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Water Flowing in Pipes -why size matters (1)These pages explain how to choose thecorrect sizes of pipe when plumbing ahouse, and why it matters. This sectionexplores the theory, and a practicalworked example is given in part 2 .

Why do plumbers use so much half-inch copper pipe?This article explains why water pipes in houses arethe sizes they are. It shows how to choose the correctsize of pipe, why it matters, and whether or not ahouse water-supply system will work properly onceit's installed.

Plumbing books say what to do, but not why. Buildingservices design books offer design rules, but notwhere they came from nor why they matter, and fluidmechanics textbooks are full of complicated theorythat doesn't seem relevant to real problems - Whydoes this pipe make a noise? - Can I add anotherradiator?

So I started from first principles, asking basicquestions and following up the answers until I couldsee what was going on. It turned out to be rathermore complicated than I thought. Calculations for areal house are in part 2.

Why does water flow?

This question seems almost too stupid to be worthasking, yet it leads to a way of heating the hot-watercylinder without needing a pump.

A pint of water weighs a pound and a quarter...

When you turn on the tap, you expect water to flowout of the tank and down the pipe. Why does it dothat?

Things don't just start moving by themselves. Theremust be a force acting on the water in the pipe for itto move, and the obvious one is its own weight. Wateris quite heavy stuff - a litre of it weighs a kilogram.

What makes waterflow?

How fast will it flow?

Real pipes in realhouses

How much pressure isneeded?

What size pipe do youneed?

How fast will thewater flow?

is quite heavy stuff - a litre of it weighs a kilogram.The water in the tank pushes down on the water inthe pipe.

So does the size of the tank matter? Common sensesuggests that a big tank that holds more water mustapply more force to the water in the pipe than a littleone would. But common sense is wrong. The forcepushing the water down the pipe has nothing to dowith the volume of the tank, nor its surface area.

The force making the water flow down the pipe mustexist at the entrance to the pipe. How big is this force?What controls it?

Suppose the water is stationary - any taps connectedto the pipe are turned off. Now think about thecolumn of water directly above the pipe entrance(shown as a dotted line). It has weight, and its weightis a force acting downwards. So,

Down-force on the water in the pipe = Weight of water inthe column above the pipe

But surely the weight of the water just outside thecolumn affects the down-force too? No, it doesn't.How can it? Weight acts downwards, not sideways.The force due to the weight of the water outside thecolumn acts downwards too - but outside the column.So the down-force in the column stays the same nomatter how much water there is around it.

In the sketch above, both tanks hold the same amountof water, but one is twice as tall as the other. Thewater surface in the taller tank is twice as far awayfrom the pipe, so there is twice as much force pushingwater out. If you punctured both tanks near thebottom, water would squirt out much faster from thetall one.

tall one.

What about the down-force at some point furtherdown inside the pipe? Since the down-force at anypoint is due solely to the weight of water above it, thisforce must be bigger at a point further below thewater surface, because the column of water above itis bigger and heavier

Suppose the pipe runs vertically, then horizontallyunder a floor, then down vertically again. The waterin the horizontal section has weight too - won't thisadd to the down-force? Well, no, it won't, for the samereason as before - weight acts downwards on thatsection of pipe, not sideways. So it turns out that theforce that makes the water flow has nothing to dowith the size of the tank, nor with the length or shapeof the pipe run. It's purely to do with the verticaldistance between the water surface in the headertank and the point where the water leaves the pipe atthe tap. This distance is known as the head of waterfor the system.

Water squirts out of a hole

The force acts on the water in the pipe, and the pipediameter is known, so it's often convenient to think ofthe force as a pressure. Pressure is simply forcedivided by area - in this case, the cross-sectional areaof the pipe.

Think of a particle of water somewhere in the headertank. With no water moving, the particle is stationary.There is no net force acting on it. If there were, itwould move. But there is a force applied to it - theweight of the water above it. And if the particlehappened to be near the wall of the tank, and youpoked a hole in the tank wall, the particle wouldescape through it. So there must also be a sidewaysforce from all the particles next to it, or it wouldn'tmove sideways out of the hole. Yet if it's not moving,all these forces must be in balance. In fact, in astationary liquid, the pressure at a point is a force thatacts in all directions at once: up, down and sideways.The particle is ready to move in any direction at amoment's notice, like the SAS. It's possible, andnormal, to talk about the pressure at a point in aliquid.

The pressure at the bottom of a vertical pipe is...

liquid.

