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Proportionate Discharge given Central Angle Formula

GoProportionate Discharge using Discharge when Pipe Running Full Formula

GoProportionate Discharge given Area of Cross-Section Formula

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Proportionate Discharge is the ratio of discharge while running partially full to running full. Check FAQs

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})

P_q - Proportionate Discharge?∠_central - Central Angle?π - Archimedes' constant?

Proportionate Discharge given Central Angle Example

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Here is how the Proportionate Discharge given Central Angle equation looks like with Values.

Here is how the Proportionate Discharge given Central Angle equation looks like with Units.

Here is how the Proportionate Discharge given Central Angle equation looks like.

0.1147 = ((\frac{120}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (120)}{2 \cdot 3.1416})) \cdot (1 - \frac{(360 \cdot \frac{3.1416}{180}) \cdot \sin (120)}{2 \cdot 3.1416 \cdot 120})

0.1147 = ((\frac{120°}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (120°)}{2 \cdot 3.1416})) \cdot (1 - \frac{(360 \cdot \frac{3.1416}{180}) \cdot \sin (120°)}{2 \cdot 3.1416 \cdot 120°})

0.1147 = ((\frac{120}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (120)}{2 \cdot 3.1416})) \cdot (1 - \frac{(360 \cdot \frac{3.1416}{180}) \cdot \sin (120)}{2 \cdot 3.1416 \cdot 120})

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Proportionate Discharge given Central Angle Solution

Follow our step by step solution on how to calculate Proportionate Discharge given Central Angle?

FIRST Step Consider the 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})

Next Step Substitute values of Variables

∴

P q = ((\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°})

Next Step Substitute values of Constants

∴

P q = ((\frac{120°}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (120°)}{2 \cdot 3.1416})) \cdot (1 - \frac{(360 \cdot \frac{3.1416}{180}) \cdot \sin (120°)}{2 \cdot 3.1416 \cdot 120°})

Next Step Convert Units

∴

P q = ((\frac{2.0944rad}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (2.0944rad)}{2 \cdot 3.1416})) \cdot (1 - \frac{(360 \cdot \frac{3.1416}{180}) \cdot \sin (2.0944rad)}{2 \cdot 3.1416 \cdot 2.0944rad})

Next Step Prepare to Evaluate

∴

P q = ((\frac{2.0944}{360 \cdot \frac{3.1416}{180}}) - (\frac{\sin (2.0944)}{2 \cdot 3.1416})) \cdot (1 - \frac{(360 \cdot \frac{3.1416}{180}) \cdot \sin (2.0944)}{2 \cdot 3.1416 \cdot 2.0944})

Next Step Evaluate

∴

P q = 0.114662051421163

LAST Step Rounding Answer

∴

P q = 0.1147

Proportionate Discharge given Central Angle Formula Elements

Variables

Constants

Functions

Proportionate Discharge

Proportionate Discharge is the ratio of discharge while running partially full to running full.

Symbol: P_q

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Proportionate Discharge

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.

Symbol: ∠_central

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Formulas to find Central Angle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

Other Formulas to find Proportionate Discharge

Go Proportionate Discharge using Discharge when Pipe Running Full

P q = \frac{q}{Q}

Go Proportionate Discharge given Area of Cross-Section

P q = \frac{V s \cdot a}{V \cdot A}

Other formulas in Proportionate Discharge category

Go Discharge when Pipe is Running Full using Proportionate Discharge

Q = (\frac{q}{P q})

Go Area of Cross-section while Running Full given Proportionate Discharge

A = \frac{a \cdot V s}{V \cdot P q}

Go Velocity while Running Full given Proportionate Discharge

V = \frac{V s \cdot a}{P q \cdot A}

How to Evaluate Proportionate Discharge given Central Angle?

Proportionate Discharge given Central Angle evaluator 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 evaluate 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 evaluate Proportionate Discharge given Central Angle using this online evaluator? To use this online evaluator for Proportionate Discharge given Central Angle, enter Central Angle (∠_central) and hit the calculate button.

FAQs on Proportionate Discharge given Central Angle

What is the formula to find Proportionate Discharge given Central Angle?

The formula of Proportionate Discharge given Central Angle is expressed as Proportionate Discharge = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi)))*(1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle)). Here is an example- 0.001242 = ((central_angle/(360*pi/180))-(sin(central_angle)/(2*pi)))*(1-((360*pi/180)*sin(central_angle))/(2*pi*central_angle)).

How to calculate Proportionate Discharge given Central Angle?

With Central Angle (∠_central) we can find Proportionate Discharge given Central Angle using the formula - Proportionate Discharge = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi)))*(1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle)). This formula also uses Archimedes' constant and Sine function(s).

What are the other ways to Calculate Proportionate Discharge?

Here are the different ways to Calculate Proportionate Discharge-

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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