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Date May 2016 Marks available 3 Reference code 16M.3.HL.TZ0.10
Level Higher level Paper Paper 3 Time zone Time zone 0
Command term Calculate and Explain Question number 10 Adapted from N/A

Question

A reservoir has a constant water level. Q is a point inside the outlet pipe at 12.0m depth, beside the tap for the outlet.

The atmospheric pressure is 1.05×105Pa and the density of water is 1.00×103kgm−3.

Calculate the pressure at Q when the tap is closed.

[1]
a.

Explain what happens to the pressure at Q when the tap is opened.

[2]
b.

The tap at Q is connected to an outlet pipe with a diameter of 0.10 m. The water flows steadily in the pipe at a velocity of 1.27ms−1. The viscosity of the water is 1.8×10−3Pas.

(i) Calculate the Reynolds number for this flow.

(ii) Explain the significance of this value.

[3]
c.

Markscheme

«118+105kPa»=2.23×105Pa

a.

ALTERNATIVE 1
«from Bernoulli’s Law» total pressure at Q = static pressure + dynamic pressure = constant «2.2×105Pa»
dynamic pressure «=\(\frac{1}{2}\)ρv2» increases from zero, so static pressure decreases

ALTERNATIVE 2
water rushes out of tap at higher velocity, so pressure is lower
due to Bernoulli’s Principle

b.

(i) \(R = \frac{{1.27 \times 0.05 \times 1.00 \times {{10}^3}}}{{1.8 \times {{10}^{ - 3}}}}\)
R=3.5×104

Allow use of diameter to give R=7.0×104.

(ii) flow is turbulent

Answers in (c)(i) and (c)(ii) must be consistent.

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

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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