Proportionate Depth 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 depth is ratio of partial to actual depth.ⓘ Proportionate Depth given Central Angle [P]

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Formula

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Proportionate Depth given Central Angle

Formula

`"P" = (1/2)*(1-cos("∠"_{"central"}/2))`

Example

`"0.03806"=(1/2)*(1-cos("45°"/2))`

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Proportionate Depth given Central Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Proportionate depth = (1/2)*(1-cos(Central Angle/2))
P = (1/2)*(1-cos(∠_central/2))
This formula uses 1 Functions, 2 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Proportionate depth - Proportionate depth is ratio of partial to actual depth.
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 = (1/2)*(1-cos(∠_central/2)) --> (1/2)*(1-cos(0.785398163397301/2))

Evaluating ... ...

P = 0.0380602337443425

STEP 3: Convert Result to Output's Unit

0.0380602337443425 --> No Conversion Required

FINAL ANSWER

0.0380602337443425 ≈ 0.03806 <-- Proportionate depth

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2200+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 4 Proportionate Depth Calculators

Depth of Partial Flow given Proportionate Depth

Go Depth at partial flow = Proportionate depth*Diameter of Pipe

Proportionate Depth given Diameter of Pipe

Go Proportionate depth = Depth at partial flow/Diameter of Pipe

Diameter of Pipe given Proportionate Depth

Go Diameter of Pipe = Depth at partial flow/Proportionate depth

Proportionate Depth given Central Angle

Go Proportionate depth = (1/2)*(1-cos(Central Angle/2))

Proportionate Depth given Central Angle Formula

Proportionate depth = (1/2)*(1-cos(Central Angle/2))
P = (1/2)*(1-cos(∠_central/2))

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 Depth given Central Angle?

Proportionate Depth given Central Angle calculator uses Proportionate depth = (1/2)*(1-cos(Central Angle/2)) to calculate the Proportionate depth, The Proportionate Depth given Central Angle calculates the ratio of depth when water is partially fill to depth of water when water is fully filled. Proportionate depth is denoted by P symbol.

How to calculate Proportionate Depth given Central Angle using this online calculator? To use this online calculator for Proportionate Depth given Central Angle, enter Central Angle (∠_central) and hit the calculate button. Here is how the Proportionate Depth given Central Angle calculation can be explained with given input values -> 0.03806 = (1/2)*(1-cos(0.785398163397301/2)).

FAQ

What is Proportionate Depth given Central Angle?

The Proportionate Depth given Central Angle calculates the ratio of depth when water is partially fill to depth of water when water is fully filled and is represented as P = (1/2)*(1-cos(∠_central/2)) or Proportionate depth = (1/2)*(1-cos(Central Angle/2)). 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 Depth given Central Angle?

The Proportionate Depth given Central Angle calculates the ratio of depth when water is partially fill to depth of water when water is fully filled is calculated using Proportionate depth = (1/2)*(1-cos(Central Angle/2)). To calculate Proportionate Depth 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 depth?

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

Proportionate depth = Depth at partial flow/Diameter of Pipe

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