Force Exerted On Plate In Direction Of Flow Of Jet On Stationary Curved Vane Calculator

Formula Used:

\[ F_{jet} = \frac{\gamma_f \cdot A_{Jet} \cdot v_{jet}^2}{g} \cdot (1 + \cos(\theta_t)) \]

Specific Weight of Liquid (γ_f):

kN/m³

Cross Sectional Area of Jet (A_Jet):

m²

Fluid Jet Velocity (v_jet):

m/s

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

degrees

Force on Plate in Direction of Jet (F_jet):

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1. What is Force on Plate in Direction of Flow of Jet?

The force exerted on a plate in the direction of flow of jet on a stationary curved vane represents the impact force generated when a fluid jet strikes a curved surface. This calculation is essential in hydraulic engineering and turbine design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_{jet} = \frac{\gamma_f \cdot A_{Jet} \cdot v_{jet}^2}{g} \cdot (1 + \cos(\theta_t)) \]

Where:

\( F_{jet} \) — Force on plate in direction of jet (N)
\( \gamma_f \) — Specific weight of liquid (kN/m³)
\( A_{Jet} \) — Cross sectional area of jet (m²)
\( v_{jet} \) — Fluid jet velocity (m/s)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( \theta_t \) — Half of angle between two tangent to vane (degrees)

Explanation: The formula calculates the force component in the direction of jet flow, accounting for the curvature of the vane through the cosine term.

3. Importance of Force Calculation

Details: Accurate force calculation is crucial for designing hydraulic machinery, determining structural requirements for vanes and plates, and optimizing energy transfer in fluid systems.

4. Using the Calculator

Tips: Enter specific weight in kN/m³, cross-sectional area in m², velocity in m/s, and angle in degrees (0-90). All values must be positive and within valid ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the angle θ_t?
A: θ_t represents half the angle between tangents to the vane at the point where the jet enters and exits, affecting how the jet's momentum is transferred to the vane.

Q2: How does specific weight differ from density?
A: Specific weight is weight per unit volume (kN/m³), while density is mass per unit volume (kg/m³). They are related by γ = ρ·g.

Q3: What are typical values for fluid jet velocity?
A: Jet velocities vary widely depending on application, ranging from 5-50 m/s in hydraulic systems to much higher values in specialized applications.

Q4: When is this formula applicable?
A: This formula applies to stationary curved vanes with steady, incompressible fluid flow and negligible friction losses.

Q5: How does vane curvature affect the force?
A: Greater curvature (smaller θ_t) increases the force component in the jet direction due to better momentum transfer efficiency.