Initial Velocity When Work Done At Vane Angle Is 90 And Velocity Is Zero Calculator

Formula Used:

\[ u = \frac{w \times G}{w_f \times v_f} \]

Work Done (w):

Specific Gravity of Fluid (G):

Weight of Fluid (w_f):

Final Velocity (v_f):

m/s

Initial Velocity (u):

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1. What Is The Initial Velocity When Work Done At Vane Angle Is 90 And Velocity Is Zero Formula?

This formula calculates the initial velocity of a fluid when work is done at a vane angle of 90 degrees and the final velocity is zero. It's derived from the relationship between work done, specific gravity, fluid weight, and velocities in fluid mechanics systems.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ u = \frac{w \times G}{w_f \times v_f} \]

Where:

\( u \) — Initial Velocity (m/s)
\( w \) — Work Done (J)
\( G \) — Specific Gravity of Fluid
\( w_f \) — Weight of Fluid (N)
\( v_f \) — Final Velocity (m/s)

Explanation: The formula calculates the initial velocity by considering the work done on the system, the specific gravity of the fluid, the weight of the fluid, and the final velocity when it reaches zero.

3. Importance Of Initial Velocity Calculation

Details: Calculating initial velocity in fluid systems with vane angles of 90 degrees is crucial for understanding energy transfer, system efficiency, and designing hydraulic machinery and fluid control systems.

4. Using The Calculator

Tips: Enter work done in joules, specific gravity as a dimensionless ratio, fluid weight in newtons, and final velocity in m/s. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What does a vane angle of 90 degrees signify?
A: A vane angle of 90 degrees indicates that the fluid is striking the vane perpendicularly, which affects the work transfer and velocity calculations.

Q2: Why is final velocity zero in this context?
A: Final velocity is zero when all the kinetic energy of the fluid has been transferred to the vane, representing maximum work extraction from the fluid.

Q3: What are typical applications of this calculation?
A: This calculation is used in hydraulic turbines, water wheels, and other fluid machinery where work is extracted from moving fluids at right angles.

Q4: How does specific gravity affect the result?
A: Higher specific gravity fluids (denser fluids) will result in higher initial velocities for the same work done, as they contain more mass per unit volume.

Q5: Are there limitations to this formula?
A: This formula assumes ideal conditions, perfect energy transfer, and doesn't account for friction losses, turbulence, or other real-world factors that may affect actual system performance.