Shear Stress At Water Surface Given Velocity At Surface Calculator

Formula Used:

\[ \tau = \frac{V_s \cdot \sqrt{2 \cdot D_f \cdot \rho_{water} \cdot \Omega_E \cdot \sin(L)}}{\pi} \]

Velocity at the Surface (V_s):

m/s

Depth of Frictional Influence (D_f):

Water Density (ρ):

kg/m³

Angular Speed of the Earth (Ω_E):

rad/s

Latitude of the Line (L):

degrees

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 represents the frictional force per unit area at the air-water interface.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \tau = \frac{V_s \cdot \sqrt{2 \cdot D_f \cdot \rho_{water} \cdot \Omega_E \cdot \sin(L)}}{\pi} \]

Where:

\( \tau \) — Shear Stress at the Water Surface (Pa)
\( V_s \) — Velocity at the Surface (m/s)
\( D_f \) — Depth of Frictional Influence (m)
\( \rho_{water} \) — Water Density (kg/m³)
\( \Omega_E \) — Angular Speed of the Earth (rad/s)
\( L \) — Latitude of the Line (degrees)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This formula calculates the shear stress at the water surface by considering the surface velocity, frictional depth influence, water density, Earth's rotation, and latitude effects.

3. Importance of Shear Stress Calculation

Details: Calculating shear stress at the water surface is crucial for understanding ocean currents, sediment transport, wave generation, and coastal erosion processes. It helps in predicting water movement patterns and designing coastal structures.

4. Using the Calculator

Tips: Enter all values in the specified units. Velocity should be in m/s, depth in meters, density in kg/m³, angular speed in rad/s, and latitude in degrees (between -90° and 90°). All values must be positive except latitude which can be negative for southern latitudes.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of shear stress values at water surfaces?
A: Shear stress values typically range from 0.01 to 1.0 Pa, depending on wind speed, water conditions, and geographical location.

Q2: How does latitude affect shear stress calculations?
A: Latitude affects the Coriolis force, which influences water movement patterns. The sine function accounts for the variation of Coriolis parameter with latitude.

Q3: What is the significance of angular speed of the Earth?
A: The Earth's rotation (approximately 7.2921159 × 10^-5 rad/s) creates the Coriolis effect, which deflects moving water and affects shear stress distribution.

Q4: How is depth of frictional influence determined?
A: Depth of frictional influence is typically estimated based on water depth, bottom roughness, and flow characteristics, often ranging from tens to hundreds of meters.

Q5: What are the limitations of this formula?
A: This formula provides an estimate and may not account for all complex factors such as wind variations, wave interactions, or complex bathymetry in specific locations.