Radial Pressure Distribution for Laminar Flow Calculator

✖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.ⓘ Pressure at Seal Inside Radius [P_i]			+10% -10%
✖Seal Fluid Density is the corresponding density of the fluid under the given conditions inside the seal.ⓘ Seal Fluid Density [ρ]			+10% -10%
✖Rotational speed of shaft inside seal is the angular velocity of the shaft rotating inside a packing seal.ⓘ Rotational speed of shaft inside seal [ω]			+10% -10%
✖Radial Position in Bush Seal is defined as radial positioning for laminar flow emanating from a common central point.ⓘ Radial Position in Bush Seal [r]			+10% -10%
✖Inner Radius of rotating member inside bush seal is the radius of the inner surface of the shaft rotating inside a bushed packing seal.ⓘ Inner Radius of Rotating Member inside Bush Seal [r₁]			+10% -10%
✖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.ⓘ Kinematic viscosity of bush seal fluid [ν]			+10% -10%
✖The 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.ⓘ Thickness of Fluid between Members [t]			+10% -10%
✖Radius of rotating member inside bush seal is the radius of the surface of the shaft rotating inside a bushed packing seal.ⓘ Radius of rotating member inside bush seal [R]			+10% -10%

✖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.ⓘ Radial Pressure Distribution for Laminar Flow [p]

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Formula

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Radial Pressure Distribution for Laminar Flow

Formula

`"p" = "P"_{"i"}+(3*"ρ"*"ω"^2)/(20*"[g]")*("r"^2-"r"_{"1"}^2)-(6*"ν")/(pi*"t"^3)*ln("r"/"R")`

Example

`"0.091989MPa"="2Pa"+(3*"1100kg/m³"*("75rad/s")^2)/(20*"[g]")*(("25mm")^2-("14mm")^2)-(6*"7.25St")/(pi*("1.92mm")^3)*ln("25mm"/"40mm")`

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Radial Pressure Distribution for Laminar Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
p = P_i+(3*ρ*ω^2)/(20*[g])*(r^2-r₁^2)-(6*ν)/(pi*t^3)*ln(r/R)
This formula uses 2 Constants, 1 Functions, 9 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Pressure at Radial Position for Bush Seal - (Measured in Pascal) - 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.
Pressure at Seal Inside Radius - (Measured in Pascal) - 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.
Seal Fluid Density - (Measured in Kilogram per Cubic Meter) - Seal Fluid Density is the corresponding density of the fluid under the given conditions inside the seal.
Rotational speed of shaft inside seal - (Measured in Radian per Second) - Rotational speed of shaft inside seal is the angular velocity of the shaft rotating inside a packing seal.
Radial Position in Bush Seal - (Measured in Meter) - Radial Position in Bush Seal is defined as radial positioning for laminar flow emanating from a common central point.
Inner Radius of Rotating Member inside Bush Seal - (Measured in Meter) - Inner Radius of rotating member inside bush seal is the radius of the inner surface of the shaft rotating inside a bushed packing seal.
Kinematic viscosity of bush seal fluid - (Measured in Square Meter per Second) - 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.
Thickness of Fluid between Members - (Measured in Meter) - The 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.
Radius of rotating member inside bush seal - (Measured in Meter) - Radius of rotating member inside bush seal is the radius of the surface of the shaft rotating inside a bushed packing seal.

STEP 1: Convert Input(s) to Base Unit

Pressure at Seal Inside Radius: 2 Pascal --> 2 Pascal No Conversion Required
Seal Fluid Density: 1100 Kilogram per Cubic Meter --> 1100 Kilogram per Cubic Meter No Conversion Required
Rotational speed of shaft inside seal: 75 Radian per Second --> 75 Radian per Second No Conversion Required
Radial Position in Bush Seal: 25 Millimeter --> 0.025 Meter (Check conversion here)
Inner Radius of Rotating Member inside Bush Seal: 14 Millimeter --> 0.014 Meter (Check conversion here)
Kinematic viscosity of bush seal fluid: 7.25 Stokes --> 0.000725 Square Meter per Second (Check conversion here)
Thickness of Fluid between Members: 1.92 Millimeter --> 0.00192 Meter (Check conversion here)
Radius of rotating member inside bush seal: 40 Millimeter --> 0.04 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

p = P_i+(3*ρ*ω^2)/(20*[g])*(r^2-r₁^2)-(6*ν)/(pi*t^3)*ln(r/R) --> 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)

