Resultant Force Acting On Completely Submerged Plate Given Vertical Distance Of Centroid Calculator

Formula Used:

\[ F_R = (P_o + (\rho_{Fluid} \times [g] \times h_c)) \times A \]

Absolute Pressure above Liquid (P₀):

Density of Fluid (ρ):

kg/m³

Vertical Distance of Centroid (h_c):

Area of Surface (A):

m²

Resultant Force (F_R):

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1. What is Resultant Force on Submerged Plate?

The resultant force on a completely submerged plate is the total force exerted by a fluid on the surface of the plate. It accounts for both the atmospheric pressure above the liquid and the hydrostatic pressure due to the fluid's weight.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F_R = (P_o + (\rho_{Fluid} \times [g] \times h_c)) \times A \]

Where:

\( F_R \) — Resultant Force (N)
\( P_o \) — Absolute Pressure above Liquid (Pa)
\( \rho_{Fluid} \) — Density of Fluid (kg/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( h_c \) — Vertical Distance of Centroid (m)
\( A \) — Area of Surface (m²)

Explanation: The formula calculates the total force by combining atmospheric pressure and hydrostatic pressure at the centroid depth, then multiplying by the surface area.

3. Importance of Resultant Force Calculation

Details: Calculating resultant force is crucial for designing submerged structures, dams, gates, and underwater equipment. It helps determine structural integrity and safety factors.

4. Using the Calculator

Tips: Enter absolute pressure in Pascals, density in kg/m³, vertical distance in meters, and area in square meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between absolute and gauge pressure?
A: Absolute pressure includes atmospheric pressure, while gauge pressure measures pressure relative to atmospheric pressure.

Q2: Why use the centroid distance in the calculation?
A: The centroid represents the average depth where the resultant force acts on a submerged plane surface.

Q3: What is the typical range for fluid density?
A: Water density is about 1000 kg/m³, while other fluids range from 700-1300 kg/m³ for most common liquids.

Q4: Can this calculator be used for inclined surfaces?
A: This specific formula is for vertical surfaces. Inclined surfaces require additional trigonometric factors.

Q5: How accurate is this calculation for real-world applications?
A: The calculation provides theoretical results. Real-world applications may require additional safety factors and considerations for fluid dynamics.