Radial Pressure Distribution Calculator

Formula first

Overview

This equation models the spatial pressure variation in a fluid layer subjected to rotational motion within an annular space. It accounts for the effects of fluid density, angular velocity, and the radius ratio defined by the inner and outer cylinder constraints. The expression provides a closed-form solution for determining pressure differentials relative to a reference point within the system.

Symbols

Variables

P - $P_{\kappa R}$ = Pressure Difference, $\rho$ = Fluid Density, ${\Omega }_0$ = Angular Velocity, $\kappa$ = Radius Ratio, R = Outer Radius

Apply it well

When To Use

When to use: Use when analyzing steady, incompressible, laminar flow in the annular region between rotating concentric cylinders.

Why it matters: Crucial for designing journal bearings, seal clearances, and understanding torque transmission in rotating machinery.

Avoid these traps

Common Mistakes

• Mixing up the inner and outer radii within the kappa parameter.
• Neglecting to convert rotational speed from RPM to rad/s (Omega_0).
• Confusing the reference pressure P_kappaR with the local pressure P.

One free problem

Practice Problem

How does the pressure distribution in an annular gap change if the fluid density is increased while maintaining the same angular velocity and geometry?

Solve for: $delt{a}_P$

Hint: Examine the role of the density term (rho) as a multiplier in the pressure distribution formula.

The full worked solution stays in the interactive walkthrough.

Keep going

Related Formulas

References

Sources

1. Fundamentals of Fluid Mechanics, 8th Edition, Munson, Young, and Okiishi.
2. NIST CODATA
3. IUPAC Gold Book
4. Wikipedia: Fluid dynamics
5. White, Frank M. Fluid Mechanics. McGraw-Hill Education, 2016.
6. Munson, Bruce R., et al. Fundamentals of Fluid Mechanics. John Wiley & Sons, 2016.