Playbook
Mechanical Properties of Fluids
124 q - 2.96/paper - 19% HARD. Two thirds surface tension, and capillary rise (38 q) has never produced a HARD question.
- Questions in the bank
- 124
- q/paper (2024–25 papers)
- 2.96
- Tagged HARD
- 19%
- Subtopics
- 5
Strand: Cornerstone
When you’ll see it
A drop or a bubble, a liquid in a capillary tube, a sphere falling through oil, or water flowing through a pipe of changing width.
How this chapter is tested
124 q at 2.96 a paper, 19% HARD — and two thirds of the chapter is surface tension. Surface Tension and Surface Energy (42 q, 29%) and Excess Pressure and Capillary Rise (38 q, 0%) together are 80 questions.
The capillary page has never produced a HARD question. It is two formulas: h = 2T cos θ / rρg, and excess pressure 2T/r in a drop or 4T/r in a soap bubble (two surfaces). The surface-energy page is where the HARD sits — work to blow a bubble, energy released when drops merge — and the bubble's two surfaces are the usual slip.
The flow pages are smaller: viscosity and terminal velocity (21 q, 19%) and Bernoulli with continuity (17 q, 18%). Pressure, Buoyancy, and Archimedes is 6 questions at 83% HARD and 0.13 a paper — last in the prep queue.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Capillary rise and excess pressure
h = 2T cos θ / rρg, so h ∝ 1/r. Drop: ΔP = 2T/r. Soap bubble: ΔP = 4T/r.
Surface energy
Work = T × (increase in area). A soap bubble has two surfaces, so blowing one of radius r takes 8πr²T.
Viscosity and terminal velocity
Stokes: F = 6πηrv. Terminal velocity ∝ r², so a drop of double radius falls four times as fast.
Continuity and Bernoulli
A₁v₁ = A₂v₂; P + ½ρv² + ρgh is constant along a streamline. Torricelli: v = √(2gh).
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Counting one surface on a soap bubble
A soap film has two surfaces. Excess pressure is 4T/r and surface energy doubles. A drop has one.
Merging drops conserve volume, not area
n drops merging into one: R = n^(1/3) r. The area falls, so energy is RELEASED. Conserving area instead gives a wrong radius.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Mechanical Properties of Fluids notesDrill every mechanical properties of fluids question
124 questions from the bank, scoped to 5 bundled subtopics.
Drill one subtopic at a time
The 5 subtopics this playbook covers, in catalog order.
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