Piezometric Gradient given Velocity Gradient with Shear Stress Calculator

✖Velocity Gradient is the difference in velocity between the adjacent layers of the fluid.ⓘ Velocity Gradient [VG]			+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%
✖The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.ⓘ Dynamic Viscosity [μ_viscosity]			+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 Velocity Gradient with Shear Stress [dhbydx]

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Formula

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Piezometric Gradient given Velocity Gradient with Shear Stress

Formula

`"dhbydx" = "VG"/(("γ"_{"f"}/"μ"_{"viscosity"})*(0.5*"d"_{"radial"}))`

Example

`"0.001731"="76.6m/s"/(("9.81kN/m³"/"10.2P")*(0.5*"9.2m"))`

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Piezometric Gradient given Velocity Gradient with Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Piezometric Gradient = Velocity Gradient/((Specific Weight of Liquid/Dynamic Viscosity)*(0.5*Radial Distance))
dhbydx = VG/((γ_f/μ_viscosity)*(0.5*d_radial))
This formula uses 5 Variables

Variables Used

Piezometric Gradient - Piezometric Gradient is defined as variation of piezometric head with respect to distance in along the pipe length.
Velocity Gradient - (Measured in Meter per Second) - Velocity Gradient is the difference in velocity between the adjacent layers of the fluid.
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.
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.
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

Velocity Gradient: 76.6 Meter per Second --> 76.6 Meter per Second No Conversion Required
Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (Check conversion here)
Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Radial Distance: 9.2 Meter --> 9.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

dhbydx = VG/((γ_f/μ_viscosity)*(0.5*d_radial)) --> 76.6/((9810/1.02)*(0.5*9.2))

Evaluating ... ...

dhbydx = 0.00173141869432256

STEP 3: Convert Result to Output's Unit

0.00173141869432256 --> No Conversion Required

FINAL ANSWER

0.00173141869432256 ≈ 0.001731 <-- Piezometric Gradient

(Calculation completed in 00.020 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 Velocity Gradient with 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 Velocity Gradient with Shear Stress Formula

Piezometric Gradient = Velocity Gradient/((Specific Weight of Liquid/Dynamic Viscosity)*(0.5*Radial Distance))
dhbydx = VG/((γ_f/μ_viscosity)*(0.5*d_radial))

What is Velocity Gradient ?

The difference in velocity between adjacent layers of the fluid is known as a velocity gradient and is given by v/x, where v is the velocity difference and x is the distance between the layers.

How to Calculate Piezometric Gradient given Velocity Gradient with Shear Stress?

Piezometric Gradient given Velocity Gradient with Shear Stress calculator uses Piezometric Gradient = Velocity Gradient/((Specific Weight of Liquid/Dynamic Viscosity)*(0.5*Radial Distance)) to calculate the Piezometric Gradient, The Piezometric Gradient given Velocity Gradient with Shear Stress formula is defined as change in pressure with respect to horizontal distance along pipe. Piezometric Gradient is denoted by dhbydx symbol.

How to calculate Piezometric Gradient given Velocity Gradient with Shear Stress using this online calculator? To use this online calculator for Piezometric Gradient given Velocity Gradient with Shear Stress, enter Velocity Gradient (VG), Specific Weight of Liquid (γ_f), Dynamic Viscosity (μ_viscosity) & Radial Distance (d_radial) and hit the calculate button. Here is how the Piezometric Gradient given Velocity Gradient with Shear Stress calculation can be explained with given input values -> 0.001731 = 76.6/((9810/1.02)*(0.5*9.2)).

FAQ

What is Piezometric Gradient given Velocity Gradient with Shear Stress?

The Piezometric Gradient given Velocity Gradient with Shear Stress formula is defined as change in pressure with respect to horizontal distance along pipe and is represented as dhbydx = VG/((γ_f/μ_viscosity)*(0.5*d_radial)) or Piezometric Gradient = Velocity Gradient/((Specific Weight of Liquid/Dynamic Viscosity)*(0.5*Radial Distance)). Velocity Gradient is the difference in velocity between the adjacent layers of the fluid, Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid, The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied & Radial distance is defined as distance between whisker sensor's pivot point to whisker-object contact point.

How to calculate Piezometric Gradient given Velocity Gradient with Shear Stress?

The Piezometric Gradient given Velocity Gradient with Shear Stress formula is defined as change in pressure with respect to horizontal distance along pipe is calculated using Piezometric Gradient = Velocity Gradient/((Specific Weight of Liquid/Dynamic Viscosity)*(0.5*Radial Distance)). To calculate Piezometric Gradient given Velocity Gradient with Shear Stress, you need Velocity Gradient (VG), Specific Weight of Liquid (γ_f), Dynamic Viscosity (μ_viscosity) & Radial Distance (d_radial). With our tool, you need to enter the respective value for Velocity Gradient, Specific Weight of Liquid, Dynamic Viscosity & 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 Velocity Gradient, Specific Weight of Liquid, Dynamic Viscosity & Radial Distance. We can use 2 other way(s) to calculate the same, which is/are as follows -

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