Velocity Profile Open Channel Flow

Velocity Profile Formula:

\[ u = \frac{(g \cdot h \cdot S)^{1/2} \cdot \ln(y / k)}{\kappa} \]

Gravity (g):

m/s²

Flow Depth (h):

Slope (S):

Distance from Bed (y):

Roughness Height (k):

Von Karman Constant (κ):

Flow Velocity (u): m/s

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1. What is the Velocity Profile in Open Channel Flow?

Definition: This calculator determines the flow velocity at a specific point in an open channel using the logarithmic velocity profile.

Purpose: It helps hydraulic engineers and researchers understand velocity distribution in rivers, canals, and other open channels.

2. How Does the Calculator Work?

The calculator uses the logarithmic velocity profile formula:

\[ u = \frac{(g \cdot h \cdot S)^{1/2} \cdot \ln(y / k)}{\kappa} \]

Where:

\( u \) — Flow velocity at height y (m/s)
\( g \) — Gravitational acceleration (m/s²)
\( h \) — Flow depth (m)
\( S \) — Channel slope (dimensionless)
\( y \) — Distance from channel bed (m)
\( k \) — Roughness height (m)
\( \kappa \) — Von Karman constant (~0.41)

Explanation: The formula describes how velocity varies with height in turbulent open channel flows.

3. Importance of Velocity Profile Calculation

Details: Understanding velocity distribution is crucial for sediment transport studies, hydraulic structure design, and ecological assessments.

4. Using the Calculator

Tips: Enter all required parameters. Default values are provided for gravity (9.81 m/s²), roughness height (0.001 m), and κ (0.41).

5. Frequently Asked Questions (FAQ)

Q1: What is the Von Karman constant?
A: A dimensionless constant (~0.41) that appears in logarithmic velocity profiles for turbulent flows.

Q2: How do I determine roughness height (k)?
A: k depends on bed material - typical values: 0.001 m for smooth concrete, 0.01-0.1 m for gravel beds.

Q3: What's the valid range for y?
A: y should be greater than k but less than h (flow depth).

Q4: When is this formula applicable?
A: For fully developed turbulent flows in wide, prismatic channels.

Q5: How does slope affect velocity?
A: Higher slopes generally produce higher velocities due to increased gravitational driving force.