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Date	May 2018	Marks available	1	Reference code	18M.3.HL.TZ1.10
Level	Higher level	Paper	Paper 3	Time zone	1
Command term	Calculate	Question number	10	Adapted from	N/A

Question

The water supply for a hydroelectric plant is a reservoir with a large surface area. An outlet pipe takes the water to a turbine.

M18/4/PHYSI/HP3/ENG/TZ1/10

The following data are available:

$\begin{array}{*{20}{l}} {{\text{density of water}}}&{ = 1.00 \times {{10}^3}{\text{ kg }}{{\text{m}}^{ - 3}}} \\ {{\text{viscosity of water}}}&{ = 1.31 \times {{10}^{ - 3}}{\text{ Pa s}}} \\ {{\text{diameter of the outlet pipe}}}&{ = 0.600{\text{ m}}} \\ {{\text{velocity of water at outlet pipe}}}&{ = 59.4{\text{ m}}{{\text{s}}^{ - 1}}} \end{array}$

State the difference in terms of the velocity of the water between laminar and turbulent flow.

[1]

The water level is a height H above the turbine. Assume that the flow is laminar in the outlet pipe.

Show, using the Bernouilli equation, that the speed of the water as it enters the turbine is given by v = $\sqrt {2gH}$ .

[3]

Calculate the Reynolds number for the water flow.

[1]

c.i.

Outline whether it is reasonable to assume that flow is laminar in this situation.

[1]

c.ii.

Markscheme

in laminar flow, the velocity of the fluid is constant «at any point in the fluid» «whereas it is not constant for turbulent flow»

Accept any similarly correct answers.

[1 mark]

P_S = P_T «as both are exposed to atmospheric pressure»

then V_T = 0 «if the surface area ofthe reservoir is large»

« $\frac{1}{2}\rho v_s^2$ + ρgz_S = ρgz_T»

$\frac{1}{2}v_S^2$ = g(z_T – z_S) = gH

and so v_S = $\sqrt {2gH}$

MP1 and MP2 may be implied by the correct substitution showing line 3 in the mark scheme.

Do not accept simple use of v = $\sqrt {2{\text{as}}}$ .

[3 marks]

R = $\frac{{59.4 \times 0.6 \times 1 \times {{10}^3}}}{{1.31 \times {{10}^{ - 3}}}}$ = 2.72 × 10⁷

Accept use of radius 0.3 m giving value 1.36 × 10⁷.

[1 mark]

c.i.

as R > 1000 it is not reasonable to assume laminar flow

[1 mark]

c.ii.

Examiners report

[N/A]

c.i.

[N/A]

c.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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