Hydrostatic force
Problem 5.439 · easy
A vertical plate shaped like a triangle with its vertex at the top and a 2-ft horizontal base 1 ft below the vertex is submerged in water with its top 2 ft below the surface. Find the force of the water on one side. (Water weighs \( \displaystyle \frac{312}{5}\ \text{lb}/\text{ft}^3 \).)
- Let y be depth below the surface. A horizontal strip at depth y has width w(y) = 2*y - 4 and pressure 312/5·y.
- \[ \int\limits_{2}^{3} \frac{312 y \left(2 y - 4\right)}{5}\, dy = \frac{832}{5} \]Force = ∫ (pressure)(width) dy over the plate.✓ Proved
Answer \( \frac{832}{5} \approx 166.4\ \text{lb} \)
Lines: 1 proved, 1 not checked. The answer was also checked a second way, without looking at the solution. The reviewers disagree about how one step is explained; every verdict is in the receipt.
The full receipt
| Line | Status | Checked by | Detail |
|---|---|---|---|
| 1 | Not checked | — | a sentence; read, not computed |
| 2 | ✓ Proved | sympy 1.14.0 | simplify(lhs - rhs) reduced to 0 |
| answer, a second way | ✓ Checked independently | sympy 1.14.0 + mpmath 1.3.0 | numerical quadrature |
Reviewers
gpt-oss:20b: passqwen3.6:27b-mlx: inconclusive — reviewer returned a non-object
Every verdict on record (4)
gpt-oss:20b: pass 2026-10-09qwen3.6:27b-mlx: inconclusive 2026-10-09 — reviewer returned a non-objectgpt-oss:20b: pass 2026-10-09qwen3.6:27b-mlx: inconclusive 2026-10-09 — reviewer returned a non-object
Proved: SymPy reduced the difference between the two sides to zero. Checked independently: a separate
method, named above, confirmed it. Checked numerically: the two sides agree at every sampled point, which is evidence,
not proof. Reviewed: a model or a person read it; that is all a sentence can have. Solution by
generator:structured/hydrostatic_force, checked 2026-10-09 with SymPy 1.14.0.