KẾT CẤU MỚI THE ENVIRONMENTAL CONSEQUENCES OF A BUILDING WITH A WIDE SPAN

VENTILATION The world is ventilated by natural movement of air. Inequalities of heat distribution drive the climatic air movements. The convection currents in the atmosphere are generally powerful enough to dilute the pollutants which we generate. However, pollution due to industrialisation is not always removed by the wind. The great fog in London in 1952, which killed in excess of 4000 people who had vulnerable lungs, and the photochemical smog in Los Angeles are examples where the natural air movements in an anticyclone are not strong enough to ventilate a city. When considering the ventilation of individual parts of a town, there is the concept of canyon streets where pollution is dispensed slowly and the concentration of Carbon Monoxide is a problem.

THE ENVIRONMENTAL CONSEQUENCES OF A BUILDING

WITH A WIDE SPAN

Max Fordham Max Fordham & Partners

Fig 1 Model for a competition in Pottsdam designed by Straub & Vogler

This paper examines the environmental consequences of

a building with a wide span

A bridge is wide span but it does not make the kind of

environmental impact which concerns me

I take it that much of this symposium is concerned with

structures like the Dome

:-Sports arenas (Sydney 2000 Stadium), cricket schools,

greenhouses (the Great Glasshouse at the National

Botanic Garden of Wales), cities in Alaska, garden

centres (Manheim), the Albert Hall, the Crystal Palace,

the Pantheon, Gothic Cathedral Enclosure of Manhattan

(Buckminster Fuller)

A wide span building is a building where the enclosing envelope is the top surface and has a wide span This means that the top surface is light in weight and is designed to carry only the minimum load

The wide spanning surface can hardly carry the load of another storey of accommodation and so we are considering single storey buildings

I am not a structural engineer but I suspect there are reasons for wide span structures to be tall at least in places Even though the enclosure of a wide span structure may be light, gravitational forces will be developed These forces are vertical and a vertical component of forces generated in the structure will have

at least to equal the weight Members which are inclined

to the horizontal can generate vertical forces even

without bending moments, so most wide span structures

seem to be carried with arches and catenaries

I dare say the structural papers will expand on this theme

and give some credit to Frei Otto who developed ideas

for forming and finding shapes which could support wide

span enclosures with bending moments only needing to

be developed for perturbing forces The wind is a big

perturbation So we get single storey, wide, high spaces

with lightweight cladding

At a smaller scale there are cyclones which are turbulent and chaotic and provide the variability in our weather The scale here is about 1000km

Cumulo nimbus clouds are limited by the height of the atmosphere where the plumes of buoyant gas fan out when they reach the tropopause

The point about this introduction is that the air in very large spaces is mixed by turbulent convection currents The other point to notice is that at the tropopause there is

a temperature inversion (the temperature increases with height), and the atmosphere is stratified

V E N T I L A T I O N

The world is ventilated by natural movement of air

Inequalities of heat distribution drive the climatic air

movements The convection currents in the atmosphere

are generally powerful enough to dilute the pollutants

which we generate However, pollution due to

industrialisation is not always removed by the wind The

great fog in London in 1952, which killed in excess of

4000 people who had vulnerable lungs, and the

photochemical smog in Los Angeles are examples where

the natural air movements in an anticyclone are not

strong enough to ventilate a city

When considering the ventilation of individual parts of a

town, there is the concept of canyon streets where pollution

is dispensed slowly and the concentration of Carbon

Monoxide is a problem

The thermal equilibrium of any part of the world is affected

by ventilation We do not particularly think of the hottest

parts of the world as being places with inadequate

ventilation, but the hottest parts of the world are generally

places subject to anticyclonic weather with low air

movement, where the temperature builds up

A wide span structure clearly modifies the ventilation of the

space it encloses Ventilation is needed to disperse pollution

and to control the thermal conditions in a space The

ventilation of a fire is a particular case where these two

requirements are combined

I believe we have to understand some basic principals about

fluid flow in enclosures so that we accept the possibility that

ventilation can look after itself Imagine looking at a plan of

Paddington station and wondering how to provide adequate

ventilation in this deep structure with combustion engines

inside In fact, the enclosure is adequately ventilated by the

openings in the top and at one end

We live in a very large enclosure It is about 12km high and

7000km radius Convection currents drive strong air

movements The major convection cells (the trade winds)

have a scale of about 10,000km, even though the atmosphere

is only 12km high

In a large span structure, convection cells are likely to develop, with a scale characterised by the size of the space itself

