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МІНІСТЕРСТВО ОСВІТИ І НАУКИ УКРАЇНИ

Запорізький національний технічний університет

Методичні вказівки

до практичних занять та самостійної роботи з дисципліни «Англійська мова»

для студентів денної форми навчання

спеціальності «Системний аналіз та управління»

2009

Методичні вказівки до практичних занять та самостійної роботи з дисципліни «Англійська мова» для студентів денної форми навчання спеціальності «Системний аналіз та управління»/Укл. Т.О. Сокол. – Запоріжжя: ЗНТУ, 2009. – 28с.

Укладач: Т.О. Сокол, ст. викл.

Рецензент: Т.М. Суворова, ст. викл.

Експерт: Г В. Корніч, професор, зав каф обч. математики

Відповідальний за випуск: Т.О. Сокол, ст. викл.

Затверджено

на засіданні кафедри

іноземних мов

Протокол № 4 від 27.01.2009

Content

1. Heating a house 4

1.1 Transfer of heat 4

1.2 Heat losses 5

1.3 Conduction heat loss 6

1.4 Convection heat loss 8

1.5 Radiation losses 10

1.6 Seasonal heating 10

1.7 Choice of installation 12

2. Investment 14

2.1 The value of money 15

3. Growth of money 18

3.1 Growth of a fixed amount 18

3.2 Growth of regular investment 19

4. Hire purchase 20

5. Buying a house 22

6. Income tax 23

6.1 Allowances 24

6.2 Taxable income 26

6.3 Standard rate and reduced rates of tax 26

6.4 Tax deducted by employer 26

7. Rates 27

7.1 Rateable value 27

7.2 lp rate 28

7.3 The rates 28

This analysis consists of solutions for application of mathematics to several situations centred upon houses, their heating and purchase, and upon taxes, hire-purchase and investment. The topics are independent of each other and it may be that the best solution is to consider different aproaches at different times.

1. Heating a house

One of the main problems that many families have to face in winter is that of keeping their homes pleasantly warm without too much cost and effort. What are the factors that you think should be considered in designing a new house, or improving one already built? If possible, obtain information on the various heating systems and methods of insulation available.

We shall first consider methods of preventing the loss of heat, and, later, the methods of obtaining heat.

1.1 Transfer of heat

Heat can be transferred in three ways:

a) Conduction. When heat is transferred through a material, that material is said to 'conduct' heat. It is conduction of heat that causes the handle of a spoon left in a bowl of hot water to become unpleasantly hot.

Different materials conduct at different rates: metals, for example, conduct quickly while polystyrene conducts very slowly and is therefore said to be a good 'insulator'. Why do metals feel colder than polystyrene in cold weather, and hotter in hot weather?

b) Radiation. We receive heat from the sun even though there is nothing between the earth and the sun to act as a conductor: the heat is transferred by 'radiation'. We also receive radiant heat from, for instance, an open flame or electric fire.

c) Convection. If part of a fluid is warmed then that part will rise, causing a circulation in the fluid and thus a transfer of heat. Any transfer by this method is referred to as 'convection'. You must have actually seen this happening in a saucepan of hot water or in the air over a radiator or fire or a hot asphalt road. What heating and what cooling systems often rely upon convection?

1.2 Heat losses

Heat escapes from a house in two main ways.

a) If walls, windows, ceiling and floor are warmed, and if the outside temperature is lower than the inside, heat is conducted through the material of the shell where it escapes partly by radiation and partly by convection through where it escapes partly by radiation and partly by convection through warming the air in contact with it. On occasions when the sun is shining, the outer surface may get warmer than the inside of the house and heat may be gained from outside. Since heat lost by conduction from the outer shell is the more important factor, it is known as 'conduction heat loss'.

b) Air in the house is warmed and drawn up the chimney, through windows, doors, or roofs. This loss of heat, through the displacement of heated air inside the building by cold air from outside, is known as the 'convection heat loss'.

1.3 Conduction heat loss

It is not possible to measure the actual amount of heat that is being lost from a whole house at any given time. The loss must be calculated from other data. What measurements do you think would have to be made? What factors does conduction heat loss depend upon?

The rate at which heat flows away from the outer shell of a house is proportional to:

1. the area of the shell;

2. the difference between the inside and outside air temperatures, t_t and t₀, that is, t_t - t₀;

c) the capacity of the material to conduct heat away and the thickness of the material.

It is sometimes necessary to measure experimentally the heat which flows through a sample piece of window or wall and then a calculation is made to determine the amount of heat that will flow through one square metre (1 m²) in one hour when the temperature difference on the two sides is one degree Celsius (1 degC). This quantity is called the 'U value' of the material of this thickness. The 'U value' is measured in kilojoules (kJ). (A kilojoule is the amount of heat required to raise the temperature of 0-24 kg of water through 1 deg C.)

The other factors to be considered are the total area and the actual temperature difference. The formula for total heat loss becomes:

H = UA×(ti-t₀) kJ/h,

where A is measured in square metres.

U values for typical constructions

u

External walls: Solid 023 m brick plaster covered 8-6

0-28 m cavity ventilated 6-8

0-28 m cavity unventilated 6-0

0-28 m cavity with foamed plastic in cavity 2-0

0-28 m cavity with light-weight block inner wall 4-6

Ground floor: Solid concrete and tiles 4-0

Wood floor on joists 7-0

Roof and top ceiling: Tiles laid on felt and battens 8-4

Tiles on battens 11-2

Tiles on boards and battens 6-0

Tiles on battens and felt with ceiling overlaid with 0.025 m

fibre glass or 0-050 m vermiculite 3-0

Windows: Ordinary 20-0

Double glazed 10-0

Doors: 0-025 m wood 10-0

Heat losses through party walls of semi-detached houses and the connecting walls, ceilings and floors of flats can be ignored if the adjoining houses or flats are heated.

Example 1

What is the heat loss per hour through a window 2m×1m if the inside temperature is 11 degC above the outside temperature?

H = 20×2×1×11 =440 kJ/h.

Example 2

Figure 1.1 shows the plans of a modern house. Assuming it is designed with an eye to comfort, using good insulation methods, the conduction losses will be as below, for an average temperature difference of 7 degC.

Area A×U×(t_t—t₀) = Mean hourly heat loss

External walls	149	×	4-6	×	7 =	4800
Ground floor	70	×	4-0	×	7 =	1960
Top ceiling	70	×	3-0	×	7 =	1470
Windows	20	×	10-0	×	7 =	1400
Doors	4×10-0×7 = Total hourly conduction loss H =					280
						9910 kJ

Exercise A

Give your answers in this and subsequent exercises in this chapter to two significant figures and then corrected to one significant figure, for greater accuracy is unreasonable. Why is that 1

1. What is the conduction heat loss per hour through each of the following?

1. An ordinary closed window 2 m x 1-5 m, if the temperature difference is 17 degC.

2. A 'tiles on battens and felt' roof 10 m x 8 m, if the temperature difference is 7 degC.

3. A wood floor on joists 10 m x 8 m, if the temperature difference is 10 degC.

4. The sides of a house 10mx8m by 5m high, if the walls are 0-28m cavity brick, ventilated, the door area is 3 m², the window area is 20 m² and the temperature difference is 10 degC.

2. What saving in heat is achieved per hour if:

a) the roof in 1 (b) has 0-025 m, fibre glass overlaid on the ceiling;

b) the window in 1 a) is double glazed;

c) the walls in 1 d) are filled with foam plastic?