Velocity For Force Exerted On Plate In Direction Of Flow Of Jet Calculator

Fluid Jet Velocity Formula:

\[ v_{jet} = \sqrt{\frac{F_{jet} \times [g]}{\gamma_f \times A_{Jet} \times (1 + \cos(\theta_t))}} \]

Force on Plate in Direction of Jet (F_jet):

Specific Weight of Liquid (γ_f):

kN/m³

Cross Sectional Area of Jet (A_Jet):

m²

Half of Angle Between Two Tangent to Vane (θ_t):

rad

Fluid Jet Velocity (v_jet):

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1. What is Fluid Jet Velocity?

Fluid Jet Velocity is the volume of fluid flowing in the given vessel per unit cross sectional area. It represents the speed at which fluid exits a nozzle or orifice and is a crucial parameter in fluid dynamics and hydraulic engineering applications.

2. How Does the Calculator Work?

The calculator uses the Fluid Jet Velocity formula:

\[ v_{jet} = \sqrt{\frac{F_{jet} \times [g]}{\gamma_f \times A_{Jet} \times (1 + \cos(\theta_t))}} \]

Where:

\( v_{jet} \) — Fluid Jet Velocity (m/s)
\( F_{jet} \) — Force on Plate in Direction of Jet (N)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( \gamma_f \) — Specific Weight of Liquid (kN/m³)
\( A_{Jet} \) — Cross Sectional Area of Jet (m²)
\( \theta_t \) — Half of Angle Between Two Tangent to Vane (rad)

Explanation: The equation calculates the velocity of a fluid jet based on the force it exerts on a curved vane, accounting for the specific weight of the liquid, cross-sectional area, and the vane geometry.

3. Importance of Fluid Jet Velocity Calculation

Details: Accurate fluid jet velocity calculation is essential for designing hydraulic systems, turbines, pumps, and various fluid machinery. It helps in determining the energy transfer efficiency and optimizing system performance in engineering applications.

4. Using the Calculator

Tips: Enter force in Newtons, specific weight in kN/m³, cross-sectional area in m², and angle in radians. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the angle θ_t in the formula?
A: θ_t represents half the angle between two tangents to the vane, which affects how the jet impacts and transfers momentum to the vane surface.

Q2: How does specific weight differ from density?
A: Specific weight is weight per unit volume (γ = ρ × g), while density is mass per unit volume. Specific weight includes the effect of gravity.

Q3: What are typical values for fluid jet velocity?
A: Jet velocities vary widely depending on application, ranging from 1-5 m/s for low-pressure systems to 50-100+ m/s for high-pressure hydraulic applications.

Q4: Can this formula be used for compressible fluids?
A: This specific formula is primarily for incompressible fluids. Compressible fluids require additional factors accounting for density changes.

Q5: What are practical applications of this calculation?
A: This calculation is used in hydraulic turbine design, jet propulsion systems, spray nozzle design, and various fluid power applications where jet impact forces are significant.