Vertical Depth Below Free Surface Given Pressure At Point In Liquid Calculator

Formula Used:

\[ h = \frac{P_{ab,H} - P_{atm}}{y \times (1 + \frac{\alpha_v}{[g]})} \]

Absolute Pressure For Both Direction:

Pascal

Atmospheric Pressure:

Pascal

Specific Weight Of Liquid:

N/m³

Constant Vertical Acceleration:

m/s²

Height Of Crack:

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1. What Is The Vertical Depth Below Free Surface Given Pressure At Point In Liquid Formula?

The formula calculates the height of crack based on pressure differences, specific weight of liquid, and vertical acceleration. It's derived from fluid mechanics principles relating pressure to depth in accelerating containers.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ h = \frac{P_{ab,H} - P_{atm}}{y \times (1 + \frac{\alpha_v}{[g]})} \]

Where:

\( h \) — Height of Crack (m)
\( P_{ab,H} \) — Absolute Pressure For Both Direction (Pa)
\( P_{atm} \) — Atmospheric Pressure (Pa)
\( y \) — Specific Weight Of Liquid (N/m³)
\( \alpha_v \) — Constant Vertical Acceleration (m/s²)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The formula accounts for the pressure difference between absolute and atmospheric pressure, adjusted by the specific weight and vertical acceleration effects.

3. Importance Of Height Of Crack Calculation

Details: Accurate calculation of crack height is crucial for structural integrity assessment, failure prediction, and safety analysis in pressurized containers and fluid systems.

4. Using The Calculator

Tips: Enter all pressure values in Pascals, specific weight in N/m³, and acceleration in m/s². Ensure all values are positive and physically meaningful.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the gravitational constant [g]?
A: The gravitational constant (9.80665 m/s²) provides the standard acceleration due to gravity used to normalize the vertical acceleration effect.

Q2: Can this formula be used for any liquid?
A: Yes, as long as the specific weight of the liquid is known and the container is undergoing constant vertical acceleration.

Q3: What happens if vertical acceleration is zero?
A: When αv = 0, the formula simplifies to h = (Pab,H - Patm)/y, which is the standard hydrostatic pressure-depth relationship.

Q4: Are there limitations to this equation?
A: The formula assumes constant vertical acceleration and incompressible fluid. It may not be accurate for rapidly changing accelerations or compressible fluids.

Q5: What units should be used for accurate results?
A: Use SI units: Pascals for pressure, N/m³ for specific weight, and m/s² for acceleration to ensure consistent results.