Diameter of Section given Slope of Channel Solution

STEP 0: Pre-Calculation Summary
Formula Used
Diameter of Section = (Shear Stress/(Bed Slope*Specific Weight of Liquid))+Horizontal Distance
dsection = (𝜏/(*γf))+R
This formula uses 5 Variables
Variables Used
Diameter of Section - (Measured in Meter) - Diameter of Section is the diameter of the circular cross-section of the beam.
Shear Stress - (Measured in Pascal) - Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Bed Slope - Bed Slope is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow.
Specific Weight of Liquid - (Measured in Newton per Cubic Meter) - Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.
Horizontal Distance - (Measured in Meter) - Horizontal Distance is the instantaneous horizontal distance cover by an object in a projectile motion.
STEP 1: Convert Input(s) to Base Unit
Shear Stress: 93.1 Pascal --> 93.1 Pascal No Conversion Required
Bed Slope: 4 --> No Conversion Required
Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (Check conversion here)
Horizontal Distance: 1.01 Meter --> 1.01 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dsection = (𝜏/(S̄*γf))+R --> (93.1/(4*9810))+1.01
Evaluating ... ...
dsection = 1.01237257900102
STEP 3: Convert Result to Output's Unit
1.01237257900102 Meter --> No Conversion Required
FINAL ANSWER
1.01237257900102 1.012373 Meter <-- Diameter of Section
(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal
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18 Laminar Flow of Fluid in an Open Channel Calculators

Slope of Channel given Mean Velocity of Flow
Go Slope of Surface of Constant Pressure = (Dynamic Viscosity*Mean Velocity)/((Diameter of Section*Horizontal Distance-(Horizontal Distance^2)/2)*Specific Weight of Liquid)
Diameter of Section given Mean Velocity of Flow
Go Diameter of Section = ((Horizontal Distance^2+(-Dynamic Viscosity*Mean Velocity*Slope of Surface of Constant Pressure/Specific Weight of Liquid)))/Horizontal Distance
Mean Velocity in flow
Go Mean Velocity = -(Specific Weight of Liquid*Piezometric Gradient*(Diameter of Section*Horizontal Distance-Horizontal Distance^2))/Dynamic Viscosity
Dynamic Viscosity given Mean Velocity of Flow in Section
Go Dynamic Viscosity = (Specific Weight of Liquid*Piezometric Gradient*(Diameter of Section*Horizontal Distance-Horizontal Distance^2))/Mean Velocity
Diameter of Section given Potential Head Drop
Go Diameter of Section = sqrt((3*Dynamic Viscosity*Mean Velocity*Length of Pipe)/(Specific Weight of Liquid*Head Loss due to Friction))
Length of Pipe given Potential Head Drop
Go Length of Pipe = (Head Loss due to Friction*Specific Weight of Liquid*(Diameter of Section^2))/(3*Dynamic Viscosity*Mean Velocity)
Potential Head Drop
Go Head Loss due to Friction = (3*Dynamic Viscosity*Mean Velocity*Length of Pipe)/(Specific Weight of Liquid*Diameter of Section^2)
Diameter of Section given Discharge per Unit Channel Width
Go Diameter of Section = ((3*Dynamic Viscosity*Discharge per Unit Width)/(Slope of bed*Specific Weight of Liquid))^(1/3)
Dynamic Viscosity given Discharge per Unit Channel Width
Go Dynamic Viscosity = (Specific Weight of Liquid*Slope of bed*Diameter of Section^3)/(3*Discharge per Unit Width)
Slope of Channel given Discharge per Unit Channel Width
Go Slope of bed = (3*Dynamic Viscosity*Discharge per Unit Width)/(Specific Weight of Liquid*Diameter of Section^3)
Discharge per unit channel width
Go Discharge per Unit Width = (Specific Weight of Liquid*Slope of bed*Diameter of Section^3)/(3*Dynamic Viscosity)
Slope of Channel given Shear Stress
Go Bed Slope = Shear Stress/(Specific Weight of Liquid*(Overall diameter of section-Horizontal Distance))
Diameter of Section given Slope of Channel
Go Diameter of Section = (Shear Stress/(Bed Slope*Specific Weight of Liquid))+Horizontal Distance
Horizontal Distance given Slope of Channel
Go Horizontal Distance = Diameter of Section-(Shear Stress/(Bed Slope*Specific Weight of Liquid))
Shear Stress given Slope of Channel
Go Shear Stress = Specific Weight of Liquid*Bed Slope*(Depth-Horizontal Distance)
Diameter of Section given Bed Shear Stress
Go Diameter of Section = Shear Stress/(Bed Slope*Specific Weight of Liquid)
Bed Slope given Bed Shear Stress
Go Bed Slope = Shear Stress/(Diameter of Section*Specific Weight of Liquid)
Bed Shear Stress
Go Shear Stress = Specific Weight of Liquid*Bed Slope*Diameter of Section

