Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder Solution

STEP 0: Pre-Calculation Summary
Formula Used
Bingham Number = (Fluid Yield Stress/Plastic Viscosity)*((Diameter of Cylinder 1/(Acceleration due to Gravity*Coefficient Of Volumetric Expansion* Change in Temperature)))^(0.5)
Bn = (ζo/μB)*((D1/(g*β* ∆T)))^(0.5)
This formula uses 7 Variables
Variables Used
Bingham Number - Bingham Number, abbreviated as Bn, is a dimensionless quantity.
Fluid Yield Stress - (Measured in Pascal) - The Fluid yield stress is defined as the stress that must be applied to the sample before it starts to flow.
Plastic Viscosity - (Measured in Pascal Second) - Plastic Viscosity is a result of friction between the liquid undergoing deformation under shear stress and the solids and liquids present.
Diameter of Cylinder 1 - (Measured in Meter) - Diameter of Cylinder 1 is the diameter of the first cylinder.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Coefficient Of Volumetric Expansion - (Measured in Per Kelvin) - The coefficient Of Volumetric Expansion is the increase in volume per unit original volume per Kelvin rise in temperature.
Change in Temperature - (Measured in Kelvin) - The Change in Temperature is the difference between the initial and final temperature.
STEP 1: Convert Input(s) to Base Unit
Fluid Yield Stress: 10 Pascal --> 10 Pascal No Conversion Required
Plastic Viscosity: 10 Pascal Second --> 10 Pascal Second No Conversion Required
Diameter of Cylinder 1: 5 Meter --> 5 Meter No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Coefficient Of Volumetric Expansion: 3 Per Kelvin --> 3 Per Kelvin No Conversion Required
Change in Temperature: 50 Kelvin --> 50 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Bn = (ζoB)*((D1/(g*β* ∆T)))^(0.5) --> (10/10)*((5/(9.8*3* 50)))^(0.5)
Evaluating ... ...
Bn = 0.0583211843519804
STEP 3: Convert Result to Output's Unit
0.0583211843519804 --> No Conversion Required
FINAL ANSWER
0.0583211843519804 0.058321 <-- Bingham Number
(Calculation completed in 00.004 seconds)

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Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder
Go Bingham Number = (Fluid Yield Stress/Plastic Viscosity)*((Diameter of Cylinder 1/(Acceleration due to Gravity*Coefficient Of Volumetric Expansion* Change in Temperature)))^(0.5)
Outside surface temperature for annular space between concentric cylinders
Go Outside Temperature = Inside Temperature-(Heat Transfer per Unit Length*((ln(Outside Diameter/Inside Diameter))/(2*pi*Thermal Conductivity)))
Inside surface temperature for annular space between concentric cylinders
Go Inside Temperature = (Heat Transfer per Unit Length*((ln(Outside Diameter/Inside Diameter))/(2*pi*Thermal Conductivity)))+Outside Temperature
Outside diameter of concentric sphere
Go Outside Diameter = Heat transfer/((Thermal Conductivity*pi*(Inside Temperature-Outside Temperature))*((Inside Diameter)/Length))
Inside diameter of concentric sphere
Go Inside Diameter = Heat transfer/((Thermal Conductivity*pi*(Inside Temperature-Outside Temperature))*((Outside Diameter)/Length))
Length of space between two concentric sphere
Go Length = (Thermal Conductivity*pi*(Inside Temperature-Outside Temperature))*((Outside Diameter*Inside Diameter)/Heat transfer)
Inside temperature of concentric sphere
Go Inside Temperature = (Heat transfer/((Thermal Conductivity*pi*(Outer Diameter*Inner Diameter)/Length)))+Outside Temperature
Length of annular space between two concentric cylinders
Go Length = ((((ln(Outer Diameter/Inner Diameter))^4)*(Rayleigh number))/(((Inner Diameter^-0.6)+(Outer Diameter^-0.6))^5))^-3
Boundary layer thickness on vertical surfaces
Go Boundary Layer Thickens = 3.93*Distance from Point to YY Axis*(Prandtl Number^(-0.5))*((0.952+Prandtl Number)^0.25)*(Local Grashof Number^(-0.25))
Thermal conductivity of fluid
Go Thermal Conductivity = Thermal Conductivity/(0.386*(((Prandtl Number)/(0.861+Prandtl Number))^0.25)*(Rayleigh Number(t))^0.25)
Diameter of rotating cylinder in fluid given Reynolds number
Go Diameter = ((Reynolds Number(w)*Kinematic Viscosity)/(pi*Rotational speed))^(1/2)
Rotational speed given Reynolds number
Go Rotational speed = (Reynolds Number(w)*Kinematic Viscosity)/(pi*Diameter^2)
Kinematic viscosity given Reynolds number based on rotational speed
Go Kinematic Viscosity = Rotational speed*pi*(Diameter^2)/Reynolds Number(w)
Prandtl number given Graetz numbber
Go Prandtl Number = Graetz Number*Length/(Reynolds Number*Diameter)
Diameter given Graetz number
Go Diameter = Graetz Number*Length/(Reynolds Number*Prandtl Number)
Length given Graetz number
Go Length = Reynolds Number*Prandtl Number*(Diameter/Graetz Number)
Convective mass transfer coefficient at distance X from leading edge
Go Convective Mass Transfer Coefficient = (2*Thermal Conductivity)/Boundary Layer Thickens
Diameter at which turbulence starts
Go Diameter = (((5*10^5)*Kinematic Viscosity)/(Rotational speed))^1/2
Kinematic viscosity of fluid
Go Kinematic Viscosity = (Rotational speed*Diameter^2)/(5*10^5)
Rotational speed of disc
Go Rotational speed = (5*10^5)*Kinematic Viscosity/(Diameter^2)
Outside radius from gap length
Go Outer Radius = Gap length+Inside Radius
Inside radius from gap length
Go Inside Radius = Outer Radius-Gap length
Gap length
Go Gap length = Outer Radius-Inside Radius

Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder Formula

Bingham Number = (Fluid Yield Stress/Plastic Viscosity)*((Diameter of Cylinder 1/(Acceleration due to Gravity*Coefficient Of Volumetric Expansion* Change in Temperature)))^(0.5)
Bn = (ζo/μB)*((D1/(g*β* ∆T)))^(0.5)

What is a Plastic fluid?

A fluid in which the shear force is not proportional to the shear rate (non-Newtonian) requires finite shear stress to start and maintain flow. Most drilling muds are characterized as either plastic or pseudoplastic fluids.

What is Bingham Number?

Bringham number is the ratio of yield stress to viscous stress, describes the extent to which the controllable yield stress can exceed the viscous stress, and is an essential descriptor of Bingham plastic behavior.

How to Calculate Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder?

Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder calculator uses Bingham Number = (Fluid Yield Stress/Plastic Viscosity)*((Diameter of Cylinder 1/(Acceleration due to Gravity*Coefficient Of Volumetric Expansion* Change in Temperature)))^(0.5) to calculate the Bingham Number, The Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder formula is defined as fluid yield stress to plastic viscosity and coefficient of volumetric expansion. Bingham Number is denoted by Bn symbol.

How to calculate Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder using this online calculator? To use this online calculator for Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder, enter Fluid Yield Stress o), Plastic Viscosity B), Diameter of Cylinder 1 (D1), Acceleration due to Gravity (g), Coefficient Of Volumetric Expansion (β) & Change in Temperature (∆T) and hit the calculate button. Here is how the Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder calculation can be explained with given input values -> 0.058321 = (10/10)*((5/(9.8*3* 50)))^(0.5).

FAQ

What is Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder?
The Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder formula is defined as fluid yield stress to plastic viscosity and coefficient of volumetric expansion and is represented as Bn = (ζoB)*((D1/(g*β* ∆T)))^(0.5) or Bingham Number = (Fluid Yield Stress/Plastic Viscosity)*((Diameter of Cylinder 1/(Acceleration due to Gravity*Coefficient Of Volumetric Expansion* Change in Temperature)))^(0.5). The Fluid yield stress is defined as the stress that must be applied to the sample before it starts to flow, Plastic Viscosity is a result of friction between the liquid undergoing deformation under shear stress and the solids and liquids present, Diameter of Cylinder 1 is the diameter of the first cylinder, Acceleration due to Gravity is acceleration gained by an object because of gravitational force, The coefficient Of Volumetric Expansion is the increase in volume per unit original volume per Kelvin rise in temperature & The Change in Temperature is the difference between the initial and final temperature.
How to calculate Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder?
The Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder formula is defined as fluid yield stress to plastic viscosity and coefficient of volumetric expansion is calculated using Bingham Number = (Fluid Yield Stress/Plastic Viscosity)*((Diameter of Cylinder 1/(Acceleration due to Gravity*Coefficient Of Volumetric Expansion* Change in Temperature)))^(0.5). To calculate Bingham Number of Plastic Fluids from Isothermal Semi-circular Cylinder, you need Fluid Yield Stress o), Plastic Viscosity B), Diameter of Cylinder 1 (D1), Acceleration due to Gravity (g), Coefficient Of Volumetric Expansion (β) & Change in Temperature (∆T). With our tool, you need to enter the respective value for Fluid Yield Stress, Plastic Viscosity, Diameter of Cylinder 1, Acceleration due to Gravity, Coefficient Of Volumetric Expansion & Change in Temperature 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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