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Proportionate Depth 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 depth refers to the ratio of the depth of fluid in a partially filled pipe to the depth when the pipe is running full.ⓘ Proportionate Depth given Central Angle [P_d]

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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_d = (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 refers to the ratio of the depth of fluid in a partially filled pipe to the depth when the pipe is 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_d = (1/2)*(1-cos(∠_central/2)) --> (1/2)*(1-cos(2.0943951023928/2))

Evaluating ... ...

P_d = 0.249999999999914

STEP 3: Convert Result to Output's Unit

0.249999999999914 --> No Conversion Required

FINAL ANSWER

0.249999999999914 ≈ 0.25 <-- Proportionate Depth

(Calculation completed in 00.020 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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< Proportionate Depth Calculators

Depth of Partial Flow given Proportionate Depth

LaTeX Go Depth at Partial Flow = Proportionate Depth*Diameter of Pipe

Proportionate Depth given Diameter of Pipe

LaTeX Go Proportionate Depth = Depth at Partial Flow/Diameter of Pipe

Diameter of Pipe given Proportionate Depth

LaTeX Go Diameter of Pipe = Depth at Partial Flow/Proportionate Depth

Proportionate Depth given Central Angle

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

Proportionate Depth given Central Angle Formula

LaTeX Go

Proportionate Depth = (1/2)*(1-cos(Central Angle/2))
P_d = (1/2)*(1-cos(∠_central/2))

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 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 is defined as the ratio of the depth of fluid in a partially filled pipe to the depth when the pipe is running full. Proportionate Depth is denoted by P_d 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(central_angle/2)).

FAQ

What is Proportionate Depth given Central Angle?

The Proportionate Depth given Central Angle is defined as the ratio of the depth of fluid in a partially filled pipe to the depth when the pipe is running full and is represented as P_d = (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 is defined as the ratio of the depth of fluid in a partially filled pipe to the depth when the pipe is running full 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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