Piezometric Gradient given Shear Stress Calculator

✖Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress [𝜏]			+10% -10%
✖Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.ⓘ Specific Weight of Liquid [γ_f]			+10% -10%
✖Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.ⓘ Radial Distance [d_radial]			+10% -10%

✖Piezometric Gradient is defined as variation of piezometric head with respect to distance in along the pipe length.ⓘ Piezometric Gradient given Shear Stress [dhbydx]

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Formula

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Piezometric Gradient given Shear Stress

Formula

`"dhbydx" = (2*"𝜏")/("γ"_{"f"}*"d"_{"radial"})`

Example

`"0.002063"=(2*"93.1Pa")/("9.81kN/m³"*"9.2m")`

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Piezometric Gradient given Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Piezometric Gradient = (2*Shear Stress)/(Specific Weight of Liquid*Radial Distance)
dhbydx = (2*𝜏)/(γ_f*d_radial)
This formula uses 4 Variables

Variables Used

Piezometric Gradient - Piezometric Gradient is defined as variation of piezometric head with respect to distance in along the pipe length.
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.
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.
Radial Distance - (Measured in Meter) - Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.

STEP 1: Convert Input(s) to Base Unit

Shear Stress: 93.1 Pascal --> 93.1 Pascal No Conversion Required
Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (Check conversion here)
Radial Distance: 9.2 Meter --> 9.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

dhbydx = (2*𝜏)/(γ_f*d_radial) --> (2*93.1)/(9810*9.2)

Evaluating ... ...

dhbydx = 0.00206311217479945

STEP 3: Convert Result to Output's Unit

0.00206311217479945 --> No Conversion Required

FINAL ANSWER

0.00206311217479945 ≈ 0.002063 <-- Piezometric Gradient

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Laminar Flow » Steady Laminar Flow in Circular Pipes – Hagen Poiseuille Law » Laminar Flow Through Inclined Pipes » Piezometric Gradient given Shear Stress

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< 15 Laminar Flow Through Inclined Pipes Calculators

Radius of Elemental Section of Pipe given Flow Velocity of Stream

Go Radial Distance = sqrt((Inclined Pipes Radius^2)+Velocity of Liquid/((Specific Weight of Liquid/(4*Dynamic Viscosity))*Piezometric Gradient))

Radius of Pipe for Flow Velocity of Stream

Go Inclined Pipes Radius = sqrt((Radial Distance^2)-((Velocity of Liquid*4*Dynamic Viscosity)/(Specific Weight of Liquid*Piezometric Gradient)))

Specific Weight of Liquid given Flow Velocity of Stream

Go Specific Weight of Liquid = Velocity of Liquid/((1/(4*Dynamic Viscosity))*Piezometric Gradient*(Inclined Pipes Radius^2-Radial Distance^2))

Piezometric Gradient given Flow Velocity of Stream

Go Piezometric Gradient = Velocity of Liquid/(((Specific Weight of Liquid)/(4*Dynamic Viscosity))*(Inclined Pipes Radius^2-Radial Distance^2))

Dynamic Viscosity given Flow Velocity of Stream

Go Dynamic Viscosity = (Specific Weight of Liquid/((4*Velocity of Liquid))*Piezometric Gradient*(Inclined Pipes Radius^2-Radial Distance^2))

Flow Velocity of Stream

Go Velocity of Liquid = (Specific Weight of Liquid/(4*Dynamic Viscosity))*Piezometric Gradient*(Inclined Pipes Radius^2-Radial Distance^2)

Piezometric Gradient given Velocity Gradient with Shear Stress

Go Piezometric Gradient = Velocity Gradient/((Specific Weight of Liquid/Dynamic Viscosity)*(0.5*Radial Distance))

Radius of Elemental Section of Pipe given Velocity Gradient with Shear Stress

Go Radial Distance = (2*Velocity Gradient*Dynamic Viscosity)/(Piezometric Gradient*Specific Weight of Liquid)

