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Radial Pressure Distribution for Laminar Flow Formula

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Pressure At Radial Position For Bush Seal is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Check FAQs

p = P i + \frac{3 \cdot ρ \cdot ω^{2}}{20 \cdot [g]} \cdot (r^{2} - {r 1}^{2}) - \frac{6 \cdot ν}{π \cdot t^{3}} \cdot \ln (\frac{r}{R})

p - Pressure At Radial Position For Bush Seal?P_i - Pressure at Seal Inside Radius?ρ - Seal Fluid Density?ω - Rotational Speed of Shaft Inside Seal?r - Radial Position in Bush Seal?r₁ - Inner Radius of Rotating Member Inside Bush Seal?ν - Kinematic Viscosity of Bush Seal Fluid?t - Thickness of Fluid Between Members?R - Radius of Rotating Member Inside Bush Seal?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Radial Pressure Distribution for Laminar Flow Example

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Here is how the Radial Pressure Distribution for Laminar Flow equation looks like with Values.

Here is how the Radial Pressure Distribution for Laminar Flow equation looks like with Units.

Here is how the Radial Pressure Distribution for Laminar Flow equation looks like.

0.092 = 2E-7 + \frac{3 \cdot 1100 \cdot 75^{2}}{20 \cdot 9.8066} \cdot (25^{2} - 14^{2}) - \frac{6 \cdot 7.25}{3.1416 \cdot {1.92}^{3}} \cdot \ln (\frac{25}{40})

0.092MPa = 2E-7MPa + \frac{3 \cdot 1100kg/m³ \cdot {75rad/s}^{2}}{20 \cdot 9.8066m/s²} \cdot ({25mm}^{2} - {14mm}^{2}) - \frac{6 \cdot 7.25St}{3.1416 \cdot {1.92mm}^{3}} \cdot \ln (\frac{25mm}{40mm})

0.092 = 2E-7 + \frac{3 \cdot 1100 \cdot 75^{2}}{20 \cdot 9.8066} \cdot (25^{2} - 14^{2}) - \frac{6 \cdot 7.25}{3.1416 \cdot {1.92}^{3}} \cdot \ln (\frac{25}{40})

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Radial Pressure Distribution for Laminar Flow Solution

Follow our step by step solution on how to calculate Radial Pressure Distribution for Laminar Flow?

FIRST Step Consider the formula

p = P i + \frac{3 \cdot ρ \cdot ω^{2}}{20 \cdot [g]} \cdot (r^{2} - {r 1}^{2}) - \frac{6 \cdot ν}{π \cdot t^{3}} \cdot \ln (\frac{r}{R})

Next Step Substitute values of Variables

∴

p = 2E-7MPa + \frac{3 \cdot 1100kg/m³ \cdot {75rad/s}^{2}}{20 \cdot [g]} \cdot ({25mm}^{2} - {14mm}^{2}) - \frac{6 \cdot 7.25St}{π \cdot {1.92mm}^{3}} \cdot \ln (\frac{25mm}{40mm})

Next Step Substitute values of Constants

∴

p = 2E-7MPa + \frac{3 \cdot 1100kg/m³ \cdot {75rad/s}^{2}}{20 \cdot 9.8066m/s²} \cdot ({25mm}^{2} - {14mm}^{2}) - \frac{6 \cdot 7.25St}{3.1416 \cdot {1.92mm}^{3}} \cdot \ln (\frac{25mm}{40mm})

Next Step Convert Units

∴

p = 0.2Pa + \frac{3 \cdot 1100kg/m³ \cdot {75rad/s}^{2}}{20 \cdot 9.8066m/s²} \cdot ({0.025m}^{2} - {0.014m}^{2}) - \frac{6 \cdot 0.0007m²/s}{3.1416 \cdot {0.0019m}^{3}} \cdot \ln (\frac{0.025m}{0.04m})

Next Step Prepare to Evaluate

∴

p = 0.2 + \frac{3 \cdot 1100 \cdot 75^{2}}{20 \cdot 9.8066} \cdot ({0.025}^{2} - {0.014}^{2}) - \frac{6 \cdot 0.0007}{3.1416 \cdot {0.0019}^{3}} \cdot \ln (\frac{0.025}{0.04})

Next Step Evaluate

∴

p = 91987.6630776709Pa

Next Step Convert to Output's Unit

∴

p = 0.0919876630776709MPa

LAST Step Rounding Answer

∴

p = 0.092MPa

Radial Pressure Distribution for Laminar Flow Formula Elements

Variables

Constants

Functions

Pressure At Radial Position For Bush Seal

Pressure At Radial Position For Bush Seal is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

Symbol: p

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Pressure At Radial Position For Bush Seal

Pressure at Seal Inside Radius

Pressure at Seal Inside Radius is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

Symbol: P_i

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Pressure at Seal Inside Radius

Seal Fluid Density

Seal Fluid Density is the corresponding density of the fluid under the given conditions inside the seal.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Seal Fluid Density

Rotational Speed of Shaft Inside Seal

Rotational Speed of Shaft Inside Seal is the angular velocity of the shaft rotating inside a packing seal.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Rotational Speed of Shaft Inside Seal

Radial Position in Bush Seal

Radial Position in Bush Seal is defined as radial positioning for laminar flow emanating from a common central point.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radial Position in Bush Seal

Inner Radius of Rotating Member Inside Bush Seal

Inner Radius of Rotating Member Inside Bush Seal is the radius of the inner surface of the shaft rotating inside a bushed packing seal.

