Critical Depth For Parabolic Channel Calculator

Critical Depth Formula:

\[ h_p = \left( \frac{3.375 \times (Q/S)^2}{g} \right)^{1/4} \]

Critical Depth of Parabolic Channel (hₚ):

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1. What is Critical Depth of Parabolic Channel?

The Critical Depth of Parabolic Channel is defined as the depth of flow where energy is at a minimum for a particular discharge. It represents the transition point between subcritical and supercritical flow conditions in an open channel with a parabolic cross-section.

2. How Does the Calculator Work?

The calculator uses the critical depth formula:

\[ h_p = \left( \frac{3.375 \times (Q/S)^2}{g} \right)^{1/4} \]

Where:

\( h_p \) — Critical Depth of Parabolic Channel (m)
\( Q \) — Discharge of Channel (m³/s)
\( S \) — Bed Slope (-)
\( g \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The formula calculates the critical depth where the specific energy is minimized for a given discharge in a parabolic channel, considering the channel's bed slope and gravitational effects.

3. Importance of Critical Depth Calculation

Details: Calculating critical depth is essential for hydraulic engineering design, flood control, irrigation systems, and understanding flow behavior in open channels. It helps determine when flow transitions between subcritical and supercritical states.

4. Using the Calculator

Tips: Enter discharge in cubic meters per second (m³/s) and bed slope as a dimensionless value. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of critical depth in channel flow?
A: Critical depth marks the transition between subcritical (tranquil) and supercritical (rapid) flow, which is crucial for hydraulic jump analysis and energy dissipation design.

Q2: How does channel shape affect critical depth?
A: Different channel shapes (rectangular, triangular, parabolic) have different critical depth formulas due to variations in cross-sectional area and hydraulic radius relationships.

Q3: What are typical values for bed slope in natural channels?
A: Bed slopes vary widely from nearly flat (0.0001) in lowland rivers to steep (0.1 or more) in mountainous streams.

Q4: When is this calculation most applicable?
A: This calculation is particularly useful for irrigation channels, spillways, and other engineered waterways with parabolic cross-sections.

Q5: What limitations should be considered?
A: The formula assumes uniform flow conditions, constant channel properties, and may not account for sediment transport effects or non-uniform channel geometry.