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Question 18M.3.HL.TZ1.10

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Date May 2018 Marks available [Maximum mark: 6] Reference code 18M.3.HL.TZ1.10
Level HL Paper 3 Time zone TZ1
Command term Calculate, Outline, Show that, State Question number 10 Adapted from N/A
10.
[Maximum mark: 6]
18M.3.HL.TZ1.10

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

(a)

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

[1]

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]

(b)

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 = 2 g H .

[3]

Markscheme

PS = PT «as both are exposed to atmospheric pressure»

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

« 1 2 ρ v s 2 + ρgzS = ρgzT»

1 2 v S 2 = g(zT – zS) = gH

and so vS = 2 g H

 

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

Do not accept simple use of v =  2 as .

[3 marks]

The following data are available:

density of water = 1.00 × 10 3  kg  m − 3 viscosity of water = 1.31 × 10 − 3  Pa s diameter of the outlet pipe = 0.600  m velocity of water at outlet pipe = 59.4  m s − 1

(c.i)

Calculate the Reynolds number for the water flow.

[1]

Markscheme

R =  59.4 × 0.6 × 1 × 10 3 1.31 × 10 − 3 = 2.72 × 107

 

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

[1 mark]

(c.ii)

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

[1]

Markscheme

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

[1 mark]

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