Symbol: r₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Inner Radius of Rotating Member Inside Bush Seal

Kinematic Viscosity of Bush Seal Fluid

Kinematic Viscosity of Bush Seal Fluid is an atmospheric variable defined as the ratio between the dynamic viscosity μ and the density ρ of the fluid.

Symbol: ν

Measurement: Kinematic ViscosityUnit: St

Note: Value should be greater than 0.

Formulas to find Kinematic Viscosity of Bush Seal Fluid

Thickness of Fluid Between Members

Thickness of Fluid Between Members refers to how resistant a fluid is to moving through it. For example, Water has a low or "thin" viscosity, while honey has a "thick" or high viscosity.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Fluid Between Members

Radius of Rotating Member Inside Bush Seal

Radius of Rotating Member Inside Bush Seal is the radius of the surface of the shaft rotating inside a bushed packing seal.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Rotating Member Inside Bush Seal

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Leakage through Bush Seals category

Go Oil Flow through Plain Axial Bush Seal due to Leakage under Laminar Flow Condition

Q = \frac{2 \cdot π \cdot a \cdot (P s - \frac{P e}{10^{6}})}{l} \cdot q

Go Oil Flow through Plain Radial Bush Seal due to Leakage under Laminar Flow Condition

Q = \frac{2 \cdot π \cdot a \cdot (P s - \frac{P e}{10^{6}})}{a - b} \cdot q

How to Evaluate Radial Pressure Distribution for Laminar Flow?

Radial Pressure Distribution for Laminar Flow evaluator uses Pressure At Radial Position For Bush Seal = Pressure at Seal Inside Radius+(3*Seal Fluid Density*Rotational Speed of Shaft Inside Seal^2)/(20*[g])*(Radial Position in Bush Seal^2-Inner Radius of Rotating Member Inside Bush Seal^2)-(6*Kinematic Viscosity of Bush Seal Fluid)/(pi*Thickness of Fluid Between Members^3)*ln(Radial Position in Bush Seal/Radius of Rotating Member Inside Bush Seal) to evaluate the Pressure At Radial Position For Bush Seal, The Radial Pressure Distribution for Laminar Flow formula is defined radial positioning for laminar flow emanating from a common central point. Pressure At Radial Position For Bush Seal is denoted by p symbol.

How to evaluate Radial Pressure Distribution for Laminar Flow using this online evaluator? To use this online evaluator for Radial Pressure Distribution for Laminar Flow, enter Pressure at Seal Inside Radius (P_i), Seal Fluid Density (ρ), Rotational Speed of Shaft Inside Seal (ω), Radial Position in Bush Seal (r), Inner Radius of Rotating Member Inside Bush Seal (r₁), Kinematic Viscosity of Bush Seal Fluid (ν), Thickness of Fluid Between Members (t) & Radius of Rotating Member Inside Bush Seal (R) and hit the calculate button.

FAQs on Radial Pressure Distribution for Laminar Flow

What is the formula to find Radial Pressure Distribution for Laminar Flow?

The formula of Radial Pressure Distribution for Laminar Flow is expressed as Pressure At Radial Position For Bush Seal = Pressure at Seal Inside Radius+(3*Seal Fluid Density*Rotational Speed of Shaft Inside Seal^2)/(20*[g])*(Radial Position in Bush Seal^2-Inner Radius of Rotating Member Inside Bush Seal^2)-(6*Kinematic Viscosity of Bush Seal Fluid)/(pi*Thickness of Fluid Between Members^3)*ln(Radial Position in Bush Seal/Radius of Rotating Member Inside Bush Seal). Here is an example- 9.2E-8 = 0.2+(3*1100*75^2)/(20*[g])*(0.025^2-0.014^2)-(6*0.000725)/(pi*0.00192^3)*ln(0.025/0.04).

How to calculate Radial Pressure Distribution for Laminar Flow?

With Pressure at Seal Inside Radius (P_i), Seal Fluid Density (ρ), Rotational Speed of Shaft Inside Seal (ω), Radial Position in Bush Seal (r), Inner Radius of Rotating Member Inside Bush Seal (r₁), Kinematic Viscosity of Bush Seal Fluid (ν), Thickness of Fluid Between Members (t) & Radius of Rotating Member Inside Bush Seal (R) we can find Radial Pressure Distribution for Laminar Flow using the formula - Pressure At Radial Position For Bush Seal = Pressure at Seal Inside Radius+(3*Seal Fluid Density*Rotational Speed of Shaft Inside Seal^2)/(20*[g])*(Radial Position in Bush Seal^2-Inner Radius of Rotating Member Inside Bush Seal^2)-(6*Kinematic Viscosity of Bush Seal Fluid)/(pi*Thickness of Fluid Between Members^3)*ln(Radial Position in Bush Seal/Radius of Rotating Member Inside Bush Seal). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Natural Logarithm (ln) function(s).

Can the Radial Pressure Distribution for Laminar Flow be negative?

Yes, the Radial Pressure Distribution for Laminar Flow, measured in Pressure can be negative.

Which unit is used to measure Radial Pressure Distribution for Laminar Flow?

Radial Pressure Distribution for Laminar Flow is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Radial Pressure Distribution for Laminar Flow can be measured.

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Radial Pressure Distribution for Laminar Flow Formula

Radial Pressure Distribution for Laminar Flow Example

Radial Pressure Distribution for Laminar Flow Solution

Radial Pressure Distribution for Laminar Flow Formula Elements

Other formulas in Leakage through Bush Seals category

How to Evaluate Radial Pressure Distribution for Laminar Flow?

FAQs on Radial Pressure Distribution for Laminar Flow

Variable Name