Specific Weight Of Liquid Given Total Pressure Force On Each End Of Cylinder Calculator

Formula Used:

\[ y = \frac{FC}{\left(\frac{\pi}{4 \cdot [g]} \cdot \left(\omega \cdot d_v^2\right)^2 + \pi \cdot d_v^3\right)} \]

Specific Weight of Liquid (y):

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1. What is Specific Weight of Liquid?

The Specific weight of liquid, also known as the unit weight, is the weight per unit volume of the liquid. For example, the specific weight of water on Earth at 4°C is 9.807 kN/m³ or 62.43 lbf/ft³.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ y = \frac{FC}{\left(\frac{\pi}{4 \cdot [g]} \cdot \left(\omega \cdot d_v^2\right)^2 + \pi \cdot d_v^3\right)} \]

Where:

\( y \) — Specific weight of liquid (N/m³)
\( FC \) — Force on cylinder (N)
\( \omega \) — Angular velocity (rad/s)
\( d_v \) — Vertical distance of flow (m)
\( \pi \) — Archimedes' constant (3.141592653589793)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)

Explanation: This formula calculates the specific weight of liquid based on the force exerted on a cylinder, considering the effects of angular velocity and vertical distance of flow.

3. Importance of Specific Weight Calculation

Details: Calculating specific weight is crucial in fluid mechanics and hydraulic engineering for determining buoyancy forces, pressure distributions, and designing fluid systems.

4. Using the Calculator

Tips: Enter force in newtons (N), angular velocity in radians per second (rad/s), and vertical distance in meters (m). All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between specific weight and density?
A: Specific weight is weight per unit volume (N/m³), while density is mass per unit volume (kg/m³). They are related by the equation: specific weight = density × gravitational acceleration.

Q2: How does angular velocity affect specific weight calculation?
A: Angular velocity contributes to the centrifugal forces in the system, which affects the total force on the cylinder and thus the calculated specific weight.

Q3: What are typical specific weight values for common liquids?
A: Water: ~9.81 kN/m³, Mercury: ~133 kN/m³, Gasoline: ~6.6-7.5 kN/m³, Sea water: ~10.0-10.1 kN/m³.

Q4: When is this specific calculation method used?
A: This particular formula is used in scenarios involving cylindrical containers or systems where rotational motion and vertical flow distance are significant factors.

Q5: Are there limitations to this equation?
A: The equation assumes ideal conditions and may need adjustments for highly viscous fluids, turbulent flows, or extreme temperature/pressure conditions.