The weight depends onthe volume of water (inm3) and its density (inkg/m3). The density ofwater is about 1,000kg/m3 - a litre weighs akilogram. So

where g is the acceleration due to gravity - about 9.8m/sec/sec. (Kilograms are about mass, not force, so ghas to be included to do the conversion.)

The pressure depends on the length of vertical pipe.In fact, the length that matters is the height differencebetween the bottom of the pipe and the water surfaceat the top - in the diagram on the left, the height h.This is known as the head. It's measured in metres, orfeet of water, or mm of mercury, or pounds persquare inch (psi), or Newtons per square metre(N/sq.m). Whatever units are used, it's still apressure.

What's a Newton?

This might be a goodpoint to talk brieflyabout units. I'm used tothinking in properengineering units likeNewtons and watts, notpounds and BTUs,whatever they may be.British Thermal

British ThermalUnderpants?

Isaac Newton was one of the first to say clearly that

Force = mass x acceleration

The down-force on your hand when you're holding anapple is the mass of the apple (0.1 kg, say) times theacceleration due to gravity (about 10 m/sec/sec). Thisforce is (0.1 kg x 10 m/sec/sec) = 1 Newton. Force thesedays is measured in Newtons. A Newton is the weightof a small apple - but then, in Newton's time theapples were smaller.

Proper forces, like the weight you can lift with onehand, are lots of Newtons. A bucket holds 9 litres ofwater (2 gallons) and weighs 8 kg (18 lb.). This weightis a force of 80 Newtons. The pressure on the bottomof the bucket is about 3,000 Newtons per squaremetre (N/sq.m), though the pressure on your fingerswhen you're carrying the bucket by its handle ismuch higher - maybe 50,000 N/sq.m, or 7 psi (lb/sq.in).

Example - 15mm pipe

What force, and what pressure, is exerted bya 1 metre vertical column of water in a 15mmpipe?

A vertical 15mm pipe 1 metre long holdsabout 0.15 litres of water, which weighs 0.15kg, giving a down-force on the bottom end of

Force = mass x acceleration = 0.15 (kg) x 9.8(m/sec/sec) ≈ 1.5 N (Newtons).

This force exerts a pressure of

Pressure = force / area = 1.5 (N) / 145 (sq.mm) =1.5 x (1,000/0.145) ≈ 10,000 N/sq.m

at the end of the pipe. This sounds huge butactually it isn't very big at all. You could pokeyour finger in the bottom of the pipe toprevent the water flowing out.

By the way, normal atmospheric pressure is ten timesgreater than this, but we don't notice it because itsurrounds us. Atmospheric pressure is the same atboth ends of the pipe, so it can't influence the flow.What matters is pressure difference.

Hot water from gravity

There are lots of ways of heating the water in thecylinder, and one of the oldest methods can be thesimplest and cheapest. It depends on the apparentlyodd fact that hot water weighs less than cold water.

Here is a boilerheating the water ina cylinder. All theboiler does is heatwater in the pipe onthe right. The wateritself does the rest.To see why, thinkabout the pressuresin the pipes on eachside of the boiler.

The right-hand pipe holds hot water at, say, 82oC. Thepressure at the bottom is then:

Similarly, the pressure at the bottom of the left-handpipe, which holds water at, say, 65oC, is:

If these two pressures are different, the water will beforced to move. And as the graph shows, water at82oC is about 1% less dense than the same water at65oC. This may not sound very much, but it's enough.

The difference in the density of the water in the flowand return pipes is about 10 kg/m3. A litre of the coldwater weighs just 10 grams more than a litre of the

water weighs just 10 grams more than a litre of thehot water. This tiny difference - less than the weightof an English robin - provides the force that makes thewater move.

The circulating pressure then seems to be:

but there is one more detail to factor in.

The water being moved is hot, so it weighs less thancold water, so the circulating pressure would make itmove slightly faster than if it were cold water. Thecorrection is easy to add:

It's more usual to express the pressure in a moregeneral way that doesn't directly involve h, becausethen you can calculate how fast the water will flowround even a complicated circuit. But this is gettingahead of the story. For now, assume that the boiler ison the ground floor and the cylinder is on the floorabove, so that h is (say) 3 metres. Then, putting in thenumbers for this example, the pressure is

This is a real pressure difference, and the cold waterwill push the hot water around. The only majordrawback is that the pressure difference is so small,which means that the pipes have to be fat for it towork well. But it does work, and it doesn't need aseparate pump.

How fast can water flow?

