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Date	May 2019	Marks available	2	Reference code	19M.3.HL.TZ1.10
Level	Higher level	Paper	Paper 3	Time zone	1
Command term	Calculate	Question number	10	Adapted from	N/A

Question

Gasoline of density 720 kg m^–3 flows in a pipe of constant diameter.

State one condition that must be satisfied for the Bernoulli equation

$\frac{1}{2}$ ρv² + ρgz + ρ = constant

to apply

[1]

Outline why the speed of the gasoline at X is the same as that at Y.

[1]

b.i.

Calculate the difference in pressure between X and Y.

[2]

b.ii.

The diameter at Y is made smaller than that at X. Explain why the pressure difference between X and Y will increase.

[2]

b.iii.

Markscheme

flow must be laminar/steady/not turbulent ✔

fluid must be incompressible/have constant density ✔

fluid must be non viscous ✔

«continuity equation says» Av = constant «and the areas are the same» ✔

b.i.

Bernoulli: « $\frac{1}{2}$ $\rho v_x^2$ + 0 + P_x = $\frac{1}{2}$ $\rho v_y^2$ + pgH + P_y » gives P_x − P_y = pgH ✔

P_x − P_y= 720 × 9.81 × 1.2 = 8.5 «kPa» ✔

Award [2] for bald correct answer.

Watch for POT mistakes.

b.ii.

the fluid speed at Y will be greater «than that at X» ✔

reducing the pressure at Y
OR
the formula used to show that the difference is increased ✔

b.iii.

Examiners report

Gasoline in a pipe. In a), most of the candidates well noted that for the Bernoulli equation, the fluid must be” non-viscous”, some noted, “laminar” and a few, “incompressible”. Some students stated vaguer and less concrete responses such as “the fluid must be ideal”.

In b) most candidates well noted and understood the application of the continuity equation.

b.i.

In b) most candidates well noted and understood the application of the continuity equation and successfully went on to correctly calculate the pressure difference.

b.ii.

Sub-question iii) well discriminated between the better and weaker candidates. As weaker candidates often wrote that “lower diameter means higher pressure” without a direct reference to the greater speed at Y implying reduced pressure.

b.iii.

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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Option B: Engineering physics » Option B: Engineering physics (Additional higher level option topics)

Option B: Engineering physics

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Markscheme

Examiners report

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