Dynamic Viscosity given Pressure Gradient Calculator

✖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]			+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%
✖The 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 Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.ⓘ Dynamic Viscosity given Pressure Gradient [μ]

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Dynamic Viscosity given Pressure Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity refers to the internal resistance of a fluid to flow when a force is applied.
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.
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) - The 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

Pressure Gradient: 17 Newton per Cubic Meter --> 17 Newton per Cubic Meter No Conversion Required
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

μ = dp|dr*(h^3)/(12*(0.5*V_mean*h-Q)) --> 17*(1.81^3)/(12*(0.5*10*1.81-1.000001))

Evaluating ... ...

μ = 1.04353633046

STEP 3: Convert Result to Output's Unit

1.04353633046 Pascal Second -->10.4353633046 Poise (Check conversion here)

FINAL ANSWER

10.4353633046 ≈ 10.43536 Poise <-- Dynamic Viscosity

(Calculation completed in 00.020 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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Dynamic Viscosity given Pressure Gradient

LaTeX 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

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

Pressure Gradient

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

Dynamic Viscosity given Pressure Gradient Formula

LaTeX Go

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

Dynamic Viscosity given Pressure Gradient calculator uses Dynamic Viscosity = Pressure Gradient*(Height of Channel^3)/(12*(0.5*Mean Velocity*Height of Channel-Discharge in Pipe)) to calculate the Dynamic Viscosity, The Dynamic Viscosity given Pressure Gradient formula is defined as the resistance offered by fluid in viscous medium which is directly proportional to the pressure gradient and the fourth power of the pipe radius, and inversely proportional to the flow rate and the pipe length. Dynamic Viscosity is denoted by μ symbol.

How to calculate Dynamic Viscosity given Pressure Gradient using this online calculator? To use this online calculator for Dynamic Viscosity given Pressure Gradient, enter Pressure Gradient (dp|dr), Height of Channel (h), Mean Velocity (V_mean) & Discharge in Pipe (Q) and hit the calculate button. Here is how the Dynamic Viscosity given Pressure Gradient calculation can be explained with given input values -> 104.3536 = 17*(1.81^3)/(12*(0.5*10*1.81-1.000001)).

FAQ

What is Dynamic Viscosity given Pressure Gradient?

The Dynamic Viscosity given Pressure Gradient formula is defined as the resistance offered by fluid in viscous medium which is directly proportional to the pressure gradient and the fourth power of the pipe radius, and inversely proportional to the flow rate and the pipe length and is represented as μ = dp|dr*(h^3)/(12*(0.5*V_mean*h-Q)) or Dynamic Viscosity = Pressure Gradient*(Height of Channel^3)/(12*(0.5*Mean Velocity*Height of Channel-Discharge in Pipe)). 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, 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 & The Discharge in Pipe refers to the volume of fluid (such as water) that passes through the pipe per unit of time.

How to calculate Dynamic Viscosity given Pressure Gradient?

The Dynamic Viscosity given Pressure Gradient formula is defined as the resistance offered by fluid in viscous medium which is directly proportional to the pressure gradient and the fourth power of the pipe radius, and inversely proportional to the flow rate and the pipe length is calculated using Dynamic Viscosity = Pressure Gradient*(Height of Channel^3)/(12*(0.5*Mean Velocity*Height of Channel-Discharge in Pipe)). To calculate Dynamic Viscosity given Pressure Gradient, you need Pressure Gradient (dp|dr), Height of Channel (h), Mean Velocity (V_mean) & Discharge in Pipe (Q). With our tool, you need to enter the respective value for Pressure Gradient, 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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