Hydrostatic Force Calculator

Hydrostatic Force Calculator

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This Hydrostatic Force Calculator is designed to compute the force exerted by a fluid on a submerged surface. It considers key parameters such as fluid density, surface area, depth to the centroid, and gravitational acceleration. This tool instantly provides results in Newtons (N), kilonewtons (kN), and pounds-force (lbf), helping you understand and compare hydrostatic forces in different unit systems.

Whether you’re analyzing tanks, dams, or fluid containers, this calculator simplifies complex calculations with just a few inputs.

What is Hydrostatic Force?

Hydrostatic force is the force that a fluid at rest exerts on a submerged surface. This force comes from the pressure of the fluid acting over an area. It is important in fields like civil, hydraulic, and mechanical engineering, particularly when looking at dams, tanks, gates, and other submerged surfaces.

Hydrostatic pressure gets stronger as you go deeper into the fluid. This pressure pushes straight against the surface it touches. The total hydrostatic force is the total of all these small pressure forces across the surface area.

How to Calculate Hydrostatic Force

To calculate hydrostatic force, use the formula:

F = ρ × g × hₐ × A

Where:

• F = Hydrostatic Force (N)
• ρ = Fluid density (kg/m³)
• g = Acceleration due to gravity (9.81 m/s²)
• hc​ = Depth to the centroid of the surface from the fluid surface (m)
• A = Area of the submerged surface (m²)

Example 1: Vertical Wall of a Tank

Problem:

A rectangular vertical gate in a tank is 2 m wide and 3 m high. The gate is submerged in water, and the centroid of the gate is 1.5 m below the water surface. Find the hydrostatic force.

Given:

• Width = 2 m
• Height = 3 m ⇒ Area A =2 × 3 = 6 m²
• ρ = 1000 kg/m3 (density of water)
• g = 9.81 m/s²

Solution:

F = ρ⋅g⋅hc⋅AF

F = 1000 ⋅ 9.8 1⋅ 1.5 ⋅ 6 = 88,290 N

Answer: The hydrostatic force is 88,290 N or 88.29 kN

Example 2:

Problem:

Find the force on a horizontal plate submerged 2 ft below the surface of oil with a density of 55 lb/ft³. The area of the plate is 4 ft².

Solution:

Convert units:

• ρ = 55 lb/ft³ = 55 × 16.0185 = 881 kg/m³
• hc = 2 ft = 0.6096 m
• A = 4 ft² = 0.3716 m²

Now plug into the formula:

F = 881 ⋅ 9.81 ⋅ 0.6096 ⋅ 0.3716 = 1,962.45N

Answer: Hydrostatic force = 1,962.45 N ≈ 2.0 kN ≈ 441 lbf