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Hydraulic Mean Depth using Central Angle Calculator

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✖Diameter of Pipe is the diameter of the pipe in which the liquid is flowing.ⓘ Diameter of Pipe [D_pipe]			+10% -10%
✖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]			+10% -10%

✖Hydraulic Mean Depth for Partially Full refers to the cross-sectional area of flow divided by the wetted perimeter, adapting to varying water levels.ⓘ Hydraulic Mean Depth using Central Angle [r_pf]

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Formula

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Hydraulic Mean Depth using Central Angle

Formula

r pf = (\frac{D pipe}{4}) \cdot (1 - (\frac{(360 \cdot \frac{π}{180}) \cdot \sin (∠ central)}{2 \cdot π \cdot ∠ central}))

Example

0.387092 m = (\frac{2.64 m}{4}) \cdot (1 - (\frac{(360 \cdot \frac{π}{180}) \cdot \sin (120 °)}{2 \cdot π \cdot 120 °}))

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Hydraulic Mean Depth using Central Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hydraulic Mean Depth for Partially Full = (Diameter of Pipe/4)*(1-(((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle)))
r_pf = (D_pipe/4)*(1-(((360*pi/180)*sin(∠_central))/(2*pi*∠_central)))
This formula uses 1 Constants, 1 Functions, 3 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

Hydraulic Mean Depth for Partially Full - (Measured in Meter) - Hydraulic Mean Depth for Partially Full refers to the cross-sectional area of flow divided by the wetted perimeter, adapting to varying water levels.
Diameter of Pipe - (Measured in Meter) - Diameter of Pipe is the diameter of the pipe in which the liquid is flowing.
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

Diameter of Pipe: 2.64 Meter --> 2.64 Meter No Conversion Required
Central Angle: 120 Degree --> 2.0943951023928 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_pf = (D_pipe/4)*(1-(((360*pi/180)*sin(∠_central))/(2*pi*∠_central))) --> (2.64/4)*(1-(((360*pi/180)*sin(2.0943951023928))/(2*pi*2.0943951023928)))

Evaluating ... ...

r_pf = 0.387092196766099

STEP 3: Convert Result to Output's Unit

0.387092196766099 Meter --> No Conversion Required

FINAL ANSWER

0.387092196766099 ≈ 0.387092 Meter <-- Hydraulic Mean Depth for Partially Full

(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri

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< Circular Sewer Section Running Full Calculators

Diameter of pipe given Area of Cross-section

Go Diameter of Pipe = (Area of Partially Full Sewers/((pi/4)*((Central Angle/(360*pi/180))-(sin(Central Angle)/(2*pi)))))^(1/2)

Diameter of Pipe using Hydraulic Mean Depth

Go Diameter of Pipe = Hydraulic Mean Depth for Partially Full/((1/4)*(1-(((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))))

Hydraulic Mean Depth using Central Angle

Go Hydraulic Mean Depth for Partially Full = (Diameter of Pipe/4)*(1-(((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle)))

Discharge when Pipe is Running Full

Go Discharge when Pipe is Running Full = Velocity While Running Full*Area of Running Full Sewers

Hydraulic Mean Depth using Central Angle Formula

Hydraulic Mean Depth for Partially Full = (Diameter of Pipe/4)*(1-(((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle)))
r_pf = (D_pipe/4)*(1-(((360*pi/180)*sin(∠_central))/(2*pi*∠_central)))

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 Hydraulic Mean Depth using Central Angle?

Hydraulic Mean Depth using Central Angle calculator uses Hydraulic Mean Depth for Partially Full = (Diameter of Pipe/4)*(1-(((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))) to calculate the Hydraulic Mean Depth for Partially Full, The Hydraulic Mean Depth using Central Angle is defined as the ratio of the cross-sectional area of fluid flow to the wetted perimeter in a channel or pipe. Hydraulic Mean Depth for Partially Full is denoted by r_pf symbol.

How to calculate Hydraulic Mean Depth using Central Angle using this online calculator? To use this online calculator for Hydraulic Mean Depth using Central Angle, enter Diameter of Pipe (D_pipe) & Central Angle (∠_central) and hit the calculate button. Here is how the Hydraulic Mean Depth using Central Angle calculation can be explained with given input values -> 0.065791 = (2.64/4)*(1-(((360*pi/180)*sin(central_angle))/(2*pi*central_angle))).

FAQ

What is Hydraulic Mean Depth using Central Angle?

The Hydraulic Mean Depth using Central Angle is defined as the ratio of the cross-sectional area of fluid flow to the wetted perimeter in a channel or pipe and is represented as r_pf = (D_pipe/4)*(1-(((360*pi/180)*sin(∠_central))/(2*pi*∠_central))) or Hydraulic Mean Depth for Partially Full = (Diameter of Pipe/4)*(1-(((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))). Diameter of Pipe is the diameter of the pipe in which the liquid is flowing & 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 Hydraulic Mean Depth using Central Angle?

The Hydraulic Mean Depth using Central Angle is defined as the ratio of the cross-sectional area of fluid flow to the wetted perimeter in a channel or pipe is calculated using Hydraulic Mean Depth for Partially Full = (Diameter of Pipe/4)*(1-(((360*pi/180)*sin(Central Angle))/(2*pi*Central Angle))). To calculate Hydraulic Mean Depth using Central Angle, you need Diameter of Pipe (D_pipe) & Central Angle (∠_central). With our tool, you need to enter the respective value for Diameter of Pipe & Central Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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