Evaluating ... ...

p = 91989.4630776709

STEP 3: Convert Result to Output's Unit

91989.4630776709 Pascal -->0.0919894630776709 Megapascal (Check conversion here)

FINAL ANSWER

0.0919894630776709 ≈ 0.091989 Megapascal <-- Pressure at Radial Position for Bush Seal

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Machine Elements » Design of Coupling » Seals » Leakage through Bush Seals » Radial Pressure Distribution for Laminar Flow

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Created by sanjay shiva

national institute of technology hamirpur (NITH ), hamirpur , himachal pradesh

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< 17 Leakage through Bush Seals Calculators

Amount of Leakage of Fluid through Face Seal

Go Oil Flow from Bush Seal = (pi*Thickness of Fluid between Members^3)/(6*Kinematic viscosity of bush seal fluid*ln(Outer Radius of rotating member inside bush seal/Inner Radius of Rotating Member inside Bush Seal))*((3*Seal Fluid Density*Rotational speed of shaft inside seal^2)/(20*[g])*(Outer Radius of rotating member inside bush seal^2-Inner Radius of Rotating Member inside Bush Seal^2)-Internal Hydraulic Pressure-Pressure at Seal Inside Radius)

Radial Pressure Distribution for Laminar Flow

Go 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)

Volumetric Flow Rate under Laminar Flow Condition for Radial Bush Seal for Incompressible Fluid

Go Volumetric Flow Rate per Unit Pressure = (Radial Clearance for Seals^3)/(12*Absolute Viscosity of Oil in Seals)*(Outer Radius of Plain Bush Seal-Inner Radius of Plain Bush Seal)/(Outer Radius of Plain Bush Seal*ln(Outer Radius of Plain Bush Seal/Inner Radius of Plain Bush Seal))

Volumetric Flow Rate under Laminar Flow Condition for Radial Bush Seal for Compressible Fluid

Go Volumetric Flow Rate per Unit Pressure = (Radial Clearance for Seals^3)/(24*Absolute Viscosity of Oil in Seals)*((Outer Radius of Plain Bush Seal-Inner Radius of Plain Bush Seal)/(Outer Radius of Plain Bush Seal))*((Minimum Percentage Compression+Exit Pressure)/(Exit Pressure))

Outside Radius of Rotating Member given Power Loss due to Leakage of Fluid through Face Seal

Go Outer Radius of rotating member inside bush seal = (Power loss for seal/(((pi*Kinematic viscosity of bush seal fluid*Nominal Packing Cross-section of Bush Seal^2)/(13200*Thickness of Fluid between Members)))+Inner Radius of Rotating Member inside Bush Seal^4)^(1/4)

Thickness of Fluid between Members given Power Loss due to Leakage of Fluid through Face Seal

Go Thickness of Fluid between Members = (pi*Kinematic viscosity of bush seal fluid*Nominal Packing Cross-section of Bush Seal^2)/(13200*Power loss for seal)*(Outer Radius of rotating member inside bush seal^4-Inner Radius of Rotating Member inside Bush Seal^4)

Kinematic Viscosity given Power Loss due to Leakage of Fluid through Face Seal

Go Kinematic viscosity of bush seal fluid = (13200*Power loss for seal*Thickness of Fluid between Members)/(pi*Nominal Packing Cross-section of Bush Seal^2*(Outer Radius of rotating member inside bush seal^4-Inner Radius of Rotating Member inside Bush Seal^4))

Power Loss or Consumption due to Leakage of Fluid through Face Seal

Go Power loss for seal = (pi*Kinematic viscosity of bush seal fluid*Nominal Packing Cross-section of Bush Seal^2)/(13200*Thickness of Fluid between Members)*(Outer Radius of rotating member inside bush seal^4-Inner Radius of Rotating Member inside Bush Seal^4)

