Home Back

Conjugate Depth y1 given Froude Number Fr1 Calculator

Formula Used:

\[ d1R = \frac{d2R}{0.5 \times (-1 + \sqrt{1 + (8 \times Fr^2)})} \]

m

Unit Converter ▲

Unit Converter ▼

From: To:

1. What is the Conjugate Depth Formula?

The conjugate depth formula calculates the depth of point 1 (d1R) in a rectangular channel given the depth of point 2 (d2R) and the Froude number (Fr). This relationship is fundamental in open channel flow analysis, particularly for hydraulic jumps and energy dissipation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d1R = \frac{d2R}{0.5 \times (-1 + \sqrt{1 + (8 \times Fr^2)})} \]

Where:

Explanation: This formula establishes the relationship between conjugate depths in a rectangular channel based on the Froude number, which characterizes the flow regime.

3. Importance of Conjugate Depth Calculation

Details: Calculating conjugate depths is essential for designing hydraulic structures, analyzing energy dissipation in hydraulic jumps, and understanding flow transitions between subcritical and supercritical regimes in open channels.

4. Using the Calculator

Tips: Enter the depth of point 2 in meters and the Froude number. Both values must be positive numbers. The calculator will compute the corresponding depth of point 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the Froude number?
A: The Froude number is a dimensionless number that represents the ratio of flow inertia to gravitational forces, used to classify flow regimes in open channels.

Q2: What are conjugate depths?
A: Conjugate depths are the two depths that occur before and after a hydraulic jump in an open channel flow, representing the same specific energy.

Q3: When is this formula applicable?
A: This formula applies specifically to rectangular channels with horizontal beds and uniform flow conditions.

Q4: What flow regimes does this cover?
A: The formula applies to both subcritical and supercritical flow conditions and is particularly relevant for analyzing hydraulic jumps.

Q5: Are there limitations to this equation?
A: This equation assumes ideal conditions with no energy losses and is specifically designed for rectangular channel cross-sections.

Conjugate Depth y1 given Froude Number Fr1 Calculator© - All Rights Reserved 2025