Dynamic Viscosity given Rate of Flow Calculator

✖Pressure Gradient is the change in pressure with respect to radial distance of element.ⓘ Pressure Gradient [dp\|dr]			+10% -10%
✖Radial Clearance or gap is the distance between two surfaces adjacent to each other.ⓘ Radial Clearance [C_R]			+10% -10%
✖Discharge in Laminar Flow is the fluid flowing per second through a channel or section of a pipe.ⓘ Discharge in Laminar Flow [Q]			+10% -10%
✖Diameter of Piston is the actual diameter of the piston while the bore is the size of the cylinder and will always be larger than the piston.ⓘ Diameter of Piston [D]			+10% -10%
✖Velocity of piston in reciprocating pump is defined as the product of sin of angular velocity and time, radius of crank and angular velocity.ⓘ Velocity of Piston [v_piston]			+10% -10%

✖The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.ⓘ Dynamic Viscosity given Rate of Flow [μ_viscosity]

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Formula

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Dynamic Viscosity given Rate of Flow

Formula

`"μ"_{"viscosity"} = ("dp|dr"*("C"_{"R"}^3)/12)/(("Q"/pi*"D")+"v"_{"piston"}*0.5*"C"_{"R"})`

Example

`"0.074346P"=("60N/m³"*(("0.45m")^3)/12)/(("55m³/s"/pi*"3.5m")+"0.045m/s"*0.5*"0.45m")`

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Dynamic Viscosity given Rate of Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Dynamic Viscosity = (Pressure Gradient*(Radial Clearance^3)/12)/((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance)
μ_viscosity = (dp|dr*(C_R^3)/12)/((Q/pi*D)+v_piston*0.5*C_R)
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
Pressure Gradient - (Measured in Newton per Cubic Meter) - Pressure Gradient is the change in pressure with respect to radial distance of element.
Radial Clearance - (Measured in Meter) - Radial Clearance or gap is the distance between two surfaces adjacent to each other.
Discharge in Laminar Flow - (Measured in Cubic Meter per Second) - Discharge in Laminar Flow is the fluid flowing per second through a channel or section of a pipe.
Diameter of Piston - (Measured in Meter) - Diameter of Piston is the actual diameter of the piston while the bore is the size of the cylinder and will always be larger than the piston.
Velocity of Piston - (Measured in Meter per Second) - Velocity of piston in reciprocating pump is defined as the product of sin of angular velocity and time, radius of crank and angular velocity.

STEP 1: Convert Input(s) to Base Unit

Pressure Gradient: 60 Newton per Cubic Meter --> 60 Newton per Cubic Meter No Conversion Required
Radial Clearance: 0.45 Meter --> 0.45 Meter No Conversion Required
Discharge in Laminar Flow: 55 Cubic Meter per Second --> 55 Cubic Meter per Second No Conversion Required
Diameter of Piston: 3.5 Meter --> 3.5 Meter No Conversion Required
Velocity of Piston: 0.045 Meter per Second --> 0.045 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

μ_viscosity = (dp|dr*(C_R^3)/12)/((Q/pi*D)+v_piston*0.5*C_R) --> (60*(0.45^3)/12)/((55/pi*3.5)+0.045*0.5*0.45)

Evaluating ... ...

μ_viscosity = 0.00743455412905416

STEP 3: Convert Result to Output's Unit

0.00743455412905416 Pascal Second -->0.0743455412905416 Poise (Check conversion here)

FINAL ANSWER

0.0743455412905416 ≈ 0.074346 Poise <-- Dynamic Viscosity

(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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< 4 Dynamic Viscosity Calculators

Dynamic Viscosity given Velocity of Flow in Oil Tank

Go Dynamic Viscosity = 0.5*Pressure Gradient*(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance)/(Fluid Velocity in Oil Tank+(Velocity of Piston*Horizontal Distance/Hydraulic Clearance))

Dynamic Viscosity for Shear Force Resisting Motion of Piston

Go Dynamic Viscosity = Shear Force/(pi*Piston Length*Velocity of Piston*(1.5*(Diameter of Piston/Radial Clearance)^2+4*(Diameter of Piston/Radial Clearance)))

Dynamic Viscosity given Rate of Flow

Go Dynamic Viscosity = (Pressure Gradient*(Radial Clearance^3)/12)/((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance)

Dynamic Viscosity for Pressure Reduction over Length of Piston

Go Dynamic Viscosity = Pressure Drop due to Friction/((6*Velocity of Piston*Piston Length/(Radial Clearance^3))*(0.5*Diameter of Piston+Radial Clearance))

Dynamic Viscosity given Rate of Flow Formula

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 Rate of Flow?