The next obvious question is, what controls the speedof the water that flows out of the tap?

This is where things start getting a little morecomplicated. Pipes have been in use for quite a longtime now, and many clever people have tried tounderstand exactly what happens when you turn on atap, but believe it or not, the physics of water flowingin pipes is still more described than explained. Theproblem lies in friction.

Sticky cylinders

Viscosity

Sticky cylinders

When the water is moving slowly, it's easy. Think ofthe water in the pipe as a series of thin-walledconcentric cylinders, one inside the other, eachsliding relative to its neighbours. This is more thanjust a convenient image. It gives a good picture ofwhat's really going on. The interesting stuff happenswhere the cylinders rub past each other. The cylindernearest the pipe wall doesn't really move at all - itseems to be stuck to the pipe. The next one in doesmove a bit, and as they slide past each other, the outercylinder exerts a frictional drag on the inner one andslows it down. Similarly, the next one in and the oneinside that are slowed down too. The cylinder right inthe centre of the pipe moves the fastest.

If you don't believe this, it's possible (but not easy) toset up an experiment to prove it. It does happen.

Some liquids flow more freely than others, and theconcept of viscosity was invented to describe theeffect. Viscosity is really a definition of how well aliquid resists shear stress - that is, the force makinglayers of the liquid slide past each other.

Viscosity is measured like this. With a layer of liquidtrapped between two parallel plates, the top one ispulled so that it slides steadily over the liquid. Theviscosity of the liquid is defined as

The units of viscosity are evidently Newton-secondsper square metre - that is, [Pressure x Time] - thoughsome people prefer "poises" or (my favourite) "feet-slug-seconds". That one really conjures up a picture.But it's useful to have the idea of viscosity, because itsays explicitly that a liquid resists being made tomove. A force is needed, and the force increases withspeed.

Engine oil has a viscosity of about 0.5 N.sec/sq.m.,

Engine oil has a viscosity of about 0.5 N.sec/sq.m.,which means that plates 1 metre square separated byan oil film 1mm thick could be slid slowly apart at 1metre/sec by a strong man applying a force of 500 N(Newtons) - about 100 lb, or 50 kg. A millimetre of coldwater, by contrast, needs a force of only 1 N - just afew ounces. A strong Newt could do it, if the Slugsdidn't get under its Feet.

If the viscosity of water is so low, why does it matter?

Think back to turning on the tap. As the water in thevertical pipe begins to move, the cylinders of waterslide reluctantly past each other. The viscous dragappears as a force acting upwards, opposing thedown-force due to the weight of water. The wateraccelerates, and since the opposing force depends onspeed, this viscous drag increases too. Eventually,when the tap is running freely, the forces exactlybalance - there is just enough down-force to overcomethe friction force at this speed of flow. Viscousfriction is the force that controls how fast the waterflows. Viscosity explains why the water leaving thetap doesn't just carry on accelerating without limit, asit would if there were no opposing force.

Now, the force pushing downwards is the pressure.More exactly, the net down-force on the water in alength of pipe is the pressure difference between itsends. This down-force is exactly balanced by theopposing up-force due to viscosity. So there must be asimple relationship between the pressure drop in apipe and the corresponding flow rate. It's not all thatdifficult to derive it from first principles, if you enjoyintegration (and I know some people do). But if youdon't feel like doing that right now, the answer is

where μ is the viscosity of the fluid flowing in a pipeof radius R and length L. Unfortunately, although thisequation is nice and simple, it comes with a warning -it's only true for slow-moving fluid. But how slow isslow?

Chaos rules

About 120 years ago, in Manchester, a man called

Reynoldsnumber

About 120 years ago, in Manchester, a man calledOsborne Reynolds was trying to understand - or atleast describe - the flow of fluids in pipes. After manycareful experiments, he decided that what happenedto the flow depended on four things - the viscosity anddensity of the fluid, the diameter of the pipe, and thespeed the fluid was moving. He put these fourquantities together like this to make a dimensionlessnumber:

Speed x Diameter x (Density / Viscosity)

The number has been known ever since as theReynolds number, Re. Respect!

Reynolds found that when the fluid moves slowly, theflow stays smooth and even, but as the speed isincreased it eventually becomes rough and turbulent -chaotic, we would say now. The transition toturbulence always happens at a Reynolds numberbetween 2,000 and 3,000, no matter what fluid is used.(The reason for the uncertainty is probably to do withsmall variations in initial conditions - chaos is likethat.)

