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Proportionate Depth given Central Angle Formula

GoProportionate Depth given Diameter of Pipe Formula

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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. Check FAQs

P d = (\frac{1}{2}) \cdot (1 - \cos (\frac{∠ central}{2}))

P_d - Proportionate Depth?∠_central - Central Angle?

Proportionate Depth given Central Angle Example

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

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

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

0.25 = (\frac{1}{2}) \cdot (1 - \cos (\frac{120}{2}))

0.25 = (\frac{1}{2}) \cdot (1 - \cos (\frac{120°}{2}))

0.25 = (\frac{1}{2}) \cdot (1 - \cos (\frac{120}{2}))

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Proportionate Depth given Central Angle Solution

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

FIRST Step Consider the formula

P d = (\frac{1}{2}) \cdot (1 - \cos (\frac{∠ central}{2}))

Next Step Substitute values of Variables

∴

P d = (\frac{1}{2}) \cdot (1 - \cos (\frac{120°}{2}))

Next Step Convert Units

∴

P d = (\frac{1}{2}) \cdot (1 - \cos (\frac{2.0944rad}{2}))

Next Step Prepare to Evaluate

∴

P d = (\frac{1}{2}) \cdot (1 - \cos (\frac{2.0944}{2}))

Next Step Evaluate

∴

P d = 0.249999999999914

LAST Step Rounding Answer

∴

P d = 0.25

Proportionate Depth given Central Angle Formula Elements

Variables

Functions

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.

Symbol: P_d

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Proportionate Depth

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Proportionate Depth

Go Proportionate Depth given Diameter of Pipe

P d = \frac{d}{D pipe}

Other formulas in Proportionate Depth category

Go Depth of Partial Flow given Proportionate Depth

d = P d \cdot D pipe

Go Diameter of Pipe given Proportionate Depth

D pipe = \frac{d}{P d}

How to Evaluate Proportionate Depth given Central Angle?

Proportionate Depth given Central Angle evaluator uses Proportionate Depth = (1/2)*(1-cos(Central Angle/2)) to evaluate 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 evaluate Proportionate Depth given Central Angle using this online evaluator? To use this online evaluator for Proportionate Depth given Central Angle, enter Central Angle (∠_central) and hit the calculate button.

FAQs on Proportionate Depth given Central Angle

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

The formula of Proportionate Depth given Central Angle is expressed as Proportionate Depth = (1/2)*(1-cos(Central Angle/2)). Here is an example- 0.03806 = (1/2)*(1-cos(central_angle/2)).

How to calculate Proportionate Depth given Central Angle?

With Central Angle (∠_central) we can find Proportionate Depth given Central Angle using the formula - Proportionate Depth = (1/2)*(1-cos(Central Angle/2)). This formula also uses Cosine function(s).

What are the other ways to Calculate Proportionate Depth?

Here are the different ways to Calculate Proportionate Depth-

Proportionate Depth=Depth at Partial Flow/Diameter of Pipe

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