Dynamic Viscosity given Rate of Flow calculator uses Dynamic Viscosity = (Pressure Gradient*(Radial Clearance^3)/12)/((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance) to calculate the Dynamic Viscosity, The Dynamic Viscosity given Rate of Flow is defined as the resistance offered by the fluid in viscous medium due to resistive forces. Dynamic Viscosity is denoted by μ_viscosity symbol.

How to calculate Dynamic Viscosity given Rate of Flow using this online calculator? To use this online calculator for Dynamic Viscosity given Rate of Flow, enter Pressure Gradient (dp|dr), Radial Clearance (C_R), Discharge in Laminar Flow (Q), Diameter of Piston (D) & Velocity of Piston (v_piston) and hit the calculate button. Here is how the Dynamic Viscosity given Rate of Flow calculation can be explained with given input values -> 113.8907 = (60*(0.45^3)/12)/((55/pi*3.5)+0.045*0.5*0.45).

FAQ

What is Dynamic Viscosity given Rate of Flow?

The Dynamic Viscosity given Rate of Flow is defined as the resistance offered by the fluid in viscous medium due to resistive forces and is represented as μ_viscosity = (dp|dr*(C_R^3)/12)/((Q/pi*D)+v_piston*0.5*C_R) or Dynamic Viscosity = (Pressure Gradient*(Radial Clearance^3)/12)/((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance). Pressure Gradient is the change in pressure with respect to radial distance of element, Radial Clearance or gap is the distance between two surfaces adjacent to each other, Discharge in Laminar Flow is the fluid flowing per second through a channel or section of a pipe, Diameter of Piston is the actual diameter of the piston while the bore is the size of the cylinder and will always be larger than the piston & Velocity of piston in reciprocating pump is defined as the product of sin of angular velocity and time, radius of crank and angular velocity.

How to calculate Dynamic Viscosity given Rate of Flow?

The Dynamic Viscosity given Rate of Flow is defined as the resistance offered by the fluid in viscous medium due to resistive forces is calculated using Dynamic Viscosity = (Pressure Gradient*(Radial Clearance^3)/12)/((Discharge in Laminar Flow/pi*Diameter of Piston)+Velocity of Piston*0.5*Radial Clearance). To calculate Dynamic Viscosity given Rate of Flow, you need Pressure Gradient (dp|dr), Radial Clearance (C_R), Discharge in Laminar Flow (Q), Diameter of Piston (D) & Velocity of Piston (v_piston). With our tool, you need to enter the respective value for Pressure Gradient, Radial Clearance, Discharge in Laminar Flow, Diameter of Piston & Velocity of Piston 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 Dynamic Viscosity?

In this formula, Dynamic Viscosity uses Pressure Gradient, Radial Clearance, Discharge in Laminar Flow, Diameter of Piston & Velocity of Piston. We can use 3 other way(s) to calculate the same, which is/are as follows -

Dynamic Viscosity = 0.5*Pressure Gradient*(Horizontal Distance*Horizontal Distance-Hydraulic Clearance*Horizontal Distance)/(Fluid Velocity in Oil Tank+(Velocity of Piston*Horizontal Distance/Hydraulic Clearance))
Dynamic Viscosity = Pressure Drop due to Friction/((6*Velocity of Piston*Piston Length/(Radial Clearance^3))*(0.5*Diameter of Piston+Radial Clearance))
Dynamic Viscosity = Shear Force/(pi*Piston Length*Velocity of Piston*(1.5*(Diameter of Piston/Radial Clearance)^2+4*(Diameter of Piston/Radial Clearance)))

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