In other words, the simple equation above relatingflow rate to pressure drop is only valid when themoving water has a Reynolds number of 2,000 or less.If Re is higher than this, the water starts bouncingaround unpredictably, and it takes more energy -more pressure - to shift it along.

As well as speed and pipe size, the Reynolds numberRe depends on the ratio of the water's density to itsviscosity, so to save having to work out (ρ/μ) eachtime you need to calculate Re I've included a table sothat you can simply look it up.

Table 1: Viscosity and density ofwater

TempoC

Viscosityμ

Densityρ ρ/μ

10 0.00133 999.7384 753,000

20 0.001 998.2 998,000

30 0.000753 996.6739 1,320,000

40 0.000567 995.1502 1,760,000

50 0.000427 993.6288 2,330,000

60 0.000321 992.1097 3,090,000

70 0.000242 990.5929 4,100,000

80 0.000182 989.0785 5,440,000

90 0.000137 987.5663 7,210,000

Example - Reynolds number

Cold water is flowing through a 15mm piperun. How fast can it go before it starts tobecome turbulent?

The Reynolds number for this flow is

Re = (Speed) x (14/1000) x (753,000) =(Speed) x 10,500

(assuming "cold" means 10 deg.C and thepipe's internal diameter is 14mm), so if Re isto be 2,000 or less, then

Speed < 2,000/10,500 ... or Speed < 0.19m/sec

Not very fast, then. How about hot water (at,say, 70 deg.C)?

Re = (Speed) x (14/1000) x (4,100,000)= (Speed) x 57,400so Speed < 2,000/57,400 ... or Speed <0.035 m/sec

which is really slow. Don't get too hung up onthe numbers, by the way. Chaos is not exact.It's enough to say that turbulence is likely tostart at around 0.2 metres/sec.

Is turbulent flow essential in domestic water systems?

Cold water flowing in 15mm pipe starts to becometurbulent at the slow speed of 0.2 metres/sec. In22mm pipe, the speed is lower still (0.13 m/sec). Doesit matter that the water is moving so slowly?

The question is, how long are you prepared to waitfor the sink or the bath to fill? A flow rate of 0.2metres/second means that just 0.2m (20cm) of thepipe's contents come out of the tap in one second.Now, 22mm pipe (the size normally used to plumb ina bath) has an internal cross-sectional area of 320sq.mm, so the volume occupied by 20cm of water isjust:

Volume = Length x Area = (320 x10-6) x (20 x10-

2) = 64 x10-6 cubic metres = 0.064 litres.

A bath holds typically 100 litres. It would take nearlyhalf an hour to fill at this rate. Clearly 0.2metres/second is far too low a speed to be useful. If ahigher speed means turbulence, then so be it.

The trouble is that allowing turbulence is really not agood idea. For one thing, the particles of water arebashing into each other all the time, and that takesenergy, and that means a much bigger force has to beapplied to move it. For another, the force you needcan't be calculated. It has to be inferred from otherpeoples' experiments.

Shake, rattle and moan

But the worstpart ofturbulence inpipes is thenoise. Inturbulent flow,particles ofwater move inrandomdirections atrandom speeds.

Well, so what? One particle of water is much likeanother. The problems begin when a particle decides,all by itself, to change into steam.

Large pressure differences can appear across verysmall volumes of turbulent water, especially when thewater flows round a bend, or through a constrictionlike a valve or a tap.

In fact, bends can cause the flow to separate from thewall of the pipe, like this. Because the water issuddenly forced to move sideways across the pipe,whilst at the same time it is moving along the pipe,vortex eddies appear. They spiral off down the pipe,wasting energy as they go, until they are damped outby viscous friction. Bends should be avoided. If theyare inevitable, then the more gradual they are, thebetter.

More speedmeans a lotmore noise

Sudden changes of velocity (that is, speed in aparticular direction) cause equally sudden - anddramatic - local changes in pressure.

This creates problems because water at a lowerpressure boils at a lower temperature. At the normalatmospheric pressure of 1 bar (14.5 psi, or 100,000N/sq.m), water boils at 100oC of course, but if thepressure drops to 0.1 bar it will boil at only 47oC. Thewater in a central heating system is hotter than this.

