Discharge through Pipe given Pressure Gradient Calculator

✖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%
✖The Pipe Radius is the radius of the pipe through which the fluid is flowing.ⓘ Pipe Radius [R]			+10% -10%
✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradient [dp\|dr]			+10% -10%

✖Discharge in pipe is the rate of flow of a liquid.ⓘ Discharge through Pipe given Pressure Gradient [Q]

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Discharge through Pipe given Pressure Gradient

Formula

`"Q" = (pi/(8*"μ"_{"viscosity"}))*("R"^4)*"dp|dr"`

Example

`"0.002374m³/s"=(pi/(8*"10.2P"))*(("138mm")^4)*"17N/m³"`

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Discharge through Pipe given Pressure Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Discharge in pipe = (pi/(8*Dynamic Viscosity))*(Pipe Radius^4)*Pressure Gradient
Q = (pi/(8*μ_viscosity))*(R^4)*dp|dr
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Discharge in pipe - (Measured in Cubic Meter per Second) - Discharge in pipe is the rate of flow of a liquid.
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.
Pipe Radius - (Measured in Meter) - The Pipe Radius is the radius of the pipe through which the fluid is flowing.
Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.

STEP 1: Convert Input(s) to Base Unit

Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Pipe Radius: 138 Millimeter --> 0.138 Meter (Check conversion here)
Pressure Gradient: 17 Newton per Cubic Meter --> 17 Newton per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = (pi/(8*μ_viscosity))*(R^4)*dp|dr --> (pi/(8*1.02))*(0.138^4)*17

Evaluating ... ...

Q = 0.0023736953603877

STEP 3: Convert Result to Output's Unit

0.0023736953603877 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

0.0023736953603877 ≈ 0.002374 Cubic Meter per Second <-- Discharge in pipe

(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 » Discharge through Pipe given Pressure Gradient

Credits

Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Calculator and 1300+ more calculators!

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 12 Steady Laminar Flow in Circular Pipes – Hagen Poiseuille Law Calculators

Distance of Element from Center Line given Velocity at any point in Cylindrical Element

Go Radial Distance = sqrt((Pipe Radius^2)-(-4*Dynamic Viscosity*Fluid Velocity in Pipe/Pressure Gradient))

Velocity at any point in Cylindrical Element

Go Fluid Velocity in Pipe = -(1/(4*Dynamic Viscosity))*Pressure Gradient*((Pipe Radius^2)-(Radial Distance^2))

Shear Stress at any Cylindrical Element given Head Loss

Go Shear Stress = (Specific Weight of Liquid*Head Loss due to Friction*Radial Distance)/(2*Length of Pipe)

Distance of Element from Center Line given Head Loss

Go Radial Distance = 2*Shear Stress*Length of Pipe/(Head Loss due to Friction*Specific Weight of Liquid)

Discharge through Pipe given Pressure Gradient

Go Discharge in pipe = (pi/(8*Dynamic Viscosity))*(Pipe Radius^4)*Pressure Gradient

Velocity Gradient given Pressure Gradient at Cylindrical Element

Go Velocity Gradient = (1/(2*Dynamic Viscosity))*Pressure Gradient*Radial Distance

Distance of Element from Center Line given Velocity Gradient at Cylindrical Element

Go Radial Distance = 2*Dynamic Viscosity*Velocity Gradient/Pressure Gradient

Mean Velocity of Fluid Flow

Go Mean Velocity = (1/(8*Dynamic Viscosity))*Pressure Gradient*Pipe Radius^2

Distance of Element from Center line given Shear Stress at any Cylindrical Element

Go Radial Distance = 2*Shear Stress/Pressure Gradient

Shear Stress at any Cylindrical Element

Go Shear Stress = Pressure Gradient*Radial Distance/2

Mean Velocity of Flow given Maximum Velocity at Axis of Cylindrical Element

Go Mean Velocity = 0.5*Maximum Velocity

Maximum Velocity at Axis of Cylindrical Element given Mean Velocity of Flow

Go Maximum Velocity = 2*Mean Velocity

Discharge through Pipe given Pressure Gradient Formula

Discharge in pipe = (pi/(8*Dynamic Viscosity))*(Pipe Radius^4)*Pressure Gradient
Q = (pi/(8*μ_viscosity))*(R^4)*dp|dr

What is Rate of Flow ?

Rate of flow may refer to: Mass flow rate, the movement of mass per time. Volumetric flow rate, the volume of a fluid which passes through a given surface per unit of time. Heat flow rate, the movement of heat per time.

How to Calculate Discharge through Pipe given Pressure Gradient?

Discharge through Pipe given Pressure Gradient calculator uses Discharge in pipe = (pi/(8*Dynamic Viscosity))*(Pipe Radius^4)*Pressure Gradient to calculate the Discharge in pipe, The Discharge through Pipe given pressure gradient is defined as the total volume of fluid coming in and going through the pipe at a section. Discharge in pipe is denoted by Q symbol.

How to calculate Discharge through Pipe given Pressure Gradient using this online calculator? To use this online calculator for Discharge through Pipe given Pressure Gradient, enter Dynamic Viscosity (μ_viscosity), Pipe Radius (R) & Pressure Gradient (dp|dr) and hit the calculate button. Here is how the Discharge through Pipe given Pressure Gradient calculation can be explained with given input values -> 0.010472 = (pi/(8*1.02))*(0.138^4)*17.

FAQ

What is Discharge through Pipe given Pressure Gradient?

The Discharge through Pipe given pressure gradient is defined as the total volume of fluid coming in and going through the pipe at a section and is represented as Q = (pi/(8*μ_viscosity))*(R^4)*dp|dr or Discharge in pipe = (pi/(8*Dynamic Viscosity))*(Pipe Radius^4)*Pressure Gradient. The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, The Pipe Radius is the radius of the pipe through which the fluid is flowing & Pressure Gradient is the change in pressure with respect to radial distance of element.

How to calculate Discharge through Pipe given Pressure Gradient?

The Discharge through Pipe given pressure gradient is defined as the total volume of fluid coming in and going through the pipe at a section is calculated using Discharge in pipe = (pi/(8*Dynamic Viscosity))*(Pipe Radius^4)*Pressure Gradient. To calculate Discharge through Pipe given Pressure Gradient, you need Dynamic Viscosity (μ_viscosity), Pipe Radius (R) & Pressure Gradient (dp|dr). With our tool, you need to enter the respective value for Dynamic Viscosity, Pipe Radius & Pressure Gradient 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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