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

Go Oil Flow from Bush Seal = (2*pi*Outer Radius of Plain Bush Seal*(Minimum Percentage Compression-Exit Pressure/10^6))/(Outer Radius of Plain Bush Seal-Inner Radius of Plain Bush Seal)*Volumetric Flow Rate per Unit Pressure

Internal Hydraulic Pressure given Zero Leakage of Fluid through Face Seal

Go Internal Hydraulic Pressure = Pressure at Seal Inside Radius+(3*Seal Fluid Density*Rotational speed of shaft inside seal^2)/20*(Outer Radius of rotating member inside bush seal^2-Inner Radius of Rotating Member inside Bush Seal^2)*1000

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

Go Oil Flow from Bush Seal = (2*pi*Outer Radius of Plain Bush Seal*(Minimum Percentage Compression-Exit Pressure/10^6))/(Depth of U Collar)*Volumetric Flow Rate per Unit Pressure

Volumetric Flow Rate under Laminar Flow Condition for Axial Bush Seal for Compressible Fluid

Go Volumetric Flow Rate per Unit Pressure = (Radial Clearance for Seals^3)/(12*Absolute Viscosity of Oil in Seals)*(Minimum Percentage Compression+Exit Pressure)/(Exit Pressure)

Thickness of Fluid between Members given Shape Factor

Go Thickness of Fluid between Members = (Outside Diameter of Packing Gasket-Inside Diameter of Packing Gasket)/(4*Shape Factor for Circular Gasket)

Shape Factor for Circular or Annular Gasket

Go Shape Factor for Circular Gasket = (Outside Diameter of Packing Gasket-Inside Diameter of Packing Gasket)/(4*Thickness of Fluid between Members)

Outside Diameter of Gasket given Shape Factor

Go Outside Diameter of Packing Gasket = Inside Diameter of Packing Gasket+4*Thickness of Fluid between Members*Shape Factor for Circular Gasket

Inside Diameter of Gasket given Shape Factor

Go Inside Diameter of Packing Gasket = Outside Diameter of Packing Gasket-4*Thickness of Fluid between Members*Shape Factor for Circular Gasket

Volumetric Efficiency of Reciprocating Compressor

Go Volumetric Efficiency = Actual volume/Piston Swept Volume

Radial Pressure Distribution for Laminar Flow Formula

What is Radial position?

Radial position is defined as radial positioning for laminar flow emanating from a common central point.

How to Calculate Radial Pressure Distribution for Laminar Flow?

Radial Pressure Distribution for Laminar Flow calculator 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 calculate 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 calculate Radial Pressure Distribution for Laminar Flow using this online calculator? To use this online calculator 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. Here is how the Radial Pressure Distribution for Laminar Flow calculation can be explained with given input values -> 9.2E-8 = 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).

FAQ

What is Radial Pressure Distribution for Laminar Flow?

The Radial Pressure Distribution for Laminar Flow formula is defined radial positioning for laminar flow emanating from a common central point and is represented as p = P_i+(3*ρ*ω^2)/(20*[g])*(r^2-r₁^2)-(6*ν)/(pi*t^3)*ln(r/R) or 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). 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, Seal Fluid Density is the corresponding density of the fluid under the given conditions inside the seal, Rotational speed of shaft inside seal is the angular velocity of the shaft rotating inside a packing seal, Radial Position in Bush Seal is defined as radial positioning for laminar flow emanating from a common central point, Inner Radius of rotating member inside bush seal is the radius of the inner surface of the shaft rotating inside a bushed packing seal, 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, The 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 & Radius of rotating member inside bush seal is the radius of the surface of the shaft rotating inside a bushed packing seal.

How to calculate Radial Pressure Distribution for Laminar Flow?

The Radial Pressure Distribution for Laminar Flow formula is defined radial positioning for laminar flow emanating from a common central point is calculated using 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 calculate Radial Pressure Distribution for Laminar Flow, you need 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). With our tool, you need to enter the respective value for Pressure at Seal Inside Radius, Seal Fluid Density, Rotational speed of shaft inside seal, Radial Position in Bush Seal, Inner Radius of Rotating Member inside Bush Seal, Kinematic viscosity of bush seal fluid, Thickness of Fluid between Members & Radius of rotating member inside bush seal 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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