| Date | May 2016 | Marks available | 1 | Reference code | 16M.3.HL.TZ0.10 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Calculate | 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.
Explain what happens to the pressure at Q when the tap is opened.
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.
Markscheme
«118+105kPa»=2.23×105Pa
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
(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.