When a strong temperature inversion develops at the top

of the space, a stratified layer is likely to develop

Hot gas<ts f l o w i n g

o t h r o u g h v e n t

1>

V" twfyl"V \ A ; « n t r c n a d by r i s i n g

% y s t r c c m ot goscs

^LAl

Formation of a layer of hot gases

Fig 2 Design of roof-venting systems for single storey buildings, Fire Research Technical Paper No 10; 1964, Fig 2 page 4 Picture on Fire Research

W a r m a i r

d i s c h a r g e

Fig 3 Heat source forming a plume in a dome

Fig 4 Multiple heat sources and plumes in a dome

If we need to ventilate a space so as to remove heat from

'h' the lower occupied section of a tall space ' H \ then the

amount of air rising in the plumes to height ' h ' must be

extracted from the upper reservoir and replacement air

allowed to enter at the base of the space

During sunny weather the temperature of the skin will build up The temperature build up depends on the wind speed, the reflection coefficient to short wave radiation

- light, and the emission coefficient to long wave radiation It is likely to be 10°C to 20°C above ambient The entering air must not cause uncomfortable air

movements in the occupied zone and it must not disrupt

the stability of the hot air reservoir Most of the envelope

of a wide span structure is likely to be subject to a low

pressure zone while the elevated pressure stagnation

zone will be developed at low level on the windward

face

It may be possible to rely on input air flowing only from

the windward with discharge at the top Often with

strong winds, too much air will come from the windward,

and it will flow out to leeward If the resulting air

currents are tolerable then the wind driven ventilation is

a good solution If the air currents are too strong then the

air inputs on the windward side have to be throttled off

so that the air enters on the leeward faces driven by the

thermo syphon effect of the reservoir of hot gas This

pattern of air movement requires input around the

perimeter and air outputs at the top I was tempted to

illustrate how this thinking might be applied to the

Millennium Dome

It is important that the warm air is stratified and stable above the occupied zone of the building

Where a hot zone of air is lying above a cooler zone, there is a region with a strong vertical temperature gradient If this region has strong air movements with the air speed changing with height, then the stratification and the turbulence will act in opposition The Richardson number (R S Scorer 1) is defined as

:-dd_

where, 6 =

z =

U =

dU

lz

temperature height horizontal velocity acceleration of gravity

If Ri > 1 then the turbulence will die down and the horizontal air flow will be restrained below the stratified layer

Fig 5 Hypothetical flow for the Millennium Dome

The internal area is, say, 80m high Strong air movement

can be tolerated round the perimeter, say 0.5m/s at the

centre

The heat from the exhibition buildings will be given out as

driven ventilation plumes at a temperature of, say, 25°C I

suggest these discharges should be ducted above the

reservoir

It is tempting to apply the ideas of stratification and displacement ventilation to the heat loads in the Dome, but the following calculation shows how quickly a plume cools down and how much input air is needed

Say there are 50,000 people in the centre of the Dome (25,000 people in the exhibition buildings, and 25,000 people clustered into 13m diameter arrays of 400 people each, producing 53kW per array, then with the addition to

temperature rise in the plume is much less than 1°C

Qf heatsource

radius of heatsource

Fire Research Paper No 7 HMSO 1983 1968 reprlr

acceleration due to gravity 9 8" m-'sec' temperature above ambient : C temperature "K

h e a t s o u r c e kW density of air at source temp 1 2 kg/rrf'

specific heat of a>s kJ/kg

height from point source to plane defined by "y

The air flow into the reservoir would be over 4000m3/s

In fact the ventilation requirement for 50,000 people is

inside the building

lOOOmYs of ventilation picking up a heat gain of, say,

temperature of the air by 10°C

If this stratifies in the top 30m of the Dome, the stack

effect is about lOPa, giving a velocity of about 3m/s

be controlled to prevent too much ventilation in cold and

of vent round the perimeter

Of course, keeping the rain out has to be addressed

This crude analysis should be a precursor to more

modern techniques such as salt water modelling and CFD

(computational fluid dynamics)

Salt water modelling gives an accurate representation of

convective turbulence, but it is not able to model the

momentum of incoming air, nor the thermal capacity of

the bounding surfaces

National Theatre warm stage - cool auditorium smoke flows towards fly-tower

cool stage - warm auditorium smoke flows towards auditorium

Fig 7 Air flows in the National Theatre

Then at the Royal Exchange Theatre Manchester which

is a very large enclosure with a theatre inside it

We worked with Professor Manfredi Nicoletti on an entry for the Cardiff Bay Opera House Competition which was to be a large glass enclosure

