Water Particle Velocity Calculator

Formula

The formula to calculate Water Particle Velocity (v) is:

\[ v = \omega \cdot A \cdot e^{kz} \cdot \cos(\omega t) \]

Where:

\( v \) is the Water Particle Velocity (m/s)
\( \omega \) is the angular frequency (rad/s), calculated as \( \omega = 2\pi f \)
\( A \) is the wave amplitude (m)
\( k \) is the wave number (1/m), approximately calculated as \( k = \frac{\omega}{\sqrt{gd}} \)
\( z \) is the position depth below the surface (m)
\( g \) is the acceleration due to gravity (9.81 m/s²)
\( t \) is the time, but in this calculator, it's simplified assuming \( \cos(\omega t) = 1 \)

What is Water Particle Velocity?

Water particle velocity refers to the velocity at which a water particle moves in a wave. It depends on the wave's amplitude, frequency, depth, and the particle's position below the water surface. This concept is crucial in understanding wave dynamics and is used in oceanography and coastal engineering.

Example Calculation

Let's consider an example:

Wave Amplitude (A): 2 m
Wave Frequency (f): 0.5 Hz
Water Depth (d): 10 m
Position Depth Below Surface (z): 1 m

Using the formula to calculate Water Particle Velocity:

\[ v = 2\pi \cdot 0.5 \cdot 2 \cdot e^{0.03 \cdot 1} \cdot \cos(2\pi \cdot 0.5 \cdot t) \approx 8.628 \, \text{m/s} \]

This demonstrates that with the given parameters, the water particle velocity is approximately 8.628 m/s.