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Question 18M.3.HL.TZ2.10

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Date May 2018 Marks available [Maximum mark: 5] Reference code 18M.3.HL.TZ2.10
Level HL Paper 3 Time zone TZ2
Command term Estimate, Outline, Show that Question number 10 Adapted from N/A
10.
[Maximum mark: 5]
18M.3.HL.TZ2.10

Two tubes, A and B, are inserted into a fluid flowing through a horizontal pipe of diameter 0.50 m. The openings X and Y of the tubes are at the exact centre of the pipe. The liquid rises to a height of 0.10 m in tube A and 0.32 m in tube B. The density of the fluid = 1.0 × 103 kg m–3.

M18/4/PHYSI/HP3/ENG/TZ2/10

(a)

Show that the velocity of the fluid at X is about 2 ms–1, assuming that the flow is laminar.

[3]

Markscheme

1 2 ρ v X 2 = p Y − p X = ρ g Δ h

vX =  2 × 9.8 × ( 0.32 − 0.10 )

vx = 2.08 «ms–1»

[3 marks]

The viscosity of water is 8.9 × 10–4 Pa s.

(b.i)

Estimate the Reynolds number for the fluid in your answer to (a).

[1]

Markscheme

R = « v r ρ η = 2.1 × 0.25 × 10 3 8.9 × 10 − 4 » 5.9 × 105

[1 mark]

(b.ii)

Outline whether your answer to (a) is valid.

[1]

Markscheme

(R > 1000) flow is not laminar, so assumption is invalid

 

OWTTE

[1 mark]

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