The modelling of a thermal plume has to be carefully

considered A person is modelled as a 100W heat input

The model should equate to 100W emitted from, say, a

450mm diameter source with an initial plume of, say, 20

1/s at a 5°C temperature rise It should not be a 100W gls

lamp, say, 100mm diameter with a plume of, say, 5 1/s at *

20°C temperature rise The difference here is

represented by different flow rates of salt solution at

different densities

Computational fluid dynamics cannot deal properly with

turbulence Assumptions about the amount of turbulence

have to be built into the finite difference equations as

dummy transfer constants The constants have been

developed for heat transfer in jet turbines, nuclear power

station boilers, meteorological forecasting, and other rich

applications The constants for buildings certainly need

examining as far as I am concerned before I am happy to

have them used in very large and very small spaces with

very different Reynolds numbers

Fig 8 Competition entry for the Cardiff Bay Opera House - Interior Designed by Manfredi Nicoletti

These ideas about ventilation and fluid flow are based on

experience When commissioning the National Theatre,

the convection currents seemed to be preventing the

ventilation operating as required by the fire officer We

turned up the thermostat controlling the stage fan

convectors and the convection currents reversed

Fig 9 Competition entry for the Cardiff Bay Opera House

Fig 10 CFD for the Cardiff Bay Opera House - Velocity Vectors

L I G H T I N G

One of the immediate consequences of the single storey property of wide span structures is that the spaces can be roof

lit

The requirements for light to enable people to see are not to

be defined too simplisticaUy

The eye is like a camera with a variable aperture pupil to control the amount of light entering and with a light sensitive membrane retina to generate signals which are focused and transmitted to the brain The signals are processed by the brain and the nerves in the retina to generate sensations which

we interpret as "seeing" The retina can integrate the photons

it receives in a variety of ways

I

CflRDff 8 6 V OPERA MOUSF 'eMPERATI

Fig 11 CFD for the Cardiff Bay Opera House - Temperature Profile

The air flow and temperature were modelled using CFD

as shown on the figure above

The air flow model immediately suggests that the air

entry slot should be above head level and slanted

upwards

There was another issue about the temperature plot We

initially modelled the solar gain onto every node of the

lowest part of the floor level The temperature plots

showed very high temperatures on the floor which we

couldn't understand However, I vaguely remembered a

lecture during which it was explained that mirages in the

desert sometimes occurred when the morning sun heated

the desert surface and the invert layer of air to a high

temperature causing a very strong temperature gradient

close to the ground and making the mirage The hot air

did not rise as a convection current because there was no

trigger to start the convection at any point The

relaxations calculation process of CFD would be similar

if all nodes were at the same temperature with the same

heat gain The heat gain would be equated to the

temperature rise and the relaxation process might be

stopped before getting a proper answer We changed the

input, putting in a double batch of solar input to half the

nodes and immediately the answers looked sensible like

the figure above

I am sure I will raise as many questions as I answer in this brief summary of seeing but I am presenting you with a working designer's basic knowledge

In the absence of light the pupil is wide open and too few photons are received to see anything The sensitivity of the eye/brain system is increased and it takes about half an hour for full sensitivity to be developed

The part of the retina most sensitive to low light levels is not

in the same location as the area most sensitive to detail, so at night air force pilots are trained to look away slightly from a dim object

At low light levels, the retina integrates different coloured photons and integrates them over a period of time before transmitting a signal to the brain Thus the image seen is monochrome and in these conditions the retina cannot catch fast moving objects

The sensitivity varies with age, but a fully adapted night eye can "see" a light coloured object under an overcast night sky

at 0.001 lux

SECURITY (;N'«IM;t.;K]Ni;

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Drawing ofiice Offices, shops Stairs, corridor

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Fig 12 Figure 4.8 from the CIBSE Applications Manual AM4: 1991 Relative light level chart showing operational ranges of

