Angular Velocity For Work Done On Wheel Per Second Calculator

Angular Velocity Formula:

\[ \omega = \frac{w \times G}{w_f \times (v_f \times r + v \times rO)} \]

Work Done:

Specific Gravity of Fluid:

Weight of Fluid:

Final Velocity:

m/s

Radius of Wheel:

Velocity of Jet:

m/s

Radius of Outlet:

Angular Velocity (ω):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Angular Velocity For Work Done On Wheel Per Second?

Angular Velocity For Work Done On Wheel Per Second refers to the rotational speed of a wheel calculated based on the work done, specific gravity of fluid, weight of fluid, velocities, and radii involved in the system. It provides a measure of how fast the wheel is rotating in radians per second.

2. How Does the Calculator Work?

The calculator uses the Angular Velocity formula:

\[ \omega = \frac{w \times G}{w_f \times (v_f \times r + v \times rO)} \]

Where:

\( \omega \) — Angular Velocity (rad/s)
\( w \) — Work Done (J)
\( G \) — Specific Gravity of Fluid
\( w_f \) — Weight of Fluid (N)
\( v_f \) — Final Velocity (m/s)
\( r \) — Radius of Wheel (m)
\( v \) — Velocity of Jet (m/s)
\( rO \) — Radius of Outlet (m)

Explanation: The equation calculates angular velocity by considering the work-energy relationship and the geometric properties of the wheel and fluid system.

3. Importance of Angular Velocity Calculation

Details: Accurate angular velocity calculation is crucial for analyzing rotational systems, designing mechanical components, optimizing energy transfer, and understanding fluid-wheel interactions in various engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (Joules for work, Newtons for weight, meters for distances, m/s for velocities). All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is angular velocity measured in?
A: Angular velocity is typically measured in radians per second (rad/s) in the SI system.

Q2: How does work done affect angular velocity?
A: Higher work done typically results in higher angular velocity, assuming other factors remain constant, as more energy is transferred to the rotational system.

Q3: What is the significance of specific gravity in this calculation?
A: Specific gravity accounts for the density difference between the fluid and a reference fluid, affecting the energy transfer in the system.

Q4: Can this formula be used for any type of wheel?
A: This formula is specifically designed for systems where work is done on a wheel through fluid interaction with known velocities and radii.

Q5: What happens if the denominator becomes zero?
A: If the denominator becomes zero, the angular velocity becomes undefined as it would require division by zero, which is mathematically impossible.