Definition
The total fluid force against a submerged surface is the integral of fluid pressure over the area of that surface.
Why It Matters
Calculating total fluid force is essential in civil engineering to design structures like dams and retaining walls that must withstand massive, distributed hydrostatic loads without failing.
Core Concepts
- Fluid Force Integral:
The total force F is obtained by integrating pressure over the area: (for vertical surfaces using horizontal strips).
- How to read: “The total force F equals the integral of w times h of y times L of y with respect to y.”
- Meaning / intuition: Because pressure is not uniform, you slice the surface into thin horizontal strips where pressure is (approximately) constant, compute dF = p dA for each, and sum via integral. Horizontal strips are used for vertical walls because depth (and thus p) is constant along each strip. This is the continuous version of “sum of forces on small areas.”
- Horizontal Strips: To calculate force on a vertical surface, we integrate over horizontal strips because pressure is constant at a constant depth.