Vertical Falling Speed Given Height At Outlet Zone With Respect To Settling Velocity Calculator

Formula Used:

\[ \text{Falling Speed} = \text{Outer Height} \times \left( \frac{\text{Settling Velocity}}{\text{Height of Crack}} \right) \] \[ v' = H \times \left( \frac{V_s}{h} \right) \]

Falling Speed (v'):

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1. What is the Falling Speed Formula?

The Falling Speed formula calculates the constant speed at which a particle falls through a fluid when the force of gravity is balanced by the drag force and buoyant force acting on the particle. It relates the outer height, settling velocity, and height of crack in a material.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ v' = H \times \left( \frac{V_s}{h} \right) \]

Where:

\( v' \) — Falling Speed (cm/s)
\( H \) — Outer Height (m)
\( V_s \) — Settling Velocity (cm/s)
\( h \) — Height of Crack (m)

Explanation: The formula calculates the falling speed by multiplying the outer height with the ratio of settling velocity to height of crack.

3. Importance of Falling Speed Calculation

Details: Calculating falling speed is crucial for understanding particle behavior in fluids, designing sedimentation systems, and analyzing material failure under stress conditions.

4. Using the Calculator

Tips: Enter outer height in meters, settling velocity in cm/s, and height of crack in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is settling velocity?
A: Settling velocity refers to the terminal velocity of a particle in still fluid when gravitational forces are balanced by drag forces.

Q2: How does height of crack affect falling speed?
A: The height of crack is inversely proportional to the falling speed - a larger crack height results in a smaller falling speed, and vice versa.

Q3: What are typical values for falling speed?
A: Falling speed values vary significantly depending on the particle size, fluid properties, and system dimensions, ranging from fractions of cm/s to several cm/s.

Q4: When is this formula applicable?
A: This formula is applicable for calculating falling speed in systems where particles settle through fluids and where crack dimensions affect the flow characteristics.

Q5: What units should be used for input values?
A: Outer height and height of crack should be in meters, while settling velocity should be in cm/s. The result will be in cm/s.