When the local pressure somewhere in the waterdrops low enough, a particle of water turnsimmediately into a bubble of steam. The bubble soonmoves back into a region of higher pressure andcollapses, and the resulting shock wave zips throughthe water, bouncing off the pipe walls. The moreturbulent the flow, the more often this happens. Theprocess is known as cavitation, and it can corrode thepipework as well as a making a disturbing amount ofnoise. If you think about it, bubbles do formspontaneously in turbulent water. A waterfall, or thewake of a ship, or rocks in a stream all cause thewater to foam. So does flushing the loo!

Measurements show that the cavitation noise fromfittings (that is, elbows and tees) goes up with thespeed the water is moving. Each increase of 1 m/sraises the noise level by a factor of about 4, and it'sgenerally agreed that a water speed above about 3metres per second makes cavitation noiseunacceptably loud.

Cavitation isn't the only source of noise. Turbulencecauses eddies to appear in the flow, and besides

causes eddies to appear in the flow, and besideswasting energy they cause noise and vibration in thepipe network. Large eddies can be moving at up to10% of the average speed of flow, and contain energyat frequencies from a minimum defined by

fmin = (Average water speed) / (Pipe diameter)

on upwards. For a 15mm pipe carrying water at 1.5metres/sec, fmin turns out to be 100 Hz. Frequenciesabove 100 Hz contain progressively less energy,because viscous friction damps them more quickly.

The energy is coupled to the pipe network and maycause some part of it to resonate. The moving wateracts rather like a white noise generator, seeking outany resonances in the pipe network. That's why pipesshould be clamped firmly to the wall at intervals of nomore than a metre or so. The speed of sound in wateris about 1450 m/sec (at 15oC) - about 30% faster thanin air - so a 1 metre length of pipe can't resonate at afrequency below about 700 Hz, and there shouldn't beenough stray energy there to worry about.

All this boils down to an engineering trade-offbetween cost and convenience. Slow-moving waterimplies large-diameter pipes, which would cost moreto install. The key question is, how much noise willpeople accept?

Most sources recommend that the speed of water inpipes should be kept to less than 2 m/sec, and somespecify a maximum speed of 1.5 or even 1 m/sec.Remember the Slug. The Reynolds numberscorresponding to usable water speeds for each size ofpipe are summarised here.

Table 2: Maximum Reynolds numbers for standard pipes

Reat... 6 mm 10

mm15

mm22

mm28

mm 35 mm 42 mm 54 mm

0.3m/s 2,600 4,800 7,300 11,000 14,000 18,000 21,000 28,000

1.0m/s 8,600 16,000 24,000 36,000 47,000 59,000 71,000 93,000

2.0m/s 17,000 32,000 49,000 73,000 94,000 120,000 140,000 190,000

The table shows clearly that the Reynolds number for

Darcy-Weisbach

The table shows clearly that the Reynolds number forwater moving at 2 metres/sec is way larger than the2,000-3,000 maximum that would guarantee non-turbulent flow. Real plumbing in real houses isdesigned on the basis that the water flow will bechaotic and turbulent. Unfortunately, there is as yetno proper theory to describe turbulent flow, sosystems have to be designed on the basis ofexperience rather than physics. The simple theory I'vebeen investigating just doesn't apply.

What happens in the real world?

So if there is no simple theory, is there a complicatedone? Pipeline systems do get built, after all, and theengineers who design them must know what they'redoing. How do they manage it?

One key tool seems to be an expression called theDarcy-Weisbach equation, which predicts how muchpressure would be needed to push a given fluid alonga pipe at a particular speed. What makes it tricky touse is that it includes a "friction factor" ( f ) whichdepends not only on the smoothness of the pipe - sincecopper is smoother than, say, concrete, you'd expect itto have a smaller friction loss - but also the Reynoldsnumber of the flow. But that in turn depends on thespeed of flow. In other words, you can only calculatethe speed if you already know the speed! It's not quiteas daft as it sounds, but it's certainly rathercomplicated if you only want to design the plumbingin a house. I've included a worked example in part 2.

Real-world engineers prefer a simpler approach. Theyuse the Hazen-Williams equation. The equation isstrictly only valid for water at below about 25oC, butthat's OK. It's much simpler than the alternatives. Touse it, we need to know the head h, the pipe's length Land the 'hydraulic radius' (Rh - half the pipe's internalradius). And because the material the pipe is madefrom can also make a difference, there's a frictioncoefficient C which for ordinary copper or plastic pipecan be taken as 150. The graph below illustrates whatthe equation predicts will happen when the head is3m, as it might be for a bath or shower. It shows thata small increase in the length of a short pipe makes abig difference to the flow-rate. On the other hand, you

Hazen-Williams

big difference to the flow-rate. On the other hand, youcould safely add another 10m length to the gardenhose without it making much difference at all.

