Radial Distance For Pressure At Any Point With Origin At Free Surface Calculator

Radial Distance Formula:

\[ dr = \sqrt{\frac{2 \cdot [g]}{y \cdot \omega^2} \cdot (P_{Abs} - P_{atm} + y \cdot h)} \]

Specific Weight of Liquid (y):

N/m³

Angular Velocity (ω):

rad/s

Absolute Pressure (P_Abs):

Atmospheric Pressure (P_atm):

Height of Crack (h):

Radial Distance from Central Axis (dr):

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1. What is Radial Distance For Pressure At Any Point With Origin At Free Surface?

The radial distance formula calculates the distance from the central axis in a rotating liquid system where pressure is measured at any point with the origin at the free surface. This is important in fluid mechanics for understanding pressure distribution in rotating containers.

2. How Does the Calculator Work?

The calculator uses the radial distance formula:

\[ dr = \sqrt{\frac{2 \cdot [g]}{y \cdot \omega^2} \cdot (P_{Abs} - P_{atm} + y \cdot h)} \]

Where:

\( dr \) — Radial distance from central axis (m)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( y \) — Specific weight of liquid (N/m³)
\( \omega \) — Angular velocity (rad/s)
\( P_{Abs} \) — Absolute pressure (Pa)
\( P_{atm} \) — Atmospheric pressure (Pa)
\( h \) — Height of crack (m)

Explanation: The formula calculates the radial position based on pressure measurements and fluid properties in a rotating system.

3. Importance of Radial Distance Calculation

Details: Accurate radial distance calculation is crucial for designing rotating machinery, understanding fluid behavior in centrifuges, and analyzing pressure distribution in rotating containers and systems.

4. Using the Calculator

Tips: Enter specific weight in N/m³, angular velocity in rad/s, pressures in Pa, and height in meters. All values must be positive and valid for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is specific weight of liquid?
A: Specific weight is the weight per unit volume of a liquid, typically measured in N/m³ or kN/m³.

Q2: How is angular velocity different from regular velocity?
A: Angular velocity measures how fast an object rotates around an axis (rad/s), while linear velocity measures straight-line speed (m/s).

Q3: Why is atmospheric pressure subtracted from absolute pressure?
A: This calculates the gauge pressure, which is the pressure relative to atmospheric pressure.

Q4: What applications use this radial distance calculation?
A: Centrifuges, rotating machinery, mixing tanks, and any system involving rotating liquids under pressure.

Q5: Are there limitations to this equation?
A: The equation assumes ideal fluid behavior and may need adjustments for viscous fluids or complex geometries.