Proportionate Area given Central Angle Calculator

✖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 area is ratio of area when water is partially full to area when water is totally full.ⓘ Proportionate Area given Central Angle [P_a]

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Formula

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Proportionate Area given Central Angle

Formula

`"P"_{"a"} = (("∠"_{"central"}/(360*pi/180))-(sin("∠"_{"central"})/(2*pi)))`

Example

`"0.01246"=(("45°"/(360*pi/180))-(sin("45°")/(2*pi)))`

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Proportionate Area given Central Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Proportionate area = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi)))
P_a = ((∠_central/(360*pi/180))-(sin(∠_central)/(2*pi)))
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 area - Proportionate area is ratio of area when water is partially full to area when water is totally 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: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_a = ((∠_central/(360*pi/180))-(sin(∠_central)/(2*pi))) --> ((0.785398163397301/(360*pi/180))-(sin(0.785398163397301)/(2*pi)))

Evaluating ... ...

P_a = 0.0124604604803549

STEP 3: Convert Result to Output's Unit

0.0124604604803549 --> No Conversion Required

FINAL ANSWER

0.0124604604803549 ≈ 0.01246 <-- Proportionate area

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Environmental Engineering » Hydraulic Designs of Sewers and S. W. Drain Sections » Hydraulic Characteristics of Circular Sewers Sections » Circular Sewer Section Running Full » Proportionate Area » Proportionate Area given Central Angle

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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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< 3 Proportionate Area Calculators

Proportionate Area given Central Angle

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

Proportionate Area given Area of Cross-section

Go Proportionate area = Area of cross-section/Area of cross-section of pipe

Area of Cross-section given Proportionate Area

Go Area of cross-section of pipe = Area of cross-section/Proportionate area

Proportionate Area given Central Angle Formula

Proportionate area = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi)))
P_a = ((∠_central/(360*pi/180))-(sin(∠_central)/(2*pi)))

What is central angle ?

Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians).

How to Calculate Proportionate Area given Central Angle?

Proportionate Area given Central Angle calculator uses Proportionate area = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi))) to calculate the Proportionate area, The Proportionate Area given Central Angle calculates the ratio of area of pipe while running partially full to running full. Proportionate area is denoted by P_a symbol.

How to calculate Proportionate Area given Central Angle using this online calculator? To use this online calculator for Proportionate Area given Central Angle, enter Central Angle (∠_central) and hit the calculate button. Here is how the Proportionate Area given Central Angle calculation can be explained with given input values -> 0.01246 = ((0.785398163397301/(360*pi/180))-(sin(0.785398163397301)/(2*pi))).

FAQ

What is Proportionate Area given Central Angle?

The Proportionate Area given Central Angle calculates the ratio of area of pipe while running partially full to running full and is represented as P_a = ((∠_central/(360*pi/180))-(sin(∠_central)/(2*pi))) or Proportionate area = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi))). 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 Area given Central Angle?

The Proportionate Area given Central Angle calculates the ratio of area of pipe while running partially full to running full is calculated using Proportionate area = ((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi))). To calculate Proportionate Area 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 area?

In this formula, Proportionate area uses Central Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -

Proportionate area = Area of cross-section/Area of cross-section of pipe

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