Week 10 Study Guide — Forces on Submerged Bodies

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⚠️ Major gap up front. The official Week 10 lecture PDF (EGD102 - Lecture Week 10) was not in the source folder when these notes were generated. Everything in this week is reconstructed from Tutorial 10. Every claim below is at best inferred. Treat this study guide as a working hypothesis to be checked against the lecture deck once available.

Directly supported

These come straight out of Tutorial 10 (the only source available):

Topic	Direct source coverage
$F_{R} = P_{C} \cdot A$ for a submerged surface	Slide 3 (Resultant Pressure Force)
$P_{C} = ρ g y_{C}$ (gauge, fluid open to atmosphere)	Slide 3, definition of $P_{C}$
Centroid lookup table (rectangle, triangle, circle)	Slide 4
$y_{R} = y_{C} + I_{C} / (y_{C} A)$ for centre of pressure	Slide 5 (Centre of Pressure)
Pressure-prism interpretation of $y_{R}$	Slide 5
$I_{C}$ formulas: rectangle $b d^{3} /12$ , triangle $b h^{3} /36$ , circle $π r^{4} /4$ , semicircle $\approx 0.1102 r^{4}$	Slide 6 (Second Moment of Area)
Three worked exercises (vertical gate, triangular gate, retaining wall)	Slides 7–11
Portfolio 10 completed in workshop	Slide 12 (Learning Activities)

The tutorial expects you to be able to:

Look up centroid and $I_{C}$ for standard shapes from memory or table.
Compute $F_{R}$ and $y_{R}$ for a vertical submerged plate, given fluid + geometry.
Apply sliding and overturning checks to a long retaining wall (per-metre-width thinking).
Use moment balance about a hinge or toe to find a holding force or safety factor.

Strongly inferred

The lecture (PDF not available) almost certainly covers, in roughly this order:

The hydrostatic pressure equation $P = ρ g h$ and gauge vs absolute pressure.
Statement of $F_{R} = P_{C} A$ with the integral derivation $F_{R} = \int P d A = ρ g \int y d A = ρ g y_{C} A$ .
Statement of $y_{R}$ with the moment-of-pressure derivation (parallel-axis theorem).
One or two worked examples of submerged plates — most likely vertical or inclined rectangles.
Sliding and overturning checks for a dam wall, with the per-metre-width convention.
The Model → Visualise → Solve → Assess template (slide 2 of the tutorial is titled “Problem Solving Approach”, suggesting this is unit-wide).

Possible lecture content (not in tutorial)

Plausible lecture topics that the tutorial doesn’t visibly cover:

Inclined submerged plates — formula changes slightly because the “depth” axis isn’t the surface axis. Often introduced via $h_{C} = y_{C} sin θ$ .
Curved submerged surfaces — typically resolved into horizontal and vertical components, with the vertical component equalling the weight of fluid above.
Buoyancy / Archimedes’ principle — often paired with fluid statics in textbooks; may or may not appear in the lecture.
Manometers and pressure measurement — referenced on slide 12’s Mastering Physics list, so likely covered in lecture.

Gaps requiring official source check

The single biggest gap is the missing lecture PDF. Specifically, verify these once you have access to the deck:

Lecture PDF presence. Is there a EGD102 - Lecture Week 10 - post.pdf in the unit’s LMS that wasn’t in the source folder? If yes, every page in this week should be re-graded from inferred to directly-supported.
Sign convention for $y$ . Some texts measure $y$ down from the free surface (positive), others up. The tutorial appears to use down-positive; confirm.
Gauge vs absolute pressure. Slide 3 labels $P_{C}$ in “Pa”, which is dimensionally pressure but ambiguous on the gauge-vs-absolute question. The worked example uses gauge consistently.
Reference for the overturning lever arm. Is $H - y_{R}$ measured from the water surface or the wall base? (The retaining wall has wall height $4$ m but water depth $3.5$ m — these differ.)
Hinge location on the triangular gate (Exercise 2) — the tutorial figure must be inspected directly.
Inclined plates and curved surfaces — does the lecture cover these? The tutorial only does vertical surfaces.
Whether $g = 9.81$ or $g = 10$ — affects numerical answers by ~2%.

Worked examples (links)

Two notes cover the topic at different depths:

Cheatsheet — every formula, lookup table, recipe, and a 15-question quiz on one page.
In-depth analysis — derivations from first principles, the pressure-prism picture, and full worked examples for the vertical gate, triangular gate, and retaining wall.
Lecture summary — the source-faithful reconstruction from Tutorial 10 (the input to this study guide).

Common mistakes

Confusing $P_{C}$ with $P_{b}$ . $P_{C}$ is at the centroid, not the deepest point.
Confusing $y_{C}$ with $y_{R}$ . Centroid is geometric; centre of pressure is fluid-dependent.
Using the wrong reference for $\overset{y}{ˉ}$ . The lookup table gives $\overset{y}{ˉ}$ relative to the shape’s base; you must add the depth of the shape’s top edge to get $y_{C}$ relative to the free surface.
Forgetting “per metre” on long walls. $F_{P}$ and $W$ must both be per metre for the comparison to be valid.
Picking the wrong pivot in overturning checks. Pivot is the toe (front-bottom corner, dry side). Pick a sign convention and stick to it.
Mixing the wall height $H$ with the water depth $h_{w}$ when they differ. The formulas all use the wetted depth.

Practice questions

The three tutorial exercises are the obvious starting points. In order of difficulty:

Tutorial Q1 — vertical rectangular gate, pressure at bottom given → find $F_{R}$ and $y_{R}$ . (medium — straight rectangle, but you have to back out $y_{C}$ from $P_{b}$ .)
Tutorial Q2 — triangular gate at known depth → find $F_{P}$ and the holding force. (medium-hard — needs centroid of a triangle, then moment balance about a hinge.)
Tutorial Q3 — concrete retaining wall, sliding and overturning. (hard — three sub-parts, two distinct design checks, per-metre-width thinking.)

If you want more, replace the shape in Q1 with a triangle or circle, or move the gate so its top edge is below the free surface — the method is identical.

Assessment relevance

Portfolio 10 is completed during the workshop (slide 12). This is the immediate assessment.
Exam: forces on submerged surfaces and the centre-of-pressure formula appear almost every paper. Dam-wall sliding/overturning is a common application question.
Mastering Physics topics for this week (slide 12): pressure measurement, forces on submerged bodies, fluid statics.

Confidence report

Directly supported: Tutorial 10 content (slides 2–12), including the three worked exercises.
Inferred: The framing, sequencing, and emphasis of the lecture — because the lecture PDF was missing from the source folder.
Gap (largest): Everything the lecture covered that the tutorial doesn’t cite — most likely inclined plates, curved surfaces, possibly buoyancy and manometers.

Bottom line: if the lecture deck contains anything beyond vertical-plate fluid statics, this study guide will be incomplete in that area. Verify against the official slides before exam revision.

Source files used

EGD102-Physics/Tutorial 10.pdf (the only source available)

Source files expected but missing:

EGD102-Physics/Lecture Week 10 (post).pdf — not in source folder. The single biggest gap in this study guide.