Side Slope Of Channel Given Critical Depth For Parabolic Channel Calculator

Bed Slope Formula:

\[ S = \sqrt{\frac{3.375 \times Q^2}{h_p^4 \times g}} \]

Bed Slope (S):

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1. What is the Bed Slope Formula?

The Bed Slope formula calculates the slope of an open channel bed using discharge and critical depth parameters for parabolic channels. It's essential for determining the shear stress at the bed during steady, uniform flow conditions.

2. How Does the Calculator Work?

The calculator uses the Bed Slope formula:

\[ S = \sqrt{\frac{3.375 \times Q^2}{h_p^4 \times g}} \]

Where:

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

Explanation: The formula calculates the bed slope required to maintain critical flow conditions in a parabolic channel based on the discharge and critical depth parameters.

3. Importance of Bed Slope Calculation

Details: Accurate bed slope calculation is crucial for designing efficient open channel systems, predicting flow behavior, and ensuring proper sediment transport in parabolic channels.

4. Using the Calculator

Tips: Enter discharge in m³/s and critical depth in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is critical depth in open channel flow?
A: Critical depth is the depth of flow where the specific energy is at a minimum for a given discharge, representing the transition between subcritical and supercritical flow.

Q2: How does channel shape affect bed slope calculations?
A: Different channel shapes (parabolic, rectangular, trapezoidal) have different hydraulic characteristics and require specific formulas for accurate bed slope calculations.

Q3: What are typical bed slope values for natural channels?
A: Bed slopes vary widely depending on channel type, from nearly flat (0.0001) for large rivers to steep slopes (0.01-0.1) for mountain streams.

Q4: When is this formula most applicable?
A: This formula is specifically designed for parabolic channels undergoing steady, uniform flow conditions where critical depth has been established.

Q5: How does bed slope affect flow velocity?
A: Steeper bed slopes generally result in higher flow velocities due to increased gravitational forces acting on the water.