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Proportionate Discharge given Central Angle Calculator

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✖A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B.ⓘ Central Angle [∠_central]

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✖Proportionate Discharge is the ratio of discharge while running partially full to running full.ⓘ Proportionate Discharge given Central Angle [P_q]

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Formula

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Proportionate Discharge given Central Angle

Formula

P q = ((\frac{∠ central}{360 \cdot \frac{π}{180}}) - (\frac{\sin (∠ central)}{2 \cdot π})) \cdot (1 - \frac{(360 \cdot \frac{π}{180}) \cdot \sin (∠ central)}{2 \cdot π \cdot ∠ central})

Example

0.114662 = ((\frac{120 °}{360 \cdot \frac{π}{180}}) - (\frac{\sin (120 °)}{2 \cdot π})) \cdot (1 - \frac{(360 \cdot \frac{π}{180}) \cdot \sin (120 °)}{2 \cdot π \cdot 120 °})

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Proportionate Discharge given Central Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Proportionate Discharge = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi)))*(1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))
P_q = ((∠_central/(360*pi/180))-(sin(∠_central)/(2*pi)))*(1-((360*pi/180)*sin(∠_central))/(2*pi*∠_central))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Proportionate Discharge - Proportionate Discharge is the ratio of discharge while running partially full to running full.
Central Angle - (Measured in Radian) - A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B.

STEP 1: Convert Input(s) to Base Unit

Central Angle: 120 Degree --> 2.0943951023928 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_q = ((∠_central/(360*pi/180))-(sin(∠_central)/(2*pi)))*(1-((360*pi/180)*sin(∠_central))/(2*pi*∠_central)) --> ((2.0943951023928/(360*pi/180))-(sin(2.0943951023928)/(2*pi)))*(1-((360*pi/180)*sin(2.0943951023928))/(2*pi*2.0943951023928))

Evaluating ... ...

P_q = 0.114662051421163

STEP 3: Convert Result to Output's Unit

0.114662051421163 --> No Conversion Required

FINAL ANSWER

0.114662051421163 ≈ 0.114662 <-- Proportionate Discharge

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< Proportionate Discharge Calculators

Proportionate Discharge given Central Angle

Go Proportionate Discharge = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi)))*(1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))

Proportionate Discharge given Area of Cross-Section

Go Proportionate Discharge = (Velocity in a Partially Running Sewer*Area of Partially Full Sewers)/(Velocity While Running Full*Area of Running Full Sewers)

Discharge when Pipe is Running Full using Proportionate Discharge

Go Discharge when Pipe is Running Full = (Discharge when Pipe is Running Partially Full/Proportionate Discharge)

Proportionate Discharge using Discharge when Pipe Running Full

Go Proportionate Discharge = Discharge when Pipe is Running Partially Full/Discharge when Pipe is Running Full

Proportionate Discharge given Central Angle Formula

What is central angle ?

The central angle is the angle subtended at the center of a circular pipe by the arc length of the wetted perimeter when the pipe is partially filled. This angle is essential for calculating flow characteristics like hydraulic radius and flow area in partially filled pipes. It helps in determining the distribution of flow within the pipe, affecting flow velocity, friction, and overall hydraulic performance, ensuring accurate design and analysis of drainage or sewer systems.

How to Calculate Proportionate Discharge given Central Angle?

Proportionate Discharge given Central Angle calculator uses Proportionate Discharge = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi)))*(1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle)) to calculate the Proportionate Discharge, The Proportionate Discharge given Central Angle is defined as the ratio of the flow rate in a partially filled pipe to the flow rate when the pipe is fully filled. Proportionate Discharge is denoted by P_q symbol.

How to calculate Proportionate Discharge given Central Angle using this online calculator? To use this online calculator for Proportionate Discharge given Central Angle, enter Central Angle (∠_central) and hit the calculate button. Here is how the Proportionate Discharge given Central Angle calculation can be explained with given input values -> 0.001242 = ((central_angle/(360*pi/180))-(sin(central_angle)/(2*pi)))*(1-((360*pi/180)*sin(central_angle))/(2*pi*central_angle)).

FAQ

What is Proportionate Discharge given Central Angle?

The Proportionate Discharge given Central Angle is defined as the ratio of the flow rate in a partially filled pipe to the flow rate when the pipe is fully filled and is represented as P_q = ((∠_central/(360*pi/180))-(sin(∠_central)/(2*pi)))*(1-((360*pi/180)*sin(∠_central))/(2*pi*∠_central)) or Proportionate Discharge = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi)))*(1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle)). A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B.

How to calculate Proportionate Discharge given Central Angle?

The Proportionate Discharge given Central Angle is defined as the ratio of the flow rate in a partially filled pipe to the flow rate when the pipe is fully filled is calculated using Proportionate Discharge = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi)))*(1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle)). To calculate Proportionate Discharge given Central Angle, you need Central Angle (∠_central). With our tool, you need to enter the respective value for Central Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Proportionate Discharge?

In this formula, Proportionate Discharge uses Central Angle. We can use 2 other way(s) to calculate the same, which is/are as follows -

Proportionate Discharge = Discharge when Pipe is Running Partially Full/Discharge when Pipe is Running Full
Proportionate Discharge = (Velocity in a Partially Running Sewer*Area of Partially Full Sewers)/(Velocity While Running Full*Area of Running Full Sewers)

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