Vertical Depth Given Pressure At Any Point With Origin At Free Surface Calculator

Formula Used:

\[ h = \frac{P_{atm} - P_{Abs} + \left(\frac{y}{[g]}\right) \times \left(0.5 \times (\omega \times dr)^2\right)}{\omega} \]

Atmospheric Pressure (P_atm):

Absolute Pressure (P_Abs):

Specific Weight of Liquid (y):

N/m³

Angular Velocity (ω):

rad/s

Radial Distance from Central Axis (dr):

Height of Crack (h):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Vertical Depth Calculation?

The Vertical Depth calculation determines the height of a crack or flaw in a material based on pressure differentials, specific weight of liquid, angular velocity, and radial distance from the central axis. This calculation is crucial for material integrity assessment and failure prediction.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{P_{atm} - P_{Abs} + \left(\frac{y}{[g]}\right) \times \left(0.5 \times (\omega \times dr)^2\right)}{\omega} \]

Where:

\( h \) — Height of Crack (m)
\( P_{atm} \) — Atmospheric Pressure (Pa)
\( P_{Abs} \) — Absolute Pressure (Pa)
\( y \) — Specific Weight of Liquid (N/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( \omega \) — Angular Velocity (rad/s)
\( dr \) — Radial Distance from Central Axis (m)

Explanation: The formula accounts for pressure differences, centrifugal forces, and gravitational effects to determine the vertical depth or height measurement.

3. Importance of Height Calculation

Details: Accurate height calculation is essential for structural integrity assessment, failure analysis, and predicting material behavior under various pressure conditions and rotational forces.

4. Using the Calculator

Tips: Enter all values in appropriate units (Pa for pressures, N/m³ for specific weight, rad/s for angular velocity, m for distance). All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of atmospheric pressure in this calculation?
A: Atmospheric pressure serves as the reference point for pressure differential calculations, providing the baseline from which absolute pressure is measured.

Q2: How does angular velocity affect the height calculation?
A: Angular velocity contributes to centrifugal forces that influence the pressure distribution and consequently affect the calculated height measurement.

Q3: What are typical values for specific weight of common liquids?
A: Water has a specific weight of approximately 9810 N/m³, while other liquids vary based on their density and gravitational acceleration.

Q4: When is this calculation most commonly used?
A: This calculation is frequently used in mechanical engineering, materials science, and structural analysis to assess crack propagation and material failure points.

Q5: Are there limitations to this formula?
A: The formula assumes ideal conditions and may need adjustments for extreme temperatures, non-Newtonian fluids, or complex material properties.