Shear Stress At Water Surface Given Water Surface Slope Calculator

Formula Used:

\[ \tau = \frac{\beta \cdot \rho \cdot [g] \cdot h}{\Delta} \]

Water Surface Slope (β):

Density of Water (ρ):

kg/m³

Eckman Constant Depth (h):

Coefficient Eckman (Δ):

Shear Stress at the Water Surface (τ):

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1. What is Shear Stress at Water Surface?

Shear Stress at the Water Surface, referred to as the "tractive force," is a measure of the internal resistance of a fluid to deformation when subjected to a force acting parallel to its surface. It's a crucial parameter in fluid dynamics and coastal engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau = \frac{\beta \cdot \rho \cdot [g] \cdot h}{\Delta} \]

Where:

\( \tau \) — Shear Stress at the Water Surface (Pa)
\( \beta \) — Water Surface Slope (-)
\( \rho \) — Density of Water (kg/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( h \) — Eckman Constant Depth (m)
\( \Delta \) — Coefficient Eckman (-)

Explanation: This formula calculates the shear stress at the water surface based on water surface slope, water density, gravitational acceleration, Eckman constant depth, and the Eckman coefficient.

3. Importance of Shear Stress Calculation

Details: Accurate shear stress calculation is crucial for understanding water flow dynamics, sediment transport, erosion patterns, and designing hydraulic structures. It helps predict how water surfaces respond to various forces and influences.

4. Using the Calculator

Tips: Enter water surface slope (dimensionless), density of water in kg/m³, Eckman constant depth in meters, and coefficient Eckman (dimensionless). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is water surface slope?
A: Water surface slope describes how the water surface inclines or changes with distance. It's pivotal in understanding water flow in channels like rivers or pipes.

Q2: What is Eckman constant depth?
A: Eckman constant depth is the depth in water where the effect of wind-induced movement lessens, influencing currents and turbulence within this specific layer of the ocean.

Q3: What is the typical range for water density?
A: Fresh water density is approximately 1000 kg/m³ at 4°C, while seawater density ranges from 1020-1030 kg/m³ depending on salinity and temperature.

Q4: What does coefficient Eckman represent?
A: Coefficient Eckman represents the change of ebb tidal energy flux across the ocean bar between natural and channel conditions.

Q5: What are typical shear stress values in natural water bodies?
A: Shear stress values vary widely depending on conditions, but typically range from 0.01 Pa in calm waters to several Pascals in high-flow conditions or during storm events.