Velocity At Outlet Given Work Done On Wheel Calculator

Formula Used:

\[ v = \frac{\left(\frac{w \times G}{wf \times \omega} - vf \times r\right)}{rO} \]

Work Done (w):

Specific Gravity of Fluid (G):

Weight of Fluid (wf):

Angular Velocity (ω):

rad/s

Final Velocity (vf):

m/s

Radius of Wheel (r):

Radius of Outlet (rO):

Velocity of Jet (v):

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1. What is Velocity At Outlet Given Work Done On Wheel?

This calculation determines the velocity of a jet at the outlet based on the work done on a wheel, taking into account various fluid dynamics parameters including specific gravity, angular velocity, and geometric dimensions of the system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ v = \frac{\left(\frac{w \times G}{wf \times \omega} - vf \times r\right)}{rO} \]

Where:

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

Explanation: The formula calculates jet velocity by considering the energy transfer through the system and the geometric constraints of the wheel and outlet.

3. Importance of Velocity Calculation

Details: Accurate velocity calculation is crucial for designing and analyzing fluid systems, optimizing energy transfer efficiency, and ensuring proper system performance in various engineering applications.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure all values are positive and within reasonable physical limits for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of this calculation?
A: This calculation helps determine the exit velocity of fluid from a system where work is being done on a wheel, which is important for analyzing energy conversion efficiency.

Q2: What are typical values for velocity of jet?
A: Jet velocity values vary widely depending on the application, ranging from a few m/s in low-pressure systems to hundreds of m/s in high-pressure applications.

Q3: How does specific gravity affect the result?
A: Higher specific gravity fluids typically result in lower jet velocities for the same work input, as more energy is required to accelerate denser fluids.

Q4: What are the limitations of this formula?
A: The formula assumes ideal conditions and may need adjustments for real-world factors like friction losses, turbulence, and fluid compressibility.

Q5: Can this be used for different fluid types?
A: Yes, the formula is applicable to various fluids as long as the specific gravity parameter accurately represents the fluid's density relative to water.