Density of Liquid using Mean Velocity given Shear Stress with Friction Factor Solution

STEP 0: Pre-Calculation Summary
Formula Used
Density of Fluid = 8*Shear Stress/(Darcy Friction Factor*(Mean Velocity^2))
ρFluid = 8*𝜏/(f*(Vmean^2))
This formula uses 4 Variables
Variables Used
Density of Fluid - (Measured in Kilogram per Cubic Meter) - Density of Fluid is defined as the mass of fluid per unit volume of the said fluid.
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.
Darcy Friction Factor - Darcy Friction Factor is denoted by f. Its value depends on the flow's Reynolds number Re and on the pipe's relative roughness ε / D. It can be obtained from Moody's chart.
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.
STEP 1: Convert Input(s) to Base Unit
Shear Stress: 93.1 Pascal --> 93.1 Pascal No Conversion Required
Darcy Friction Factor: 5 --> No Conversion Required
Mean Velocity: 10.1 Meter per Second --> 10.1 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ρFluid = 8*𝜏/(f*(Vmean^2)) --> 8*93.1/(5*(10.1^2))
Evaluating ... ...
ρFluid = 1.46024899519655
STEP 3: Convert Result to Output's Unit
1.46024899519655 Kilogram per Cubic Meter --> No Conversion Required
FINAL ANSWER
1.46024899519655 1.460249 Kilogram per Cubic Meter <-- Density of Fluid
(Calculation completed in 00.020 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal
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14 Darcy – Weisbach Equation Calculators

Diameter of Pipe given Head Loss due to Frictional Resistance
Go Diameter of Pipe = Darcy Friction Factor*Length of Pipe*(Mean Velocity^2)/(2*[g]*Head Loss due to Friction)
Length of Pipe given Head Loss due to Frictional Resistance
Go Length of Pipe = (Head Loss due to Friction*2*[g]*Diameter of Pipe)/(Darcy Friction Factor*Mean Velocity*2)
Head Loss due to Frictional Resistance
Go Head Loss due to Friction = Darcy Friction Factor*Length of Pipe*(Mean Velocity^2)/(2*[g]*Diameter of Pipe)
Diameter of Pipe given Friction Factor
Go Diameter of Pipe = (64*Dynamic Viscosity)/(Darcy Friction Factor*Mean Velocity*Density of Fluid)
Dynamic Viscosity given Friction Factor
Go Dynamic Viscosity = (Darcy Friction Factor*Mean Velocity*Diameter of Pipe*Density of Fluid)/64
Density of Fluid given Friction Factor
Go Density of Fluid = Dynamic Viscosity*64/(Darcy Friction Factor*Diameter of Pipe*Mean Velocity)
Density of Liquid given Shear Stress and Darcy Friction Factor
Go Density of Fluid = 8*Shear Stress/(Darcy Friction Factor*Mean Velocity*Mean Velocity)
Pressure Gradient given Total Required Power
Go Pressure Gradient = Power/(Length of Pipe*Cross Sectional Area of Pipe*Mean Velocity)
Area of Pipe given Total Required Power
Go Cross Sectional Area of Pipe = Power/(Length of Pipe*Pressure Gradient*Mean Velocity)
Shear Stress given Friction Factor and Density
Go Shear Stress = Density of Fluid*Darcy Friction Factor*Mean Velocity*Mean Velocity/8
Total Required Power
Go Power = Pressure Gradient*Cross Sectional Area of Pipe*Mean Velocity*Length of Pipe
Density of Liquid using Mean Velocity given Shear Stress with Friction Factor
Go Density of Fluid = 8*Shear Stress/(Darcy Friction Factor*(Mean Velocity^2))
Shear Velocity
Go Shear Velocity = Mean Velocity*sqrt(Darcy Friction Factor/8)
Reynolds Number given Friction Factor
Go Reynolds Number = 64/Darcy Friction Factor

Density of Liquid using Mean Velocity given Shear Stress with Friction Factor Formula

Density of Fluid = 8*Shear Stress/(Darcy Friction Factor*(Mean Velocity^2))
ρFluid = 8*𝜏/(f*(Vmean^2))

What is Darcy's Friction Factor?

The Darcy friction factor is a dimensionless quantity used in the Darcy-Weisbach equation for the description of friction losses in pipe flow as well as open channel flow. It is also known as the Darcy-Weisbach friction factor or Moody friction factor and is four times larger than the Fanning friction factor.

How to Calculate Density of Liquid using Mean Velocity given Shear Stress with Friction Factor?

Density of Liquid using Mean Velocity given Shear Stress with Friction Factor calculator uses Density of Fluid = 8*Shear Stress/(Darcy Friction Factor*(Mean Velocity^2)) to calculate the Density of Fluid, The Density of Liquid using Mean Velocity given Shear Stress with Friction Factor formula is defined as mass per unit volume of fluid. Density of Fluid is denoted by ρFluid symbol.

How to calculate Density of Liquid using Mean Velocity given Shear Stress with Friction Factor using this online calculator? To use this online calculator for Density of Liquid using Mean Velocity given Shear Stress with Friction Factor, enter Shear Stress (𝜏), Darcy Friction Factor (f) & Mean Velocity (Vmean) and hit the calculate button. Here is how the Density of Liquid using Mean Velocity given Shear Stress with Friction Factor calculation can be explained with given input values -> 1.460249 = 8*93.1/(5*(10.1^2)).

FAQ

What is Density of Liquid using Mean Velocity given Shear Stress with Friction Factor?
The Density of Liquid using Mean Velocity given Shear Stress with Friction Factor formula is defined as mass per unit volume of fluid and is represented as ρFluid = 8*𝜏/(f*(Vmean^2)) or Density of Fluid = 8*Shear Stress/(Darcy Friction Factor*(Mean Velocity^2)). Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress, Darcy Friction Factor is denoted by f. Its value depends on the flow's Reynolds number Re and on the pipe's relative roughness ε / D. It can be obtained from Moody's chart & Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.
How to calculate Density of Liquid using Mean Velocity given Shear Stress with Friction Factor?
The Density of Liquid using Mean Velocity given Shear Stress with Friction Factor formula is defined as mass per unit volume of fluid is calculated using Density of Fluid = 8*Shear Stress/(Darcy Friction Factor*(Mean Velocity^2)). To calculate Density of Liquid using Mean Velocity given Shear Stress with Friction Factor, you need Shear Stress (𝜏), Darcy Friction Factor (f) & Mean Velocity (Vmean). With our tool, you need to enter the respective value for Shear Stress, Darcy Friction Factor & Mean Velocity 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 Density of Fluid?
In this formula, Density of Fluid uses Shear Stress, Darcy Friction Factor & Mean Velocity. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Density of Fluid = Dynamic Viscosity*64/(Darcy Friction Factor*Diameter of Pipe*Mean Velocity)
  • Density of Fluid = 8*Shear Stress/(Darcy Friction Factor*Mean Velocity*Mean Velocity)
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