The graphs illustrate that the flow rate you can getfrom a given head drops off dramatically as the pipelength increases. But using the equation to design theplumbing in a house would lead to a lot of tediouscalculation. There is a better and simpler approach,which I describe in part 2.

Real pipes for real houses

In the real world the range of pipe sizes you canactually buy is quite restricted. Builders' merchantsusually stock the standard sizes listed in the tablebelow. The size given (eg. 15 mm) is the outside

Pipedimensions

below. The size given (eg. 15 mm) is the outsidediameter of the pipe.

Table 3: Standard plumbing pipe sizes

Plumbers'merchants

call it ...

10mm

15mm

22mm

28mm

35mm

42mm

54mm

Someplumbersknow it as

...

3/8in

1/2in

3/4in

1 in 11/4in

11/2in

2 in

Internaldiameter

(mm)8.8 13.6 20.2 26.2 32.6 39.6 51.6

Cross-sectionalarea (inmm2)

61 145 320 539 835 1,232 2,091

In passing, it's worth pointing out that the standardsizes changed slightly when metrication wasintroduced. This might matter if the half-inch pipethat was installed in your kitchen thirty years ago isnot exactly the same size as the new 15mm pipeyou've just bought to plumb in the new dishwasher.The fittings may not quite, er, fit.

Smaller pipe must be cheaper and easier to install, sowhy isn't 10mm pipe used for everything? (In France,it often is!)

Small isn't always beautiful

A bath should fill in five minutes or so. Suppose in theinterests of economy you decide to plumb it in with10mm pipe. The bath holds about 100 litres, so to fill itin 300 seconds will require a flow rate of (100 / 300) =0.33 litres/second. Now, the internal cross-sectionalarea of 10mm pipe is about 61 sq.mm, so a 1 metrelength of it holds about 61 cubic millimetres, or 61milli-litres (ml). A flow rate of 0.33 litres/sec thereforemeans a water speed of about (0.33 / 61 x10-3) = 5.4metres/second - about 12 mph. Given enough pressureyou probably could do it, but the roaring noise wouldfrighten children and small animals, and cavitationdamage would mean you'd have to replace the pipesand fittings after a few years anyway. It's probably abad idea.

Maximum quietflow rates

Each size of pipe is intended to carry a specific flowrate, quietly. Cross-sectional area is what mattershere. A simple calculation of volumes shows that, atthe maximum recommended water speed of 2metres/second, the maximum flow rates are:

Table 4: Quiet flow rates (litres/sec) ofstandard pipes

10mm

15mm

22mm

28mm

35mm

42mm

54mm

1.5m/sec 0.08 0.22 0.45 0.82 1.3 1.9 3.1

2.0m/sec 0.1 0.3 0.6 1.1 1.7 2.5 4.2

To check the actual flow rate, get a bucket and awatch. A bucket usually holds 2 gallons ( = 16 pints, =9.1 litres). At a 15mm pipe's maximum flow rate of 0.3litres/sec, the bucket will fill in 30 seconds. At a 22mmpipe's maximum flow rate of 0.6 litres/sec, it will take15 seconds.

Bath taps and sink taps

If 10mm pipe is not an option for the bath, then whatis?

The idea is to choose the pipe sizes so that the waterflows fast enough to fill the bath or the sink in asensible time without making too much noise. Akitchen sink holds 10 or 12 litres of water. So to fill a10 litre sink with water moving at 2 m/sec would take85 seconds using 10mm pipe, 34 seconds with 15mm,15 seconds with 22mm ... and just 2 seconds with54mm pipe.

Now, if the sink filled in 2 seconds it wouldn't savemuch time on the washing up, and besides, waterwould splash all over the kitchen. Most people don'tmind waiting half a minute or so for the sink to fill,and that's why kitchen sink taps are designed to beconnected to 15mm pipe.

A bath holds about ten times as much as a sink: 100 to120 litres. If both the hot and cold pipes are 22mm,and you run both at once, the flow rate is over 1.2

litres/second, so the bath fills in less than a minuteand a half. Bath taps are designed for 22mm pipe.

If you want to know how to calculate real flow ratesin a real system, the method is given here in Part 2.

Be warned - the numbers I use all refer to copper pipe.If you want to use plastic pipe you should be aware ofthe differences. You may find John Cantor's siteinteresting.

Copyright © John Hearfield 2007, 2012