Diameter of Section given Slope of Channel Formula

Diameter of Section = (Shear Stress/(Bed Slope*Specific Weight of Liquid))+Horizontal Distance
dsection = (𝜏/(*γf))+R

What is Specific Weight of Liquid?

In fluid mechanics, specific weight represents the force exerted by gravity on a unit volume of a fluid. For this reason, units are expressed as force per unit volume (e.g., N/m3 or lbf/ft3). Specific weight can be used as a characteristic property of a fluid.

How to Calculate Diameter of Section given Slope of Channel?

Diameter of Section given Slope of Channel calculator uses Diameter of Section = (Shear Stress/(Bed Slope*Specific Weight of Liquid))+Horizontal Distance to calculate the Diameter of Section, The Diameter of Section given Slope of Channel is defined as depth of section of flow with respect to centre distance of section. Diameter of Section is denoted by dsection symbol.

How to calculate Diameter of Section given Slope of Channel using this online calculator? To use this online calculator for Diameter of Section given Slope of Channel, enter Shear Stress (𝜏), Bed Slope (S̄), Specific Weight of Liquid f) & Horizontal Distance (R) and hit the calculate button. Here is how the Diameter of Section given Slope of Channel calculation can be explained with given input values -> 1.012373 = (93.1/(4*9810))+1.01.

FAQ

What is Diameter of Section given Slope of Channel?
The Diameter of Section given Slope of Channel is defined as depth of section of flow with respect to centre distance of section and is represented as dsection = (𝜏/(S̄*γf))+R or Diameter of Section = (Shear Stress/(Bed Slope*Specific Weight of Liquid))+Horizontal Distance. Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress, Bed Slope is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow, Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid & Horizontal Distance is the instantaneous horizontal distance cover by an object in a projectile motion.
How to calculate Diameter of Section given Slope of Channel?
The Diameter of Section given Slope of Channel is defined as depth of section of flow with respect to centre distance of section is calculated using Diameter of Section = (Shear Stress/(Bed Slope*Specific Weight of Liquid))+Horizontal Distance. To calculate Diameter of Section given Slope of Channel, you need Shear Stress (𝜏), Bed Slope (S̄), Specific Weight of Liquid f) & Horizontal Distance (R). With our tool, you need to enter the respective value for Shear Stress, Bed Slope, Specific Weight of Liquid & Horizontal Distance 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 Diameter of Section?
In this formula, Diameter of Section uses Shear Stress, Bed Slope, Specific Weight of Liquid & Horizontal Distance. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Diameter of Section = ((Horizontal Distance^2+(-Dynamic Viscosity*Mean Velocity*Slope of Surface of Constant Pressure/Specific Weight of Liquid)))/Horizontal Distance
  • Diameter of Section = ((3*Dynamic Viscosity*Discharge per Unit Width)/(Slope of bed*Specific Weight of Liquid))^(1/3)
  • Diameter of Section = sqrt((3*Dynamic Viscosity*Mean Velocity*Length of Pipe)/(Specific Weight of Liquid*Head Loss due to Friction))
  • Diameter of Section = Shear Stress/(Bed Slope*Specific Weight of Liquid)
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