Pressure At Any Point With Origin At Free Surface Calculator

Formula Used:

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

Atmospheric Pressure (P_atm):

Specific Weight of Liquid (γ):

N/m³

Angular Velocity (ω):

rad/s

Radial Distance from Central Axis (d_r):

Height of Crack (h):

Absolute Pressure (P_Abs):

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1. What is the Pressure at Any Point with Origin at Free Surface Formula?

The formula calculates the absolute pressure at any point in a rotating fluid container, taking into account atmospheric pressure, specific weight of the liquid, angular velocity, radial distance from the central axis, and height of the point from the reference surface.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula accounts for both static pressure components and dynamic pressure effects due to rotational motion of the fluid.

3. Importance of Absolute Pressure Calculation

Details: Accurate pressure calculation is crucial for designing rotating machinery, analyzing fluid behavior in centrifugal systems, and ensuring structural integrity in applications involving rotating fluids.

4. Using the Calculator

Tips: Enter all values in appropriate units. Atmospheric pressure and specific weight must be positive values. Angular velocity, radial distance, and height should be non-negative values.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between absolute and gauge pressure?
A: Absolute pressure is measured relative to a perfect vacuum, while gauge pressure is measured relative to atmospheric pressure. Absolute pressure = Gauge pressure + Atmospheric pressure.

Q2: Why is gravitational acceleration constant used in the formula?
A: The gravitational acceleration constant (g) is used to convert specific weight (weight per unit volume) to mass density, which is needed for the dynamic pressure calculation in rotating systems.

Q3: What applications use this pressure calculation?
A: This calculation is used in centrifugal pumps, rotating machinery, mixing tanks, and any system where fluids are subjected to rotational motion.

Q4: How does angular velocity affect the pressure distribution?
A: Higher angular velocity increases the centrifugal force, leading to higher pressure at the outer edges and lower pressure near the center of rotation.

Q5: What are the limitations of this formula?
A: This formula assumes ideal fluid behavior, constant angular velocity, and doesn't account for viscosity effects or turbulent flow conditions.