Diameter Of Section Given Hydraulic Radius For Channel Calculator

Formula Used:

\[ D = \frac{R_h}{0.25 \times \left(1 - \frac{\sin(\theta)}{\frac{180}{\pi} \times \theta}\right)} \]

Diameter of Section:

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1. What is the Diameter of Section Formula?

The diameter of section formula calculates the diameter of a circular channel section based on the hydraulic radius and the subtended angle. This is particularly useful in hydraulic engineering for determining channel dimensions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D = \frac{R_h}{0.25 \times \left(1 - \frac{\sin(\theta)}{\frac{180}{\pi} \times \theta}\right)} \]

Where:

\( D \) — Diameter of Section (m)
\( R_h \) — Hydraulic Radius of Circular Channel (m)
\( \theta \) — Subtended Angle in Radians (rad)
\( \pi \) — Archimedes' constant (approximately 3.14159)
\( \sin \) — Sine trigonometric function

Explanation: The formula relates the hydraulic radius to the diameter of a circular channel section, accounting for the subtended angle which affects the flow characteristics.

3. Importance of Diameter Calculation

Details: Accurate diameter calculation is crucial for designing efficient hydraulic systems, ensuring proper flow rates, and optimizing channel dimensions for various engineering applications.

4. Using the Calculator

Tips: Enter hydraulic radius in meters and subtended angle in radians. Both values must be positive numbers for valid calculations.

5. Frequently Asked Questions (FAQ)

Q1: What is hydraulic radius?
A: Hydraulic radius is the ratio of the cross-sectional area of flow to the wetted perimeter of the channel.

Q2: Why is the subtended angle important?
A: The subtended angle determines the portion of the circular channel that is in contact with the fluid, affecting the hydraulic radius calculation.

Q3: What are typical values for hydraulic radius?
A: Hydraulic radius values vary depending on channel size and flow conditions, typically ranging from 0.1m to several meters in large channels.

Q4: Can this formula be used for partially full pipes?
A: Yes, this formula is specifically designed for circular channels that may be flowing partially full.

Q5: What are the limitations of this formula?
A: The formula assumes a perfect circular cross-section and may not be accurate for irregular channels or those with significant surface roughness.