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Proportionate Velocity Given Central Angle Calculator

Proportionate Velocity Formula:

\[ Pv = \left(1 - \frac{(360 \times \pi/180) \times \sin(\theta)}{2 \times \pi \times \theta}\right)^{2/3} \]

radians

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1. What is Proportionate Velocity?

Proportionate Velocity is the ratio of velocity when water is partially full to velocity when water is totally full in a circular channel or pipe. It's an important parameter in hydraulic engineering for flow calculations.

2. How Does the Calculator Work?

The calculator uses the Proportionate Velocity formula:

\[ Pv = \left(1 - \frac{(360 \times \pi/180) \times \sin(\theta)}{2 \times \pi \times \theta}\right)^{2/3} \]

Where:

Explanation: The formula calculates the velocity ratio based on the central angle of the partially filled circular section, accounting for the geometric properties of circular flow.

3. Importance of Proportionate Velocity Calculation

Details: Accurate calculation of proportionate velocity is crucial for designing efficient water distribution systems, sewer systems, and irrigation channels. It helps engineers determine flow characteristics in partially filled pipes.

4. Using the Calculator

Tips: Enter the central angle in radians. The central angle must be a positive value greater than zero. For degrees, convert to radians first (radians = degrees × π/180).

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid central angle values?
A: The central angle should be between 0 and 2π radians (0-360 degrees) for meaningful results in circular flow calculations.

Q2: How does central angle affect proportionate velocity?
A: As the central angle increases (more filled pipe), the proportionate velocity approaches 1 (full flow velocity). The relationship is non-linear and follows the given formula.

Q3: Can this formula be used for non-circular channels?
A: No, this specific formula is derived for circular cross-sections. Other geometric shapes have different hydraulic relationships.

Q4: What are typical applications of this calculation?
A: This calculation is used in water supply systems, wastewater treatment plants, stormwater management, and irrigation system design.

Q5: Why is the sine function used in this formula?
A: The sine function accounts for the trigonometric relationship between the central angle and the wetted perimeter in circular cross-sections, which affects flow velocity.

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