Resultant Force Acting On Completely Submerged Rectangular Flat Plate Calculator

Resultant Force Formula:

\[ F_R = \left(P_o + \rho_{Fluid} \cdot g \cdot \left(s + \frac{b}{2}\right) \cdot \sin(\theta_T)\right) \cdot (a \cdot b) \]

Absolute Pressure above Liquid (P₀):

Density of Fluid (ρ):

kg/m³

Distance of Top Edge from Free Surface (s):

Height of Rectangular Plate (b):

Tilt Angle (θ):

rad

Width of Rectangular Plate (a):

Resultant Force (F_R):

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1. What is the Resultant Force Formula?

The Resultant Force formula calculates the total force acting on a completely submerged rectangular flat plate. It accounts for atmospheric pressure, fluid density, plate dimensions, and tilt angle to determine the net hydrostatic force.

2. How Does the Calculator Work?

The calculator uses the Resultant Force formula:

\[ F_R = \left(P_o + \rho_{Fluid} \cdot g \cdot \left(s + \frac{b}{2}\right) \cdot \sin(\theta_T)\right) \cdot (a \cdot b) \]

Where:

\( P_o \) — Absolute pressure above liquid (Pa)
\( \rho_{Fluid} \) — Density of fluid (kg/m³)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( s \) — Distance of top edge from free surface (m)
\( b \) — Height of rectangular plate (m)
\( \theta_T \) — Tilt angle (rad)
\( a \) — Width of rectangular plate (m)

Explanation: The formula combines atmospheric pressure with hydrostatic pressure at the centroid of the plate, multiplied by the plate area to get the resultant force.

3. Importance of Resultant Force Calculation

Details: Accurate resultant force calculation is crucial for structural design of submerged components, dam design, underwater construction, and marine engineering applications where fluid pressure forces must be properly accounted for.

4. Using the Calculator

Tips: Enter all values in SI units. Pressure in Pascals, density in kg/m³, distances in meters, 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 tilt angle?
A: The tilt angle affects the effective depth of the plate and the distribution of hydrostatic pressure across the surface.

Q2: Why use absolute pressure instead of gauge pressure?
A: Absolute pressure includes atmospheric pressure, which contributes to the total force acting on the submerged surface.

Q3: What assumptions are made in this formula?
A: The formula assumes the fluid is incompressible, the plate is completely submerged, and the fluid is at rest (hydrostatic conditions).

Q4: How does plate orientation affect the resultant force?
A: The orientation affects the pressure distribution and the location of the center of pressure, though the magnitude calculation remains the same.

Q5: Can this formula be used for curved surfaces?
A: No, this specific formula is designed for flat rectangular plates. Curved surfaces require different integration methods.