Velocity of Vane given Exerted Force by Jet Calculator

Formula Used:

\[ v = -\left( \sqrt{\frac{F \cdot G}{\gamma_f \cdot A_{Jet} \cdot (1 + \cos(\theta))}} \right) - V_{absolute} \]

Force exerted by Jet (F):

Specific Gravity of Fluid (G):

Specific Weight of Liquid (γf):

kN/m³

Cross Sectional Area of Jet (A_Jet):

m²

Theta (θ):

rad

Absolute Velocity of Issuing Jet (V_absolute):

m/s

Velocity of Jet (v):

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1. What is Velocity of Vane given Exerted Force by Jet?

The Velocity of Vane given Exerted Force by Jet calculation determines the velocity of a vane based on the force exerted by a jet of fluid. This is important in fluid mechanics and hydraulic engineering applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ v = -\left( \sqrt{\frac{F \cdot G}{\gamma_f \cdot A_{Jet} \cdot (1 + \cos(\theta))}} \right) - V_{absolute} \]

Where:

\( v \) — Velocity of Jet (m/s)
\( F \) — Force exerted by Jet (N)
\( G \) — Specific Gravity of Fluid
\( \gamma_f \) — Specific Weight of Liquid (kN/m³)
\( A_{Jet} \) — Cross Sectional Area of Jet (m²)
\( \theta \) — Theta (radians)
\( V_{absolute} \) — Absolute Velocity of Issuing Jet (m/s)

Explanation: The formula calculates the velocity of the vane by considering the force exerted by the jet, fluid properties, jet geometry, and the absolute velocity of the issuing jet.

3. Importance of Velocity Calculation

Details: Accurate velocity calculation is crucial for designing hydraulic systems, turbines, and other fluid machinery where jet forces impact vane movement and system performance.

4. Using the Calculator

Tips: Enter all required values in appropriate units. Ensure force, specific gravity, specific weight, and area are positive values. Theta should be in radians, and velocities should be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the negative sign in the formula?
A: The negative sign indicates the direction of the velocity relative to the coordinate system used in the derivation.

Q2: How does the angle theta affect the velocity calculation?
A: Theta represents the angle of the jet impact, and the cosine function accounts for the directional component of the force.

Q3: What are typical applications of this calculation?
A: This calculation is used in hydraulic turbines, jet propulsion systems, and various fluid machinery designs.

Q4: What units should be used for input values?
A: Force in Newtons (N), specific weight in kN/m³, area in m², angle in radians, and velocities in m/s.

Q5: How accurate is this calculation for real-world applications?
A: While the formula provides a theoretical basis, real-world applications may require additional factors such as friction losses, turbulence, and fluid viscosity considerations.