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Date	November 2018	Marks available	2	Reference code	18N.3.HL.TZ0.10
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Calculate	Question number	10	Adapted from	N/A

Question

A horizontal pipe is inserted into the cylindrical tube so that its centre is at a depth of 5.0 m from the surface of the water. The diameter D of the pipe is half that of the tube.

When the pipe is opened, water exits the pipe with speed u and the surface of the water in the tube moves downwards with speed v.

An ice cube floats in water that is contained in a tube.

The ice cube melts.

Suggest what happens to the level of the water in the tube.

[2]

a.

Outline why u = 4v.

[2]

b.i.

The density of water is 1000 kg m^–3. Calculate u.

[2]

b.ii.

Markscheme

ice displaces its own weight of water / OWTTE

OR

melted ice volume equals original volume displaced / OWTTE ✔

no change will take place ✔

a.

continuity equation says v × A₁ = u × A₂ ✔

«and» A₁ = 4A₂ ✔

«giving result»

b.i.

Bernoulli:

« $\frac{1}{2}\rho {v^2} + \rho gH + {P_{{\text{atm}}}} = \frac{1}{2}\rho {u^2} + 0 + {P_{{\text{atm}}}}$ » gives $\frac{1}{2} \times 1000 \times \frac{{{u^2}}}{{16}} + 1000 \times 9.8 \times 5.0 = \frac{1}{2} \times 1000 \times {u^2}$ ✔

u = 10.2 «m s^–1» ✔

Accept solving directly via conservation of energy.

b.ii.

Examiners report

[N/A]

a.

[N/A]

b.i.

[N/A]

b.ii.

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Additional higher level option topics) » B.3 – Fluids and fluid dynamics (HL only)

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