Slope of Channel given Mean Velocity of Flow Solution

STEP 0: Pre-Calculation Summary
Formula Used
Slope of Surface of Constant Pressure = (Dynamic Viscosity*Mean Velocity)/((Diameter of Section*Horizontal Distance-(Horizontal Distance^2)/2)*Specific Weight of Liquid)
S = (μviscosity*Vmean)/((dsection*R-(R^2)/2)*γf)
This formula uses 6 Variables
Variables Used
Slope of Surface of Constant Pressure - Slope of Surface of Constant Pressure is slope at which free surface is inclined with horizontal.
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.
Mean Velocity - (Measured in Meter per Second) - Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.
Diameter of Section - (Measured in Meter) - Diameter of Section is the diameter of the circular cross-section of the beam.
Horizontal Distance - (Measured in Meter) - Horizontal Distance is the instantaneous horizontal distance cover by an object in a projectile motion.
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.
STEP 1: Convert Input(s) to Base Unit
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Mean Velocity: 10 Meter per Second --> 10 Meter per Second No Conversion Required
Diameter of Section: 5 Meter --> 5 Meter No Conversion Required
Horizontal Distance: 1.01 Meter --> 1.01 Meter No Conversion Required
Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
S = (μviscosity*Vmean)/((dsection*R-(R^2)/2)*γf) --> (1.02*10)/((5*1.01-(1.01^2)/2)*9810)
Evaluating ... ...
S = 0.000229023524858634
STEP 3: Convert Result to Output's Unit
0.000229023524858634 --> No Conversion Required
FINAL ANSWER
0.000229023524858634 0.000229 <-- Slope of Surface of Constant Pressure
(Calculation completed in 00.004 seconds)

Credits

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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

Slope of Channel given Mean Velocity of Flow Formula

Slope of Surface of Constant Pressure = (Dynamic Viscosity*Mean Velocity)/((Diameter of Section*Horizontal Distance-(Horizontal Distance^2)/2)*Specific Weight of Liquid)
S = (μviscosity*Vmean)/((dsection*R-(R^2)/2)*γf)

What is Channel?

A channel is a passageway, a means of access for a thing, a communication, or an idea. Think of a channel as sort of a tunnel or a funnel that moves something directly through. The noun channel can be used for many such avenues.

How to Calculate Slope of Channel given Mean Velocity of Flow?

Slope of Channel given Mean Velocity of Flow calculator uses Slope of Surface of Constant Pressure = (Dynamic Viscosity*Mean Velocity)/((Diameter of Section*Horizontal Distance-(Horizontal Distance^2)/2)*Specific Weight of Liquid) to calculate the Slope of Surface of Constant Pressure, The Slope of Channel given Mean Velocity of Flow is defined as inclination of the channel or gradient to which head is made. Slope of Surface of Constant Pressure is denoted by S symbol.

How to calculate Slope of Channel given Mean Velocity of Flow using this online calculator? To use this online calculator for Slope of Channel given Mean Velocity of Flow, enter Dynamic Viscosity viscosity), Mean Velocity (Vmean), Diameter of Section (dsection), Horizontal Distance (R) & Specific Weight of Liquid f) and hit the calculate button. Here is how the Slope of Channel given Mean Velocity of Flow calculation can be explained with given input values -> 0.000229 = (1.02*10)/((5*1.01-(1.01^2)/2)*9810).

FAQ

What is Slope of Channel given Mean Velocity of Flow?
The Slope of Channel given Mean Velocity of Flow is defined as inclination of the channel or gradient to which head is made and is represented as S = (μviscosity*Vmean)/((dsection*R-(R^2)/2)*γf) or Slope of Surface of Constant Pressure = (Dynamic Viscosity*Mean Velocity)/((Diameter of Section*Horizontal Distance-(Horizontal Distance^2)/2)*Specific Weight of Liquid). The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T, Diameter of Section is the diameter of the circular cross-section of the beam, Horizontal Distance is the instantaneous horizontal distance cover by an object in a projectile motion & Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.
How to calculate Slope of Channel given Mean Velocity of Flow?
The Slope of Channel given Mean Velocity of Flow is defined as inclination of the channel or gradient to which head is made is calculated using Slope of Surface of Constant Pressure = (Dynamic Viscosity*Mean Velocity)/((Diameter of Section*Horizontal Distance-(Horizontal Distance^2)/2)*Specific Weight of Liquid). To calculate Slope of Channel given Mean Velocity of Flow, you need Dynamic Viscosity viscosity), Mean Velocity (Vmean), Diameter of Section (dsection), Horizontal Distance (R) & Specific Weight of Liquid f). With our tool, you need to enter the respective value for Dynamic Viscosity, Mean Velocity, Diameter of Section, Horizontal Distance & Specific Weight of Liquid 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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