Specific Weight of Liquid given Velocity Gradient with Shear Stress

Go Specific Weight of Liquid = (2*Velocity Gradient*Dynamic Viscosity)/(Piezometric Gradient*Radial Distance)

Velocity Gradient given Piezometric Gradient with Shear Stress

Go Velocity Gradient = (Specific Weight of Liquid/Dynamic Viscosity)*Piezometric Gradient*0.5*Radial Distance

Dynamic Viscosity given Velocity Gradient with Shear Stress

Go Dynamic Viscosity = (Specific Weight of Liquid/Velocity Gradient)*Piezometric Gradient*0.5*Radial Distance

Radius of Elemental Section of Pipe given Shear Stress

Go Radial Distance = (2*Shear Stress)/(Specific Weight of Liquid*Piezometric Gradient)

Specific Weight of Fluid given Shear Stress

Go Specific Weight of Liquid = (2*Shear Stress)/(Radial Distance*Piezometric Gradient)

Piezometric Gradient given Shear Stress

Go Piezometric Gradient = (2*Shear Stress)/(Specific Weight of Liquid*Radial Distance)

Shear Stresses

Go Shear Stress = Specific Weight of Liquid*Piezometric Gradient*Radial Distance/2

Piezometric Gradient given Shear Stress Formula

Piezometric Gradient = (2*Shear Stress)/(Specific Weight of Liquid*Radial Distance)
dhbydx = (2*𝜏)/(γ_f*d_radial)

What is Piezometric Gradient ?

Hydraulic head or piezometric head is a specific measurement of liquid pressure above a vertical datum. The hydraulic head can be used to determine a hydraulic gradient between two or more points.

How to Calculate Piezometric Gradient given Shear Stress?

Piezometric Gradient given Shear Stress calculator uses Piezometric Gradient = (2*Shear Stress)/(Specific Weight of Liquid*Radial Distance) to calculate the Piezometric Gradient, The Piezometric Gradient given Shear Stress is defined as change in hydraulic head with respect pipe length distance. Piezometric Gradient is denoted by dhbydx symbol.

How to calculate Piezometric Gradient given Shear Stress using this online calculator? To use this online calculator for Piezometric Gradient given Shear Stress, enter Shear Stress (𝜏), Specific Weight of Liquid (γ_f) & Radial Distance (d_radial) and hit the calculate button. Here is how the Piezometric Gradient given Shear Stress calculation can be explained with given input values -> 0.002063 = (2*93.1)/(9810*9.2).

FAQ

What is Piezometric Gradient given Shear Stress?

The Piezometric Gradient given Shear Stress is defined as change in hydraulic head with respect pipe length distance and is represented as dhbydx = (2*𝜏)/(γ_f*d_radial) or Piezometric Gradient = (2*Shear Stress)/(Specific Weight of Liquid*Radial Distance). Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress, Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid & Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.

How to calculate Piezometric Gradient given Shear Stress?

The Piezometric Gradient given Shear Stress is defined as change in hydraulic head with respect pipe length distance is calculated using Piezometric Gradient = (2*Shear Stress)/(Specific Weight of Liquid*Radial Distance). To calculate Piezometric Gradient given Shear Stress, you need Shear Stress (𝜏), Specific Weight of Liquid (γ_f) & Radial Distance (d_radial). With our tool, you need to enter the respective value for Shear Stress, Specific Weight of Liquid & Radial 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 Piezometric Gradient?

In this formula, Piezometric Gradient uses Shear Stress, Specific Weight of Liquid & Radial Distance. We can use 2 other way(s) to calculate the same, which is/are as follows -

Piezometric Gradient = Velocity Gradient/((Specific Weight of Liquid/Dynamic Viscosity)*(0.5*Radial Distance))
Piezometric Gradient = Velocity of Liquid/(((Specific Weight of Liquid)/(4*Dynamic Viscosity))*(Inclined Pipes Radius^2-Radial Distance^2))

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