Twenty minutes or less.

⚠️ The official Week 10 lecture PDF was missing from the source folder. This prep page is built from Tutorial 10 only. Confidence is inferred — sanity-check any numeric answer against the lecture deck if you have it.

5-minute version

Three connected questions, one sentence each.

• How big is the push? $F_R=\rho g{y}_{C}A$ (pressure at the centroid, times wetted area).
• Where does it act? $y_R=y_C+I_C/(y_{C}A)$ — always below the centroid.
• Will the wall hold? Sliding: $\mu W\ge F_P$. Overturning: $M_{\text{restoring}}>M_{\text{overturning}}$ about the toe.

Open the cheatsheet quiz, do 3 easy questions, close it. You’re prepped.

20-minute prep plan

Time	Action
0–5 min	Skim the cheatsheet tables: centroid lookup, $I_C$ lookup, the three formulas.
5–10 min	Re-do Exercise 1 (vertical gate) from Tutorial 10 longhand, covering the worked answer.
10–15 min	Take the cheatsheet quiz. Aim for the medium/hard ones.
15–20 min	Skim the in-depth note — specifically the pressure-prism picture and the retaining-wall overturning check.

What to revise first

Two slips appear most often:

1. Confusing $P_C$ with $P_b$. Pressure at the centroid, not at the bottom. For a rectangle with its top at the free surface, $P_C=P_b/2$.
2. Missing the “per metre” convention on long walls. Both $F_P$ and $W$ must be per metre, then the sliding inequality and the moment ratio compare like for like.

Key formulas

$$F_R=P_C\cdot A=\rho g{y}_{C}A$$ $$y_R=y_C+\frac{I_C}{y_{C}A}$$ $$\text{Sliding:}\mu W\ge F_P\Rightarrow t\ge \frac{F_P}{\mu {\rho }_{c}gH}$$ $$\text{Overturning:}\underset{M_{\text{restoring}}}{\underbrace{W\cdot \frac{t}{2}}}>\underset{M_{\text{overturning}}}{\underbrace{F_P\cdot (H-y_R)}}$$

Lookups to have at your fingertips (rectangle is the most common):

Shape	$A$	$\bar{y}$ (from base)	$I_C$
Rectangle ($b\times d$)	$bd$	$d/2$	$b{d}^3/12$
Triangle ($b\times h$)	$bh/2$	$h/3$	$b{h}^3/36$
Circle (radius $r$)	$\pi r^2$	centre	$\pi r^4/4$
Semicircle (radius $r$)	$\pi r^2/2$	$4r/(3\pi )$ from flat edge	$\approx 0.1102r^4$

Likely workshop tasks

Task type	What the setup usually looks like
Vertical rectangular gate	Find $F_R$ and $y_R$. Watch out for the gate not starting at the free surface.
Triangular gate	Find $F_P$ and the holding force at the hinge. Centroid is at $h/3$, not $h/2$.
Retaining wall	Per-metre $F_P$, then sliding ($t$ minimum), then overturning ($t$ adequacy).

Workshop 10 finishes with Portfolio 10. Make sure your written solution follows the unit’s Model → Visualise → Solve → Assess structure.

Mistakes to avoid

• Treating $P_b$ (bottom-edge pressure) as $P_C$.
• Forgetting that $\bar{y}$ in the lookup table is relative to the shape, not the free surface.
• Confusing $y_C$ and $y_R$ — they are equal only for a horizontal plate.
• Mixing wall height with water depth (they’re often different — water doesn’t fill the wall).
• Dropping units, especially on $I_C$ (m⁴), $F_R$ (N or kN), and per-metre quantities (kN/m, kN·m/m).
• Picking the wrong moment pivot for the overturning check (always: toe of the wall, downstream side).

Mini self-test

Try these without notes. Five minutes total.

1. A vertical rectangular gate $2$ m wide and $4$ m tall has its top edge at the free surface (water, $\rho =1000$ kg/m³). Find $F_R$ and the depth of the centre of pressure $y_R$.
2. A retaining wall (concrete ${\rho }_c=2400$ kg/m³) is $5$ m high and $1.2$ m thick, retaining water $5$ m deep. Friction coefficient $\mu =0.45$. Does it pass the sliding check, per metre of wall?
3. For the same wall, compute $M_{\text{restoring}}$ and $M_{\text{overturning}}$ per metre. Pass or fail overturning?

Answers:

Question	Answer
1	$y_C=2$ m, $A=8$ m². $F_R=1000\times 9.81\times 2\times 8\approx 156.96$ kN. $I_C=2\cdot 4^3/12=10.67$ m⁴. $y_R=2+10.67/(2\times 8)=2.667$ m (i.e. $2H/3$).
2	$F_P=1000\times 9.81\times 2.5\times 5\approx 122.6$ kN/m. $W=2400\times 9.81\times 1.2\times 5\approx 141.3$ kN/m. $\mu W=0.45\times 141.3=63.6$ kN/m $<F_P$. Fails sliding — wall is too thin.
3	$I_C=1\cdot 5^3/12\approx 10.42$ m⁴. $y_R=2.5+10.42/(2.5\times 5)=3.33$ m. Lever arm above base = $5-3.33=1.67$ m. $M_{\text{over}}=122.6\times 1.67\approx 204.7$ kN·m/m. $M_{\text{rest}}=141.3\times 0.6\approx 84.8$ kN·m/m. Fails overturning too (factor $\approx 0.41$). The wall needs to be thicker.

If you got Q1 right and at least one of Q2/Q3, you’re workshop-ready. If not, redo Tutorial 10 Exercise 3 longhand.

Done checklist

• Centroid table memorised (rectangle, triangle, circle).
• $I_C$ table memorised (or written on your formula sheet).
• Tutorial 10 Exercise 1 completed without looking at worked answer.
• Cheatsheet quiz attempted.
• Mini self-test attempted; sliding/overturning logic feels routine.
• Per-metre-width convention understood.

That’s it. Close the laptop.

Source files used

• EGD102-Physics/Tutorial 10.pdf

Source files expected but missing:

• The official Week 10 lecture PDF — re-check this prep page against the lecture deck if it becomes available.