Radial Pressure Distribution For Laminar Flow Calculator

Radial Pressure Distribution Formula:

\[ p = P_i + \frac{3\rho\omega^2}{20g}(r^2 - r_1^2) - \frac{6\nu}{\pi t^3} \ln\left(\frac{r}{R}\right) \]

Pressure at Seal Inside Radius (P_i):

Seal Fluid Density (ρ):

kg/m³

Rotational Speed of Shaft (ω):

rad/s

Radial Position (r):

Inner Radius of Rotating Member (r₁):

Kinematic Viscosity (ν):

m²/s

Thickness of Fluid Between Members (t):

Radius of Rotating Member (R):

Pressure At Radial Position (p):

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1. What is Radial Pressure Distribution For Laminar Flow?

The Radial Pressure Distribution For Laminar Flow equation calculates the pressure at any radial position in a bush seal for laminar flow conditions. It considers factors like fluid density, rotational speed, viscosity, and geometric parameters to determine pressure distribution.

2. How Does the Calculator Work?

The calculator uses the Radial Pressure Distribution formula:

\[ p = P_i + \frac{3\rho\omega^2}{20g}(r^2 - r_1^2) - \frac{6\nu}{\pi t^3} \ln\left(\frac{r}{R}\right) \]

Where:

\( p \) — Pressure at radial position (Pa)
\( P_i \) — Pressure at seal inside radius (Pa)
\( \rho \) — Seal fluid density (kg/m³)
\( \omega \) — Rotational speed of shaft (rad/s)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( r \) — Radial position (m)
\( r_1 \) — Inner radius of rotating member (m)
\( \nu \) — Kinematic viscosity of bush seal fluid (m²/s)
\( t \) — Thickness of fluid between members (m)
\( R \) — Radius of rotating member (m)

Explanation: The equation accounts for centrifugal forces and viscous effects in determining the pressure distribution in laminar flow conditions within a bush seal.

3. Importance of Pressure Distribution Calculation

Details: Accurate pressure distribution calculation is crucial for seal design, predicting leakage rates, optimizing seal performance, and ensuring proper lubrication in rotating machinery.

4. Using the Calculator

Tips: Enter all parameters in SI units. Ensure values are positive and physically meaningful. The calculator provides pressure in Pascals (Pa) at the specified radial position.

5. Frequently Asked Questions (FAQ)

Q1: What is laminar flow in bush seals?
A: Laminar flow refers to smooth, orderly fluid motion where fluid particles move in parallel layers with minimal mixing between layers, typically occurring at lower Reynolds numbers.

Q2: When is this equation applicable?
A: This equation is valid for laminar flow conditions in bush seals with Newtonian fluids and assumes isothermal operation with constant fluid properties.

Q3: What are typical values for kinematic viscosity?
A: Kinematic viscosity varies widely: water ≈ 1×10⁻⁶ m²/s, air ≈ 1.5×10⁻⁵ m²/s, engine oil ≈ 1×10⁻⁴ m²/s at room temperature.

Q4: How does rotational speed affect pressure distribution?
A: Higher rotational speeds increase centrifugal forces, leading to higher pressure gradients in the radial direction.

Q5: What are the limitations of this equation?
A: This model assumes laminar flow, Newtonian fluid behavior, constant fluid properties, and neglects thermal effects and surface roughness.