Hydraulic Radius Given Angle Calculator

Hydraulic Radius Formula:

\[ Rh(cir) = 0.25 \times d_{section} \times (1 - \frac{\sin(\theta_{Angle})}{(180/\pi) \times \theta_{Angle}}) \]

Hydraulic Radius of Circular Channel:

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1. What is Hydraulic Radius of Circular Channel?

The Hydraulic Radius of a Circular Channel is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wet perimeter of the conduit. It is a key parameter in fluid mechanics and hydraulic engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Rh(cir) = 0.25 \times d_{section} \times (1 - \frac{\sin(\theta_{Angle})}{(180/\pi) \times \theta_{Angle}}) \]

Where:

\( d_{section} \) — Diameter of Section (m)
\( \theta_{Angle} \) — Subtended Angle in Radians (rad)
\( \pi \) — Archimedes' constant (approximately 3.1416)
\( \sin \) — Sine trigonometric function

Explanation: This formula calculates the hydraulic radius for a circular channel based on the diameter and the subtended angle, accounting for the geometric properties of the circular cross-section.

3. Importance of Hydraulic Radius Calculation

Details: The hydraulic radius is crucial in determining flow characteristics, resistance, and efficiency in open channel flow and pipe flow systems. It helps in designing efficient hydraulic structures.

4. Using the Calculator

Tips: Enter the diameter of the section in meters and the subtended angle in radians. Both values must be positive numbers for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of hydraulic radius in fluid mechanics?
A: Hydraulic radius is used to characterize flow efficiency and resistance in channels and pipes, influencing velocity distribution and energy loss calculations.

Q2: How does subtended angle affect hydraulic radius?
A: The subtended angle determines the portion of the circular cross-section that is in contact with fluid, directly affecting the wetted perimeter and thus the hydraulic radius.

Q3: What are typical values for hydraulic radius in circular channels?
A: Values vary based on diameter and flow conditions, but typically range from a few centimeters to several meters depending on the application.

Q4: Are there limitations to this formula?
A: This formula is specifically for circular channels and assumes uniform flow conditions. It may not be accurate for non-circular or irregular channels.

Q5: Can this calculator be used for partially full pipes?
A: Yes, this formula is particularly useful for calculating hydraulic radius in partially full circular pipes where the subtended angle is known.