## Shear stress in turbulent flow Solution

STEP 0: Pre-Calculation Summary
Formula Used
Shear Stress = (Friction factor*Density of Fluid*Velocity^2)/2
𝜏 = (f*ρFluid*v^2)/2
This formula uses 4 Variables
Variables Used
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.
Friction factor - The Friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number.
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.
Velocity - (Measured in Meter per Second) - Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.
STEP 1: Convert Input(s) to Base Unit
Friction factor: 0.6 --> No Conversion Required
Density of Fluid: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Velocity: 60 Meter per Second --> 60 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
𝜏 = (f*ρFluid*v^2)/2 --> (0.6*1.225*60^2)/2
Evaluating ... ...
𝜏 = 1323
STEP 3: Convert Result to Output's Unit
1323 Pascal --> No Conversion Required
1323 Pascal <-- Shear Stress
(Calculation completed in 00.016 seconds)
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## < 10+ Turbulent Flow Calculators

Head Loss due to Friction given Power Required in Turbulent Flow

## Head Loss due to Friction given Power Required in Turbulent Flow

Formula
"h"_{"f"} = "P"/("ρ"_{"Fluid"}*"[g]"*"Q")

Example
"14.15116m"="170W"/("1.225kg/m³"*"[g]"*"1m³/s")

Calculator
LaTeX
Head loss due to friction = Power/(Density of Fluid*[g]*Discharge)
Discharge through Pipe given Head Loss in Turbulent Flow

## Discharge through Pipe given Head Loss in Turbulent Flow

Formula
"Q" = "P"/("ρ"_{"Fluid"}*"[g]"*"h"_{"f"})

Example
"1.010797m³/s"="170W"/("1.225kg/m³"*"[g]"*"14m")

Calculator
LaTeX
Discharge = Power/(Density of Fluid*[g]*Head loss due to friction)
Power Required to Maintain Turbulent Flow

## Power Required to Maintain Turbulent Flow

Formula
"P" = "ρ"_{"Fluid"}*"[g]"*"Q"*"h"_{"f"}

Example
"168.184W"="1.225kg/m³"*"[g]"*"1m³/s"*"14m"

Calculator
LaTeX
Power = Density of Fluid*[g]*Discharge*Head loss due to friction
Average height of irregularities for turbulent flow in pipes

## Average height of irregularities for turbulent flow in pipes

Formula
"k" = ("R"_{"e"}*"ν")/"V"_{"*"}

Example
"0.001208m"=("10"*"7.25St")/"6m/s"

Calculator
LaTeX
Average Height Irregularities = (Roughness reynold number*Kinematic viscosity)/Shear Velocity
Roughness Reynold number for turbulent flow in pipes

## Roughness Reynold number for turbulent flow in pipes

Formula
"R"_{"e"} = ("V"_{"*"}*"k")/"ν"

Example
"6"=("6m/s"*"0.000725m")/"7.25St"

Calculator
LaTeX
Roughness reynold number = (Shear Velocity*Average Height Irregularities)/Kinematic viscosity
Shear stress in turbulent flow

## Shear stress in turbulent flow

Formula
"𝜏" = ("f"*"ρ"_{"Fluid"}*"v"^2)/2

Example
"1323Pa"=("0.6"*"1.225kg/m³"*"60m/s"^2)/2

Calculator
LaTeX
Shear Stress = (Friction factor*Density of Fluid*Velocity^2)/2
Shear velocity for turbulent flow in pipes

## Shear velocity for turbulent flow in pipes

Formula
"V"_{"*"} = sqrt("𝜏"/"ρ"_{"Fluid"})

Example
"6.388766m/s"=sqrt("50Pa"/"1.225kg/m³")

Calculator
LaTeX
Shear Velocity = sqrt(Shear Stress/Density of Fluid)
Boundary layer thickness of laminar sublayer

## Boundary layer thickness of laminar sublayer

Formula
"δ" = (11.6*"ν")/("V"_{"*"})

Example
"0.001402m"=(11.6*"7.25St")/("6m/s")

Calculator
LaTeX
Boundary layer thickness = (11.6*Kinematic viscosity)/(Shear Velocity)
Shear stress due to viscosity

## Shear stress due to viscosity

Formula
"𝜏" = ("μ"_{"viscosity"}*"dv")

Example
"20.4Pa"=("10.2P"*"20m/s")

Calculator
LaTeX
Shear Stress = (Dynamic Viscosity*Change in Velocity)
Shear stress developed for turbulent flow in pipes

## Shear stress developed for turbulent flow in pipes

Formula
"𝜏" = ("V"_{"*"}^2)*"ρ"_{"Fluid"}

Example
"44.1Pa"=("6m/s"^2)*"1.225kg/m³"

Calculator
LaTeX
Shear Stress = (Shear Velocity^2)*Density of Fluid

## Shear stress in turbulent flow Formula

Shear Stress = (Friction factor*Density of Fluid*Velocity^2)/2
𝜏 = (f*ρFluid*v^2)/2

## What happens to the wall shear stress in turbulent flow?

In turbulent flow, inertia forces are significant as compared to viscous forces. Hence in the turbulent pipe flow shear stress varies linearly with the radius.

## How is shear stress developed in laminar and turbulent fluid flow?

The shear stress in laminar flow is a direct result of momentum transfer among the randomly moving molecules (a microscopic phenomenon). The shear stress in turbulent flow is largely a result of momentum transfer among the randomly moving, finite-sized fluid particles (a macroscopic phenomenon).

## How to Calculate Shear stress in turbulent flow?

Shear stress in turbulent flow calculator uses Shear Stress = (Friction factor*Density of Fluid*Velocity^2)/2 to calculate the Shear Stress, The Shear stress in turbulent flow formula is defined as the maximum at the center and decreases linearly towards the wall in it. Shear Stress is denoted by 𝜏 symbol.

How to calculate Shear stress in turbulent flow using this online calculator? To use this online calculator for Shear stress in turbulent flow, enter Friction factor (f), Density of Fluid Fluid) & Velocity (v) and hit the calculate button. Here is how the Shear stress in turbulent flow calculation can be explained with given input values -> 1323 = (0.6*1.225*60^2)/2.

### FAQ

What is Shear stress in turbulent flow?
The Shear stress in turbulent flow formula is defined as the maximum at the center and decreases linearly towards the wall in it and is represented as 𝜏 = (f*ρFluid*v^2)/2 or Shear Stress = (Friction factor*Density of Fluid*Velocity^2)/2. The Friction factor or Moody chart is the plot of the relative roughness (e/D) of a pipe against Reynold's number, Density of Fluid is defined as the mass of fluid per unit volume of the said fluid & Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.
How to calculate Shear stress in turbulent flow?
The Shear stress in turbulent flow formula is defined as the maximum at the center and decreases linearly towards the wall in it is calculated using Shear Stress = (Friction factor*Density of Fluid*Velocity^2)/2. To calculate Shear stress in turbulent flow, you need Friction factor (f), Density of Fluid Fluid) & Velocity (v). With our tool, you need to enter the respective value for Friction factor, Density of Fluid & 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 Shear Stress?
In this formula, Shear Stress uses Friction factor, Density of Fluid & Velocity. We can use 2 other way(s) to calculate the same, which is/are as follows -
• Shear Stress = (Shear Velocity^2)*Density of Fluid
• Shear Stress = (Dynamic Viscosity*Change in Velocity)
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