Hydraulic Radius Given Boundary Shear Stress Calculator

Hydraulic Radius Formula:

\[ R_H = \frac{\zeta_0}{\gamma_l \times S} \]

Hydraulic Radius of Channel (Rₕ):

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1. What is Hydraulic Radius?

The Hydraulic Radius is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wetted perimeter of the conduit. It's a fundamental parameter in open channel flow calculations.

2. How Does the Calculator Work?

The calculator uses the hydraulic radius formula:

\[ R_H = \frac{\zeta_0}{\gamma_l \times S} \]

Where:

\( R_H \) — Hydraulic Radius of Channel (m)
\( \zeta_0 \) — Shear Stress of Wall (Pa)
\( \gamma_l \) — Liquid Specific Weight (N/m³)
\( S \) — Bed Slope (-)

Explanation: This formula calculates the hydraulic radius based on the boundary shear stress, liquid specific weight, and bed slope of the channel.

3. Importance of Hydraulic Radius Calculation

Details: Hydraulic radius is crucial for determining flow characteristics in open channels, designing drainage systems, calculating flow rates, and analyzing sediment transport in rivers and canals.

4. Using the Calculator

Tips: Enter shear stress in Pascals, liquid specific weight in N/m³, and bed slope as a dimensionless value. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between hydraulic radius and hydraulic diameter?
A: Hydraulic radius is the cross-sectional area divided by wetted perimeter, while hydraulic diameter is four times the hydraulic radius.

Q2: How does bed slope affect hydraulic radius?
A: Bed slope influences the shear stress distribution and flow velocity, which in turn affects the hydraulic radius calculation.

Q3: What are typical values for hydraulic radius?
A: Hydraulic radius values vary widely depending on channel size and shape, from a few centimeters for small channels to several meters for large rivers.

Q4: Can this formula be used for pressurized pipe flow?
A: While the concept of hydraulic radius applies, this specific formula is primarily used for open channel flow calculations.

Q5: How accurate is this calculation method?
A: The formula provides a good estimation for uniform flow conditions in open channels with consistent cross-sections.