Conjugate Depth Y2 Given Critical Depth Calculator

Formula Used:

\[ Depth\ of\ Point\ 2\ for\ Rectangular\ Channel = 0.5 \times Depth\ of\ Point\ 1\ for\ Rectangular\ Channel \times (-1 + \sqrt{1 + \frac{8 \times (Critical\ Depth\ of\ Weir)^3}{(Depth\ of\ Point\ 1\ for\ Rectangular\ Channel)^3}}) \]

Depth of Point 2 for Rectangular Channel (d2R):

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1. What is the Conjugate Depth Formula?

The conjugate depth formula calculates the depth of point 2 in a rectangular channel based on the depth of point 1 and the critical depth of the weir. This relationship is important in hydraulic engineering for analyzing flow characteristics in open channels.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d2R = 0.5 \times d1R \times (-1 + \sqrt{1 + \frac{8 \times hc^3}{d1R^3}}) \]

Where:

\( d2R \) — Depth of Point 2 for Rectangular Channel (m)
\( d1R \) — Depth of Point 1 for Rectangular Channel (m)
\( hc \) — Critical Depth of Weir (m)

Explanation: This formula calculates the conjugate depth (depth after hydraulic jump) based on the initial depth and critical depth parameters.

3. Importance of Conjugate Depth Calculation

Details: Accurate conjugate depth calculation is crucial for designing hydraulic structures, analyzing flow transitions, and ensuring proper energy dissipation in open channel flows.

4. Using the Calculator

Tips: Enter depth of point 1 and critical depth of weir in meters. Both values must be positive numbers greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is conjugate depth in hydraulic engineering?
A: Conjugate depth refers to the depth relationship before and after a hydraulic jump, representing the sequent depths in open channel flow.

Q2: When is this formula typically used?
A: This formula is used in the design and analysis of hydraulic structures like weirs, spillways, and energy dissipators where hydraulic jumps occur.

Q3: What are the limitations of this formula?
A: This formula applies specifically to rectangular channels and assumes uniform flow conditions. It may not be accurate for irregular channel shapes or complex flow patterns.

Q4: How does critical depth affect the conjugate depth?
A: Critical depth represents the minimum energy condition. As critical depth increases relative to the initial depth, the conjugate depth (depth after jump) increases accordingly.

Q5: Can this calculator be used for non-rectangular channels?
A: No, this specific formula is designed for rectangular channels only. Different formulas apply for trapezoidal, circular, or other channel shapes.