1. What is the Subtended Angle Formula?

The formula calculates the angle subtended by a chord in a circular channel. It uses the inverse sine function to determine the angle based on the ratio of the top width to the diameter of the section.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \theta_{Angle} \) — Subtended angle in radians
• \( T_{cir} \) — Top width of circular channel (m)
• \( d_{section} \) — Diameter of section (m)

Explanation: The formula calculates the central angle subtended by a chord of length equal to the top width in a circle of given diameter.

3. Importance of Angle Calculation

Details: Calculating the subtended angle is crucial in hydraulic engineering, fluid mechanics, and circular channel design to determine flow characteristics and cross-sectional properties.

4. Using the Calculator

Tips: Enter top width and diameter in meters. Both values must be positive, and top width cannot exceed diameter. The calculator provides results in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid inputs?
A: Top width must be between 0 and diameter (0 < T_cir ≤ d_section). Both values must be positive.

Q2: Why does the formula use arcsin?
A: Arcsin is used because the ratio T_cir/d_section represents the sine of half the subtended angle in a right triangle formed by the radius and chord.

Q3: What are typical applications of this calculation?
A: This calculation is used in circular channel flow analysis, pipe flow calculations, and hydraulic engineering design.

Q4: Can the angle exceed 180 degrees?
A: No, the maximum angle is 180 degrees (π radians) when the top width equals the diameter.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect circular sections and precise input values.