DSE Physics | Pressure in Fluids Lesson-Prep Guide (Tutor Edition) | p = F/A, p = rho g h, Upthrust and Hydraulics

2026-11-02

Tutor lesson-prep guides · Secondary Physics

Students can quote p = F/A and still say a full bottle presses harder than a tall thin tube. This lesson makes depth, not volume, the deciding variable.

Objectives — Students can: (1) compute pressure from force and area and explain why the same force gives more pressure on a smaller area; (2) use p = rho g h to compare pressures at depth, including the effect of adding atmospheric pressure; (3) calculate upthrust from displaced volume, decide whether an object floats, and use Pascal’s principle in a hydraulic system.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Force and weight	How do mass and weight differ	W = mg, weight in newtons
Density	What is density	Mass divided by volume
Area units	How many square metres in 20 square centimetres	0.0020 square metres

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-10 min	Pressure and area	p = F/A with the same force on two areas	Get 30,000 Pa then 120,000 Pa
10-24 min	Depth	p = rho g h, independent of shape	Get 29,430 Pa at 3 m
24-36 min	Absolute and gauge	Add or subtract atmospheric pressure	State which one is asked
36-46 min	Upthrust	Weight of displaced fluid, float or sink	Get 19.62 N
46-56 min	Hydraulics	Same pressure, different areas, force multiplied	Get 10,000 N out
56-60 min	Exit check	Three questions marked on the spot	All three right

03 Teaching script (read it out)

Scene 1: Pressure is force shared over an area

A force of 600 N spread over 0.02 square metres gives p = 600 / 0.02 = 30,000 Pa. The same force on 0.005 square metres, a quarter of the area, gives 120,000 Pa, exactly four times more.
This is why a drawing pin works: the thumb applies a modest force to a large head and the point delivers enormous pressure to a tiny area. It is also why snowshoes help a walker: the same weight is spread over a bigger area, so the pressure on the snow falls.
Keep the units honest: 1 Pa is 1 N per square metre, and 1 square centimetre is 0.0001 square metres, so a student who forgets the conversion is out by a factor of 10,000.

Ask students: why does a sharp knife cut better than a blunt one at the same force (smaller contact area, higher pressure).

Scene 2: Depth sets the pressure, not the amount of water

In a liquid at rest, p = rho g h. Water at 3 m depth: p = 1000 x 9.81 x 3 = 29,430 Pa, which is a gauge pressure. Add the atmosphere and the absolute pressure is 130,755 Pa.
Shape and width do not appear in the formula, so a narrow tube and a wide tank give the same pressure at the same depth. That is why a dam is thickest at the bottom and why connected vessels settle at one level.
Mercury is 13.6 times denser than water, so only 0.15 m of mercury gives 20,012 Pa, more than half the water column at 3 m. Density matters as much as depth.

Ask students: does a wider tank give more pressure at the same depth (no, only depth and density matter).

Scene 3: Upthrust and hydraulics come from the same rule

A block of volume 0.002 cubic metres fully under water displaces 0.002 cubic metres, so the upthrust is the weight of that water: 1000 x 9.81 x 0.002 = 19.62 N.
If the block weighs 15 N, less than the upthrust, it rises until the displaced weight equals 15 N, which happens when about 76.5% of its volume is submerged.
In a hydraulic press, a 200 N force on 0.005 square metres creates 40,000 Pa, and the same pressure on 0.25 square metres produces 10,000 N: the force is multiplied 50 times. Nothing is free, because the large piston moves 50 times less distance, so the work done is unchanged.
That last sentence is the mark that separates a Grade 5 answer from a Grade 3 one.

Ask students: if force is multiplied 50 times, what is not multiplied (the distance moved, so energy is conserved).

04 Question types and worked steps

Type	Example	Steps	Answer
Calculation	Pressure from force and area	Convert area to square metres, then divide	30,000 Pa
Calculation	Pressure at depth	p = rho g h, then decide gauge or absolute	29,430 Pa
Calculation	Upthrust and floating	Weight of displaced fluid; compare with weight	19.62 N
Calculation	Hydraulic press	Same pressure at both pistons, then F = pA	10,000 N

Sanity check (teach this): Use weight in newtons, not mass in kilograms; a 60 kg person weighs about 589 N.
Convert square centimetres to square metres before dividing, multiplying by 0.0001.
Pressure at depth depends on depth and density only, so a smaller volume at the same depth gives the same pressure.
Upthrust equals the weight of fluid displaced, not the weight of the object; a floating object displaces its own weight, a sunk one displaces its own volume.

05 Independent practice (3 questions)

Question	Answer	What to watch
600 N over 0.02 square metres	30,000 Pa	Force divided by area
Gauge pressure at 3 m in water	29,430 Pa	1000 x 9.81 x 3
Upthrust on 0.002 cubic metres fully submerged	19.62 N	Density x g x volume

06 Common mistakes and what to say

Mistake	Student writes	Say this
Using mass instead of weight	Answering p = 60 / 0.02 = 3000 Pa	Multiply the mass by 9.81 first: weight is about 589 N.
Skipping the area conversion	Answering 600 / 20 = 30 Pa	20 square centimetres is 0.002 square metres, so the answer is far larger.
Assuming more water means more pressure	Answering that a wide tank presses harder	At the same depth the pressure is identical; only depth and density matter.
Claiming a hydraulic press creates energy	Answering that force and distance are both multiplied	The small piston moves further; the work done is the same.

07 Homework (paper, section and question numbers)

Secondary physics chapter index — All chapters and practice
All lesson-prep guides — Compare other subjects

08 Exit check (last 5 minutes)

Question	Answer	Decision
600 N over 0.005 square metres	120,000 Pa	All three right: move to thermal physics
Pressure at 3 m in water	29,430 Pa	One wrong: reteach density times depth
Upthrust on 0.002 cubic metres	19.62 N	Two wrong: return to act three

09 Tutor FAQ

Do students need to memorise atmospheric pressure?

Knowing 101,325 Pa helps, but the key skill is deciding whether the question wants gauge or absolute pressure.

Why does a ship float when steel sinks?

The hull displaces a weight of water greater than the ship’s weight, so the average density of the vessel is below that of water.

Is p = rho g h valid for gases?

Only over small height changes; gas density varies with pressure, so the simple formula fails over large heights.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.