Hydrostatic force
Problem 5.503 · easy
A vertical plate shaped like a rectangle 1 m wide and 1 m tall is submerged in water with its top 1 m below the surface. Find the force of the water on one side. (Water weighs \( \displaystyle 9800\ \text{N}/\text{m}^3 \).)
- Let y be depth below the surface. A horizontal strip at depth y has width w(y) = 1 and pressure 9800·y.Reviewed
- \[ \int\limits_{1}^{2} 9800 y\, dy = 14700 \]Force = ∫ (pressure)(width) dy over the plate.✓ Proved
Answer \( 14700 \approx 14700\ \text{N} \)
✓ Nihil obstat Lines: 1 proved, 1 reviewed. The answer was also checked a second way, without looking at the solution. Reviewers found nothing wrong with the explanation.
The full receipt
| Line | Status | Checked by | Detail |
|---|---|---|---|
| 1 | Reviewed | reviewers: gpt-oss:20b, qwen3.6:27b-mlx | 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: pass — The solution correctly sets up the hydrostatic force integral using depth y, with correct bounds (1 to 2) and pressure formula.
Every verdict on record (4)
gpt-oss:20b: pass 2026-10-12qwen3.6:27b-mlx: pass 2026-10-12 — The solution correctly sets up the hydrostatic force integral using depth y, with correct bounds (1 to 2) and pressure formula.gpt-oss:20b: pass 2026-10-12qwen3.6:27b-mlx: pass 2026-10-12 — The setup correctly identifies the depth variable, pressure formula, and integration bounds for the submerged plate. The calculation is correct.
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 2026-10-12 with SymPy 1.14.0.