1. What is Critical Speed?

Critical Speed (CS) is the speed at which surface gravity waves propagate in water of a given depth. It represents the minimum speed required for disturbances to travel as waves in shallow water conditions.

2. How Does the Calculator Work?

The calculator uses the critical speed formula:

Where:

• \( CS \) — Critical speed (m/s)
• \( g \) — Acceleration due to gravity (9.81 m/s²)
• \( d \) — Water depth (m)

Explanation: The formula calculates the wave propagation speed in shallow water, where the water depth is much smaller than the wavelength.

3. Importance of Critical Speed Calculation

Details: Critical speed calculation is essential in hydraulic engineering, coastal engineering, and fluid dynamics for designing structures, predicting wave behavior, and analyzing flow conditions in shallow water environments.

4. Using the Calculator

Tips: Enter water depth in meters and gravity acceleration in m/s². Standard gravity is 9.81 m/s². All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of critical speed in fluid dynamics?
A: Critical speed determines whether flow is subcritical or supercritical, which affects wave propagation and hydraulic jump formation.

Q2: How does depth affect critical speed?
A: Critical speed increases with the square root of water depth. Deeper water allows waves to travel faster.

Q3: When is this formula applicable?
A: This formula applies to shallow water conditions where water depth is much smaller than the wavelength (typically d < λ/20).

Q4: What are typical critical speed values?
A: Critical speed ranges from about 1 m/s for shallow depths (0.1m) to over 10 m/s for deeper waters (10m+).

Q5: How is critical speed used in engineering applications?
A: It's used in designing spillways, weirs, channels, and coastal structures, and in predicting tsunami wave speeds.