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%
✖Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.ⓘ Height [h]			+10% -10%
✖Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T.ⓘ Mean Velocity [V_mean]			+10% -10%
✖Discharge in pipe is the rate of flow of a liquid.ⓘ Discharge in pipe [Q]			+10% -10%

✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradient [dp|dr]

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Formula

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Pressure Gradient

Formula

`"dp|dr" = (12*"μ"_{"viscosity"}/("h"^3))*(0.5*"V"_{"mean"}*"h"-"Q")`

Example

`"16.61658N/m³"=(12*"10.2P"/(("1.81m")^3))*(0.5*"10m/s"*"1.81m"-"1.000001m³/s")`

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Pressure Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pressure Gradient = (12*Dynamic Viscosity/(Height^3))*(0.5*Mean Velocity*Height-Discharge in pipe)
dp|dr = (12*μ_viscosity/(h^3))*(0.5*V_mean*h-Q)
This formula uses 5 Variables

Variables Used

Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
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.
Height - (Measured in Meter) - Height is the distance between the lowest and highest points of a person/ shape/ object standing upright.
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.
Discharge in pipe - (Measured in Cubic Meter per Second) - Discharge in pipe is the rate of flow of a liquid.

STEP 1: Convert Input(s) to Base Unit

Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Height: 1.81 Meter --> 1.81 Meter No Conversion Required
Mean Velocity: 10 Meter per Second --> 10 Meter per Second No Conversion Required
Discharge in pipe: 1.000001 Cubic Meter per Second --> 1.000001 Cubic Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

dp|dr = (12*μ_viscosity/(h^3))*(0.5*V_mean*h-Q) --> (12*1.02/(1.81^3))*(0.5*10*1.81-1.000001)

Evaluating ... ...

dp|dr = 16.6165752871837

STEP 3: Convert Result to Output's Unit

16.6165752871837 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

16.6165752871837 ≈ 16.61658 Newton per Cubic Meter <-- Pressure Gradient

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Laminar Flow » Laminar Flow of Fluid in an Open Channel » Lubrication Mechanics - Slipper Bearing » Pressure Gradient

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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National Institute of Technology (NIT), Warangal

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Dynamic Viscosity given Pressure Gradient

Go Dynamic Viscosity = Pressure Gradient*(Height^3)/(12*(0.5*Mean Velocity*Height-Discharge in pipe))

Pressure Gradient

Go Pressure Gradient = (12*Dynamic Viscosity/(Height^3))*(0.5*Mean Velocity*Height-Discharge in pipe)

Rate of Flow given Pressure Gradient

Go Rate of Flow = 0.5*Mean Velocity*Height-(Pressure Gradient*(Height^3)/(12*Dynamic Viscosity))

Pressure Gradient Formula

Pressure Gradient = (12*Dynamic Viscosity/(Height^3))*(0.5*Mean Velocity*Height-Discharge in pipe)
dp|dr = (12*μ_viscosity/(h^3))*(0.5*V_mean*h-Q)

What is Pressure Gradient?

Pressure gradient is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pascals per metre.

How to Calculate Pressure Gradient?

Pressure Gradient calculator uses Pressure Gradient = (12*Dynamic Viscosity/(Height^3))*(0.5*Mean Velocity*Height-Discharge in pipe) to calculate the Pressure Gradient, The Pressure Gradient is defined as the rate at which pressure is changing with respect to change in distance along the pipe length. Pressure Gradient is denoted by dp|dr symbol.

How to calculate Pressure Gradient using this online calculator? To use this online calculator for Pressure Gradient, enter Dynamic Viscosity (μ_viscosity), Height (h), Mean Velocity (V_mean) & Discharge in pipe (Q) and hit the calculate button. Here is how the Pressure Gradient calculation can be explained with given input values -> 16.61658 = (12*1.02/(1.81^3))*(0.5*10*1.81-1.000001).

FAQ

What is Pressure Gradient?

The Pressure Gradient is defined as the rate at which pressure is changing with respect to change in distance along the pipe length and is represented as dp|dr = (12*μ_viscosity/(h^3))*(0.5*V_mean*h-Q) or Pressure Gradient = (12*Dynamic Viscosity/(Height^3))*(0.5*Mean Velocity*Height-Discharge in pipe). The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Height is the distance between the lowest and highest points of a person/ shape/ object standing upright, Mean velocity is defined as the average velocity of a fluid at a point and over an arbitrary time T & Discharge in pipe is the rate of flow of a liquid.

How to calculate Pressure Gradient?

The Pressure Gradient is defined as the rate at which pressure is changing with respect to change in distance along the pipe length is calculated using Pressure Gradient = (12*Dynamic Viscosity/(Height^3))*(0.5*Mean Velocity*Height-Discharge in pipe). To calculate Pressure Gradient, you need Dynamic Viscosity (μ_viscosity), Height (h), Mean Velocity (V_mean) & Discharge in pipe (Q). With our tool, you need to enter the respective value for Dynamic Viscosity, Height, Mean Velocity & Discharge in pipe 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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