Proportionate Velocity 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 velocity is ratio of velocity when water is partially full to velocity when water is totally full.ⓘ Proportionate Velocity given Central Angle [P_v]

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Formula

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Proportionate Velocity given Central Angle

Formula

`"P"_{"v"} = (1-((360*pi/180)*sin("∠"_{"central"}))/(2*pi*"∠"_{"central"}))^(2/3)`

Example

`"0.214989"=(1-((360*pi/180)*sin("45°"))/(2*pi*"45°"))^(2/3)`

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Proportionate Velocity given Central Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Proportionate velocity = (1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))^(2/3)
P_v = (1-((360*pi/180)*sin(∠_central))/(2*pi*∠_central))^(2/3)
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 velocity - Proportionate velocity is ratio of velocity when water is partially full to velocity 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_v = (1-((360*pi/180)*sin(∠_central))/(2*pi*∠_central))^(2/3) --> (1-((360*pi/180)*sin(0.785398163397301))/(2*pi*0.785398163397301))^(2/3)

Evaluating ... ...

P_v = 0.214988907482393

STEP 3: Convert Result to Output's Unit

0.214988907482393 --> No Conversion Required

FINAL ANSWER

0.214988907482393 ≈ 0.214989 <-- Proportionate velocity

(Calculation completed in 00.004 seconds)

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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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< 7 Proportionate Velocity Calculators

Roughness Coefficient while Running Full given Proportionate Velocity

Go Roughness coefficient full = (Proportionate velocity*Roughness coefficient partially full)/(Hydraulic mean depth/Hydraulic mean depth while running full)^(2/3)

Proportionate Velocity given Roughness Coefficient

Go Proportionate velocity = (Roughness coefficient full/Roughness coefficient partially full)*(Hydraulic mean depth/Hydraulic mean depth)^(2/3)

Proportionate Velocity given Central Angle

Go Proportionate velocity = (1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))^(2/3)

Hydraulic Mean Depth while Running Full given Proportionate Velocity

Go Hydraulic mean depth while running full = ((Hydraulic mean depth)^(2/3)/Proportionate velocity)^(3/2)

Proportionate Velocity when Roughness Coefficient does not Vary with Depth

Go Proportionate velocity = (Hydraulic mean depth/Hydraulic mean depth while running full)^(2/3)

Proportionate Velocity given Velocity while Running Partially Full

Go Proportionate velocity = Velocity while running partially full/Velocity while running full

Velocity while Running Full given Proportionate Velocity

Go Velocity while running full = Velocity while running partially full/Proportionate velocity

Proportionate Velocity given Central Angle Formula

Proportionate velocity = (1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))^(2/3)
P_v = (1-((360*pi/180)*sin(∠_central))/(2*pi*∠_central))^(2/3)

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 Velocity given Central Angle?

Proportionate Velocity given Central Angle calculator uses Proportionate velocity = (1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))^(2/3) to calculate the Proportionate velocity, The Proportionate Velocity given Central Angle calculates the proportionate velocity when we have prior information of other parameters. Proportionate velocity is denoted by P_v symbol.

How to calculate Proportionate Velocity given Central Angle using this online calculator? To use this online calculator for Proportionate Velocity given Central Angle, enter Central Angle (∠_central) and hit the calculate button. Here is how the Proportionate Velocity given Central Angle calculation can be explained with given input values -> 0.214989 = (1-((360*pi/180)*sin(0.785398163397301))/(2*pi*0.785398163397301))^(2/3).

FAQ

What is Proportionate Velocity given Central Angle?

The Proportionate Velocity given Central Angle calculates the proportionate velocity when we have prior information of other parameters and is represented as P_v = (1-((360*pi/180)*sin(∠_central))/(2*pi*∠_central))^(2/3) or Proportionate velocity = (1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))^(2/3). 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 Velocity given Central Angle?

The Proportionate Velocity given Central Angle calculates the proportionate velocity when we have prior information of other parameters is calculated using Proportionate velocity = (1-((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))^(2/3). To calculate Proportionate Velocity 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 velocity?

In this formula, Proportionate velocity uses Central Angle. We can use 3 other way(s) to calculate the same, which is/are as follows -

Proportionate velocity = (Roughness coefficient full/Roughness coefficient partially full)*(Hydraulic mean depth/Hydraulic mean depth)^(2/3)
Proportionate velocity = (Hydraulic mean depth/Hydraulic mean depth while running full)^(2/3)
Proportionate velocity = Velocity while running partially full/Velocity while running full

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