"See" must mean differentiate between two levels of

brightness of objects of a certain size (not too small) so

the reflective properties of the field of view are

important When I say "see" in quotes I mean the whole

eye/brain process

As the general light level increases, the eye/brain adapts to

the changed signals With more photons arriving the cells

can differentiate between different colours and can send/fire

off signals to the brain at shorter intervals and the brain can

"see" colour and fast moving images

There is a limit to the rate at which a cell can send signals to

the brain After receiving light and sending a signal it has to

reset itself So, as the light received by a cell increases, the

frequency of sending signals increases until it is saturated

and can simply report maximum brightness Indeed, if too

much light is received the cell can overheat and die

I was reminded of the ancient Egyptians who worshipped the

sun god Ra A person accused of offending the god was tied

down on their back in the open and their eyelids cut off At

the end of the day, if they could still see they were innocent

but usually the retina was burnt out by the bright sun and this

was taken as a proof of guilt Bright sun at 100,000 lux

If there is an unevenly lit field of view but all the cells report

saturation, the field of view is not being "seen" very well

The eye needs to adapt so that the bright part of the field of

view just fails to saturate any cells Of course the dimmest

part of the field must provide enough light for good, fast

colour vision Thus, there is a maximum ratio of brightest to

dimmest light for good vision The eye adapts to the average

illumination

If a field of view is uniformly lit then the eye simply receives

a uniform vision and there is very Utile differentiation

between planes and objects I experienced this once when I

went very early to an exhibition at the Satehi gallery The

gallery was painted white all over and lit with fluorescent

uplighters Light was diffusely reflected off the ceiling in all

directions There were very few exhibits and very few

people so everything was white and I felt very disorientated

In order to "see" the field of view must not be uniformly

bright

Hold a pencil vertically up on a sheet of paper and look at the

shadows I hope there are some - usually several A shadow

represents a place where one of the brightest light sources

cannot shine on the paper behind the shadow The light in

the shadow comes from all other sources The contrast

between the brightness of the paper generally and the

brightness in the shadow represents the contrast between the

general diffuse light and the directional light from the source

Set this up in a more disciplined way and we can define the

vector/scalar ratio of an illumination field

Imagine looking at a hemisphere on a table In diffuse light where every surface is uniformly illuminated the hemisphere looks like a disc In purely vector light, the shaded part looks black (like a half moon) A mixture of diffuse and directed light is needed in order to perceive the shape of the hemisphere

Horizontal light from right Generally diffuse light

Fig 13 From Table 10 - Relationship of vector/scalar ratio to assessment of directional qualities of the lighting IES Code for Interior Lighting 1977

The overcast sky is very diffuse and the design minimum figure is taken at about 5000 lux

Under an overcast sky the field of view reflects back a diverse field of light because of different reflection coefficients and different colours The lighting/seeing is pretty adequate despite being viewed in very diffuse light

Inside a building the outside light is usually introduced from a transparent window The light then has a vector component, and shapes and shadows can be seen even on

an object with a uniform surface Compared to outside the light level is reduced but the "seeing" is improved because the light has a stronger vector component

As an illustration of the need for diffuse light, think back

to the difficulty of seeing anything in the region of a matt black motor car engine by the light of a single torch, even when it doesn't wobble

The reason for this discussion is to try to get you away from the view that the amount of light needed in a space can be defined by a single, simple figure of the amount

of light

The contrast between inside and outside is important The shading over a motorway underpass assumes that the speed limit is being kept and the light level can be halved every 3 seconds

In the Mediterranean one walks from the bright sunlight outside at 100,000 lux into a room with the shutters closed It takes some time before you can see anything

I guess the shuttered room allows about 0 1 % of the

diffuse sky light (10,000 lux) into the room so that the

light level is about 10 lux

So on entering the room the light level drops from bright

sunlight at 100,000 lux to 10 lux or 1:10,000, ie 213.3 =

10,000 It takes 3 seconds for the eye to adapt to a

halving of the light level and therefore takes 40 seconds

(3 x 13.3 + 40) to adapt to a light level of 10 lux

In the UK, well designed rooms with fixed windows

keep most direct sun out and then provide a daylight

factor of about 1% or 2% I believe this should be

increased for new buildings so as to reduce the amount of

fossil fuel and electricity used for lighting However, this

aim of mine carries an increased risk of buildings getting

too hot in summer

The indoor cricket schools at Lord's and Edgbaston try to

exclude most direct sun and to provide a daylight factor

of 5% to 6% and so give 1000 to 1200 lux on an overcast

day

These buildings do not fit my idea of wide span

enclosures but the cricket school at Lord's was won in a

competition where we expected the opposition would

offer air supported or other lightweight solutions We put

forward a case for natural lighting

A diffuse skin with a transparency of 20 to 2 5 % provides

a light level of 1000 to 1250 lux as required

However, in strong sun the internal light level rises to 20,000 to 26,000 lux and the direct solar gain rises to 200

translucent skin

Another disadvantage of the overall diffuse skin is that it gives a very diffuse light inside The lighting inside a tent or marquee is very diffuse and gives poor figuring to three dimensional shapes

