Pressure Gradient Calculator

✖The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.ⓘ Dynamic Viscosity [μ]			+10% -10%
✖The Height of Channel refers to the flow depth or water level within the channel. Height refers to the flow depth or water level within the channel.ⓘ Height of Channel [h]			+10% -10%
✖The Mean Velocity refers to the average rate at which an object or fluid moves over a given time interval.ⓘ Mean Velocity [V_mean]			+10% -10%
✖Discharge in Pipe refers to the volume of fluid (such as water) that passes through the pipe per unit of time.ⓘ Discharge in Pipe [Q]			+10% -10%

✖The Pressure Gradient refers to the rate of change of pressure in a particular direction indicating how quickly the pressure increases or decreases around a specific location.ⓘ Pressure Gradient [dp|dr]

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Formula

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Pressure Gradient

Formula

dp|dr = (12 \cdot \frac{μ}{h^{3}}) \cdot (0.5 \cdot V mean \cdot h - Q)

Example

16.61658 N/m³ = (12 \cdot \frac{10.2 P}{{1.81 m}^{3}}) \cdot (0.5 \cdot 10 m/s \cdot 1.81 m - 1.000001 m³/s)

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Download Laminar Flow of Fluid in an Open Channel Formulas PDF PDF Image

Pressure Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Pressure Gradient - (Measured in Newton per Cubic Meter) - The Pressure Gradient refers to the rate of change of pressure in a particular direction indicating how quickly the pressure increases or decreases around a specific location.
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.
Height of Channel - (Measured in Meter) - The Height of Channel refers to the flow depth or water level within the channel. Height refers to the flow depth or water level within the channel.
Mean Velocity - (Measured in Meter per Second) - The Mean Velocity refers to the average rate at which an object or fluid moves over a given time interval.
Discharge in Pipe - (Measured in Cubic Meter per Second) - Discharge in Pipe refers to the volume of fluid (such as water) that passes through the pipe per unit of time.

STEP 1: Convert Input(s) to Base Unit

Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Height of Channel: 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/(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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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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< Lubrication Mechanics Slipper Bearing Calculators

Dynamic Viscosity given Pressure Gradient

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

Rate of Flow given Pressure Gradient

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

Pressure Gradient

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

Pressure Gradient Formula

Pressure Gradient = (12*Dynamic Viscosity/(Height of Channel^3))*(0.5*Mean Velocity*Height of Channel-Discharge in Pipe)
dp|dr = (12*μ/(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.

What is Dynamic Viscosity?

The dynamic viscosity η (η = "eta") is a measure of the viscosity of a fluid (fluid: liquid, flowing substance). The higher the viscosity, the thicker (less liquid) the fluid; the lower the viscosity, the thinner (more liquid) it is.

How to Calculate Pressure Gradient?

Pressure Gradient calculator uses Pressure Gradient = (12*Dynamic Viscosity/(Height of Channel^3))*(0.5*Mean Velocity*Height of Channel-Discharge in Pipe) to calculate the Pressure Gradient, The Pressure Gradient formula 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), Height of Channel (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 formula 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/(h^3))*(0.5*V_mean*h-Q) or Pressure Gradient = (12*Dynamic Viscosity/(Height of Channel^3))*(0.5*Mean Velocity*Height of Channel-Discharge in Pipe). The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied, The Height of Channel refers to the flow depth or water level within the channel. Height refers to the flow depth or water level within the channel, The Mean Velocity refers to the average rate at which an object or fluid moves over a given time interval & Discharge in Pipe refers to the volume of fluid (such as water) that passes through the pipe per unit of time.

How to calculate Pressure Gradient?

The Pressure Gradient formula 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 of Channel^3))*(0.5*Mean Velocity*Height of Channel-Discharge in Pipe). To calculate Pressure Gradient, you need Dynamic Viscosity (μ), Height of Channel (h), Mean Velocity (V_mean) & Discharge in Pipe (Q). With our tool, you need to enter the respective value for Dynamic Viscosity, Height of Channel, 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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