Resultant Force Acting On Completely Submerged Plate Given Intersecting Angle Calculator

Formula Used:

\[ \text{Resultant Force} = (\text{Absolute Pressure above Liquid} + (\text{Density of Fluid} \times [g] \times \text{Distance of the Centroid from X-Axis} \times \sin(\text{Intersecting Angle}))) \times (\text{Area of Surface}) \] \[ F_R = (P_o + (\rho_{\text{Fluid}} \times [g] \times y_c \times \sin(\theta_{\text{Intersect}}))) \times A \]

Absolute Pressure above Liquid (P_o):

Density of Fluid (ρ):

kg/m³

Distance of the Centroid from X-Axis (y_c):

Intersecting Angle (θ):

rad

Area of Surface (A):

m²

Resultant Force (F_R):

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1. What is the Resultant Force on a Submerged Plate?

The resultant force on a completely submerged plate is the total hydrostatic force acting on the surface due to fluid pressure. It accounts for both atmospheric pressure above the liquid and the pressure due to the fluid column above the centroid of the surface.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_R = (P_o + (\rho \times [g] \times y_c \times \sin(\theta))) \times A \]

Where:

\( F_R \) — Resultant Force (N)
\( P_o \) — Absolute Pressure above Liquid (Pa)
\( \rho \) — Density of Fluid (kg/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( y_c \) — Distance of the Centroid from X-Axis (m)
\( \theta \) — Intersecting Angle (rad)
\( A \) — Area of Surface (m²)

Explanation: This formula calculates the total force acting on a submerged surface by considering both atmospheric pressure and the hydrostatic pressure due to the fluid depth at the centroid of the surface.

3. Importance of Resultant Force Calculation

Details: Calculating the resultant force is crucial for designing submerged structures, dams, gates, and various hydraulic systems. It helps engineers determine the structural requirements and safety factors for components exposed to fluid pressure.

4. Using the Calculator

Tips: Enter all values in the specified units. Absolute pressure should be in Pascals, density in kg/m³, distances in meters, angle in radians, and area in square meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the intersecting angle?
A: The intersecting angle determines how the surface is oriented relative to the horizontal free surface, affecting the vertical depth of the centroid and thus the hydrostatic pressure.

Q2: Why is absolute pressure used instead of gauge pressure?
A: Absolute pressure includes atmospheric pressure, which acts on both sides of the surface in submerged applications, providing a more accurate calculation of the net force.

Q3: How does the centroid distance affect the resultant force?
A: The centroid distance determines the average depth of the surface, which directly influences the hydrostatic pressure acting on the surface.

Q4: Can this formula be used for partially submerged surfaces?
A: This specific formula is designed for completely submerged surfaces. Partially submerged surfaces require different calculations as the pressure distribution changes.

Q5: What are typical applications of this calculation?
A: This calculation is used in designing submerged gates, dams, ship hulls, underwater structures, and various hydraulic engineering applications where fluid pressure forces need to be determined.