In saying this I am offering opinions which could inform the development of the design of lightweight, wide span enclosures I realise that diffuse skins are provided for indoor tennis centres, millennium domes and so on As structural engineers gain confidence in making lightweight wide span structures using glass as the membrane, then I think the design, for example, of ventilating roof lights will be able to be developed The thinking about the type of lighting needs also to be developed

A solution with 7 5 % to 80% opaque area with 20% to 25% horizontal, transparent area supplies the same level

of light as a diffuse skin It is then possible to insulate the opaque area

1 0 0 , 0 0 0 Lux in

direction of sun

Light Cloud Blue Sky Overcast Sky

2 0 , 0 0 0 Lux 1 0 , 0 0 0 Lux £ , 0 0 0 Lux

No to option one - dark building fitted with fluorescent lighting

No to option two - fabric/translucent roof In sunlight 24,000 Lux

internally can quickly be reduced to 2400 by a small cloud

\

1 1200 - 4 8 0 0 Lux I

Fig 15 Interior of the Indoor Cricket School at Lord's Ground Photograph by Dennis Gilbert

The transparent areas possibly need blinds or shades to protect the space from direct sunlight Or the transparent areas can be diffusing with high transparency

Yes to option three -north roof light Only diffuse light admitted

Light levels in excess of 1200 Lux except after sunset in winter

Fig 14 Sawtooth roof arrangement at the Indoor Cricket School at

J H K

Fig 16 Interior of Bespak Stage 1 showing diffusing roof lights

Designed by the Cambridge Design Group

Fig 17 The Menil Collection, Houston Designed by Renzo Piano

Photograph by Hickey Robertson

The lighting solution for the Menil Gallery is a special

case where the external condition was generally strong

direct sun (100,000 lux) and the light level inside had to

be kept low for conservation purposes (50 to 100 lux), so

0 1 % of the light was required and multiple reflections

provided a really clever solution

So a wide span, single storey building can easily provide

adequate light

A light transparency of 2 to 2 5 % is feasible and provides

adequate light

A lighting strategy can be developed to provide shading

for direct sunlight and improve the overall thermal

efficiency of the skin at the expense of a less

homogenous solution

H E A T I N G

The air movement in a large, tall space is likely to be violent The subject of ventilation and air movement has been addressed

The roof of the structure is likely to subtend an angle of 2p steradians from a person so that its radiant temperature will be an important factor

One of the main issues with wide span buildings is that if the skin is to be light and transparent then a single or possibly double skin of fabric is unlikely to meet the Building Regulations for energy conservation

A justification might run

:-1 A conventional building deemed to satisfy the Building Regulations

We need a light level of 1000 lux and a building with

generated by fossil fuel, ie a U-value of 0.3 x 10°C mean

2 Lightweight wide span skin

During a 24 hour mean day with a mean inside to outside temperature difference of 10°C, we have

:-Opaque Conventional Roof Transparent Roof

single skin double skin

U-value Temperature Difference Heat Loss

Heat Loss in 24 hours Electric Light (12 hours) (at 30W/m 2 >

Watt hours per day

0.3 6 3 10°C 10°C 10°C 3W 60W 30W 72Whr 1440Whr 720Whr lOoOWhr

1152 1440 720

This argument can be developed for different conditions The light saved in the summer will improve the argument but for a lower light level, say 500 lux, the electrical energy saved is less impressive

Of course if the space is unheated the insulation value is unimportant

For a competition entry for the Cardiff Bay Opera House (shown previously in Figures 8, 9, 10, and 11), we had postulated a roof of 50% double glazing and 50% insulated panels The enclosed space was a foyer so the electrical energy saved by lighting to 100 lux or so was not significant

