values must be positive numbers with density typically around 1025 kg/m³ for seawater.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical density value for seawater?
A: Seawater density typically ranges from 1020 to 1030 kg/m³, with 1025 kg/m³ being a commonly used average value.

Q2: How does pressure under wave differ from static pressure?
A: Pressure under wave includes both hydrostatic pressure from the water column and dynamic pressure components caused by wave motion.

Q3: What units should be used for pressure input?
A: Pressure should be entered in Pascals (Pa). 1 kPa = 1000 Pa, and atmospheric pressure is approximately 101325 Pa.

Q4: Can this formula be used for freshwater calculations?
A: Yes, but the density value should be adjusted to approximately 1000 kg/m³ for pure freshwater.

Q5: What is the significance of the gravitational constant?
A: The gravitational constant (g) converts between pressure and equivalent water height, representing the acceleration due to gravity.