Week 9 Study Guide — Pressure Measurement + Submerged Surfaces

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Directly supported by notes

The following sub-topics are explicitly worked in the lecture slides, the lecturer’s worked notes, or the tutorial:

Topic	Direct source coverage
Resultant pressure force $F_{R} = ρ g y_{C} A$	Lecture slides p. 2, Tutorial p. 7. Worked in Examples 1, 3, Tutorial 3, Tutorial 4.
Centroids of standard shapes	Lecture slides pp. 3–5 (centroid table).
Vertical dam simplification	Lecture slide p. 7. Recovered numerically in Tutorial Ex 3 ( $h /3$ above base).
Centre of pressure $y_{R} = y_{C} + I_{C} / (y_{C} A)$	Lecture slides pp. 8–9, Tutorial p. 9. Worked in Examples 1, 2, 3, Tutorial 3, Tutorial 4.
Second moment of area	Lecture slide p. 10 (formulas for rect, tri, circle, semicircle).
Manometer + absolute vs gauge pressure	Tutorial pp. 3–4, Exercises 1 and 2 with full solutions.
Hinged-gate moment balance	Example 1 part (b), explicit FBD and $\sum M_{H} = 0$ in lecturer’s notes.

The tutorial directly tests both threads: Exercises 1–2 are manometer / pressure-measurement problems, Exercises 3–4 are submerged-surface problems (rectangle + triangle).

The workshop expects you to be able to:

Identify the centroid and area of a standard plane shape on sight.
Compute $F_{R}$ on a vertical or inclined submerged plate using the formula sheet.
Locate the centre of pressure using $y_{R} = y_{C} + I_{C} / (y_{C} A)$ .
Walk a manometer between two points using the $+ ρ g h$ / $- ρ g h$ sign convention.
Set up the free-body diagram of a hinged gate and solve a single moment equation.

Strongly inferred from workshop materials

The lecture almost certainly covers, in this order:

Recap of hydrostatic pressure $p = ρ g h$ from Week 8.
Definition of the resultant pressure force on a submerged plane surface.
Centroid review using the supplied standard-shape table.
Centre of pressure as the centroid of the pressure prism (the 3-D wedge).
Why $y_{R} > y_{C}$ — geometric / pressure-prism argument before the formula.
Second moment of area as the geometric quantity tying $y_{R}$ to $y_{C}$ .
An L-shaped or counter-weighted gate example (Example 4 in the slide deck — the hardest in the set).
Absolute vs gauge pressure and the manometer walk as the bridge back to Week 8.

Possible lecture content (not in notes)

May appear in the lecture, but is not in the workshop PDFs:

Inclined submerged surfaces (plates tilted relative to vertical).
Curved submerged surfaces (would need horizontal + vertical force resolution and the buoyancy argument).
Submerged surfaces with the top edge above the free surface (only the wetted part contributes).
Buoyancy and Archimedes’ principle (closes out fluid statics in some textbooks).
Practical pressure-measurement devices beyond U-tubes (Bourdon tubes, piezometers, inclined manometers).

Gaps requiring official source check

The lecture’s exact ordering of topics — particularly whether the manometer material is delivered before or after the submerged-surface material.
Whether Example 4 (L-shaped gate with counter-weight) is fully solved on the slides or only set up.
Whether the exam will use $g = 9.81$ or $g = 9.8$ — the lecture and tutorial materials are inconsistent. Check the formula sheet for your sitting.
The lecturer’s preferred convention for triangle problems (apex up vs apex down). Tutorial Ex 4 uses apex up; the centroid then sits $d /3$ below the apex.

Worked examples

Three notes cover the topic at different depths:

Lecture summary — the directly-supported reconstruction. All four tutorial exercises and all four lecture examples worked end-to-end.
Cheatsheet — every rule, table, and recipe in one page. Includes the full quiz (12–18 MCQs, mixed difficulty, reshuffles every visit).
In-depth analysis — why each formula is the shape it is: the parallel-axis derivation of $y_{R}$ , the pressure-prism argument for $y_{R} > y_{C}$ , the manometer walk as a path integral, and a full exam-style worked example.

Common mistakes

Measuring $y_{C}$ from the top of the plate instead of from the free surface.
Using $b h^{3} /12$ for a triangle’s $I_{C}$ instead of $b h^{3} /36$ .
Putting the centre of pressure above the centroid (it’s always below for plates beneath the free surface).
Mixing absolute and gauge pressure on a gate exposed to atmosphere on both sides. Use gauge — atmosphere cancels.
Wrong sign in the manometer walk. Down adds, up subtracts.
Treating $S G$ as a density (it isn’t — multiply by $ρ_{water} = 1000$ ).
Forgetting that the moment arm of $F_{R}$ goes to $y_{R}$ , not $y_{C}$ .

Practice questions

Pick any from the tutorial. Recommended for a first pass:

Pressure measurement: Tutorial Exercises 1 (single-fluid manometer) and 2 (double U-tube — the higher-difficulty manometer problem).
Submerged rectangles: Tutorial Exercise 3 (sea-water lock — also exercises the vertical-dam shortcut).
Submerged triangles: Tutorial Exercise 4 (right triangle — the highest-value drill for triangle-specific mistakes).
Hinged gates: lecturer’s Example 1 (rectangular gate with horizontal holding force) — full FBD + moment balance.
Stretch: Example 4 from the slides (L-shaped gate with counter-weight).

Assessment relevance

Submerged-surface problems appear on essentially every EGD102 paper. Expect either a rectangular gate or a triangular plate.
Manometer problems are common short-answer items, often worth $3$ – $5$ marks each.
Portfolio tasks expect you to draw and label the pressure prism, not just compute numbers.
The L-shaped counter-weighted gate is the highest-difficulty variant — if it appears, it carries disproportionate marks.

Confidence report

Directly supported: $F_{R}$ , $y_{R}$ , $I_{C}$ formulas; centroid table; manometer walk rule; all four tutorial exercises and four lecture examples with their numbers.
Inferred: the lecture’s ordering and pedagogical framing; the precise wording of definitions (e.g. “pressure prism”) relative to the slides.
Gap: any lecture content beyond what the tutorial exercises directly imply — especially inclined / curved surfaces and buoyancy if introduced this week.

Source files used

EGD102-Physics/Lecture9_CTP1.pdf
EGD102-Physics/EGD102_Week9_Lecture.pdf
EGD102-Physics/Tutorial 9.pdf
EGD102-Physics/Tutorial 9_Solutions.pdf