However spaces which formed the brief were huddled

together rather like a Greek village or the National

Theatre

Fig 18 Sketch by Max Fordham for Cardiff Bay Opera House

competition with Manfredi Nicoletti

The surface area of this convoluted shape implied a heat

loss through walls and windows with ventilation which

we evaluated and compared to the heat loss of the simply

shaped envelope The envelope had a lower heat loss

than that deemed to satisfy the building so the Building

Regulations were satisfied The internal buildings could

have simple, un-insulated walls which notionally helped

to pay for the whole scheme

Fig 19 Buckminster Fuller Dome over mid town Manhattan

This argument follows Buckminster Fuller's for the

dome over mid town Manhattan where the extended heat

transfer of the buildings is replaced by the smooth,

reduced envelope of the dome

In both cases there is a problem enabling heat and

pollution to escape from the inner layer of buildings and

this is basically the ventilation problem addressed in the

next section

Heating large high spaces depends on several levels of consideration

:-Heat Loss

Firstly we have to decide on the heat loss The U-value

of the cladding is important Next, the amount of winter ventilation; how airtight will the enclosure be and what stack effect is likely How much temperature gradient will there be to increase the heat loss at the top

Ventilation air will tend to come in at the bottom and on the windward side The incoming cold, fresh air needs to

be heated before it can lead to discomfort A 4 or 5m/s wind speed coming through the windward cracks or open doors must be heated

Most 50m high buildings have lobbied entrances

A 50m high stack with a 20°C temperature difference will produce air movement through openings of about 8m/s The temperature gradient in the space depends on the types of heat source It is difficult for any part of the space to get hotter than any individual object inside Direct fuel fired warm air heating is designed to be cheap

by recirculating air into a space at around 70°C and using heaters of 300 to 600kW capacity

The air flow is of the order 6 to 12kg/s and the air has to

be supplied at a very high velocity to ensure that it mixes into the room before losing momentum and drifting up to the ceiling

At the necessary velocity noise generation is the problem The parameters of air flow, heat load, noise generation, and temperature gradient have to be considered

In working out warm air heating we have relied on a hypothesis advanced by Holmes and Caygill [2] and repeated by P J Jackman [3], that

:-if thermal forces are not to dominate the pattern of air circulation

This relationship was originally postulated for a specific set of conditions but we have used it successfully in much more extreme situations

Where a heating system provides W kg/s of air at q°C specific heat c kJ/kg = 1 at velocity V

then the momentum M = WV and the heat load q = Wcq The relationship, where H = height, becomes

:-wv f 0.07 WOH

or V > qH 0.07

We have used the relation at Churchill College, St Mary's

Church Barnes, and the CZWG office in Bowling Green

Lane

At St Mary's Church Barnes we deliver 4mVs of air at

lOm/s from a nozzle at 70°C into a 10m high space This

does not generate a noise

Fig 20 St Mary's Church, Barnes

At Churchill College, the space is 10.5m x 18.5m x 22m

and the air supply to a dining room is at 12m/s

I have started with crude warm air heating because I

believe it is suitable for large open space of

indeterminate use

Of course, radiant heat has its advocates for tall spaces I

don't want to give a detailed case as to why I am not in

favour Where competing design solutions coexist in a

market then the reasons favouring one rather than the

other are probably marginal

Of course, if a group of open air dining spaces were

under a wide span canopy, radiant heaters to each space

would be a good solution

The behaviour of the air in a space with heat sources

inside it is largely defined by the behaviour of the

plumes A plume is a rising current of air which is

warmer than the surroundings The behaviour of plumes

is described in the book "Environmental Aerodynamics"

by Scorer and it has become a very important topic for

fire engineers

The plume is a particular case of jet flow It is a hot jet Jets are also described by Scorer and are very important

to HVAC engineers in considering how air flows in space and how grilles need to be sized

The best visualisation of a jet which I know and which I expect most of you can visualise is a stream running under a humped back bridge

I idealise the flow in the following figure

r

1

I

^ — Streamline flow

^ — Flow starts to converge Flow remains radial Velocity on circle/sphere

^ — Stagnant: weeds thrive

^ — Rapids form at centre of stream Level drops

Jet expands Velocity drops Momentum is conserved

^ — Quantity of flow in jet increases then reduces as flow is bled off

to serve the eddies

^ — Status quo reinstated

Fig 21 Idealised flow at a hump backed bridge at a quiet stream

C O N D E N S A T I O N

Moisture movement in buildings is not perfectly understood We should remember that the moisture content of air and water vapour has an upper limit The upper limit is a function of temperature

Air and water • separate out into cloud/mist ,

Water content

Upper limit of water content

Temperature

Fig 22