Like many homes, my water supply is metered, and I am billed according to the amount I use. Each unit on the meter corresponds to 1 m^{3}, or 1 kilolitre.

The cubic metre isn’t used for many everyday transactions, but for the metering of water usage it is a very convenient unit for visualising the large amounts used over several months.

However, in their billing information, Severn Trent Water see the need to convert water usage in cubic metres into other “units”, such as “cups of tea” and “showers”. They even tell me how much I use per day in pints (presumably not dry pints, or US pints, which are different from the UK pints still used for draft beer).

Severn Trent struggle to find an everyday unit to express 0.12 m^{3}

However, even amongst all the conversions, Severn Trent Water somehow manage to not mention litres anywhere on my bill. Yet, if an everyday unit is wanted, then the litre ought to be the obvious one. One litre being equal to 1 dm^{3}, which is exactly 1⁄1000 of one cubic metre.

So in the example above, 0.12 m^{3} = 120 litres. Simple.

For comparison purposes too, nothing could be handier than the fact that bottled drinking water comes in sizes that are multiples of one litre. Has drinking water ever been sold in pints?

Conversely, I have no idea how to visualise the amount of water in “one shower”, and the amount of water I use in “one cup of tea” depends on which cup I use. So, if it is felt necessary to show how much one cubic metre is in smaller everyday units, why not just use the litre?

If “dumming down” is the practice of making things simpler for a perceived target audience, could these meaningless extra units in my water bill be a case of “dumbing up”?

Readers are invited to compare their experiences of billing information from other water companies.

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This sort of think makes my 5 L of blood boil!

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You are stating a measure of water in litres and then cubic mtrs ,which is not liquid measure, this is where confusion sets in with Metric system,

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My Anglian Water bill only mentions one unit – the cubic metre.

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With Imperial this would be pints and gallons, not squre feet or square yards or acres!

It is this stupidy with using the metric system that causes confusion.

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The comments from imperialyes highlight a complication of imperial that is missing from metric. Imperial has different measures for volumes of liquids (for example tea/dessert/tablespoons, fluid ounces, pints, gallons), of gases (cubic feet) and of solids (for example cubic inches, cubic feet and of course ‘spoons’ as for liquids). These date back to the imperial system’s origins in medieval times. But the world has moved on. . Metric does not distinguish. Litres and cubic metres are used for solids, liquids and gases. Hooray for simplicity.

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Thats not simplicity at all when liquid is measured in litres AND cubic metres, thats like a metric term AND imperial!

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@ imperialyes : 2021-11-04 at 17:38

You are so totally wrong in your reasoning. We have been here before, just a few weeks ago.

The fact that volume, mass and length (and everything else) is inter-related is the main reason for the success and existence of SI. In real life, fuel for an airliner may well be measured in litres, but you can be sure it is actually calculated in kg. Even more so for an F1 racing car which is allowed 95 (I think) kg of fuel at the start of the race. Volume of a liquid has no meaning as it varies with temperature and pressure, as well you know I suspect.

One squirt of fuel at atmospheric pressure is quite different when vaporised under vacuum to fill the cylinder, then squashed into a ball for ignition.

Some years ago when arctic oil fields opened up tonnes of oil had to be dumped at sea when overfilled tankers reached the tropics. Even over filled cars used to eject fuel in summer as the cold fill warmed up. But then, I suspect you know all that also.

Back to the pint of prawns then, Oh yes, please do explain the pint of prawns in your beloved imperial mishmash of measures. So the circle goes round and round. You are wrong, get over it and move on.

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Imperialyes seems to be as confused as any imperial user can be. Of course volume units can not equate to square units, but they can and do relate to other volume units such as cubic inches, cubic feet cubic yards, cubic miles, etc. All of which will have a non-consistent number attached. Also ounces, pints, quarts and gallons have different versions depending on the user. Confusion is not with metric but with imperial.

Now with metric, if you have 0.12 m³ which happens to be 0.12 kL, without a calculator I can relate that to 120 L or 120 dm³, 1.2 hL, or any number of prefixed units. Easy to understand due to its consistency and coherency.

BTW, spoons today are more metric than imperial as a teaspoon is 5 mL, a dessert spoon is 10 mL and a tablespoon is 15 mL (except Australia where it is 20 mL).

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I hope this doesn’t sound overly critical. However, to someone who understands the metric system, it is “obvious” that 1 m³ = 1000 L (the SI Brochure defines 1 L = 0.001 m³), and goes “without saying.” To someone who doesn’t, the relation to Imperial measure may be more relevant (who remembers all those irregular factors). I’m in the US and my water is billed by units of 1000 (US) gallons, which I have to remember to multiply by the always convenient 3.785 411 784 if I need to convert to cubic meters. Other water authorities bill in units of 100 cubic feet (CCF), so it is hard to compare my water usage to other areas.

1.336 806 CCF = 1 kilogallon.

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You certainly don’t have to convert 0.12 cubic metres to litres using Dimensional Analysis!

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@BrianAC wrote “One squirt of fuel at atmospheric pressure …”.

This reminded me that a motor vehicle’s fuel consumption is measured in mpg (distance per unit volume) in imperial units, but in L/100 km (volume per unit distance) in metric units.

If L/100 km is reduced to base units, we find that one L/100 km is equal to 10^-8 m^2 or 0.01 mm^2. If we now consider a fine “thread” of fuel of cross-section 0.1 mm^2 (10 L/100 km), then every time the engine draws in more fuel, the amount of fuel drawn in will be a “squirt” of cross-section 0.1 mm^2 and length equal to the distance the car travelled since the last “squirt” was drawn in.

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John Steele,

Is the measurement of your water usage in US gallons that precise that you need a conversion factor to litres with 9 decimal places? Wouldn’t 3.785, 3.8 or even 4 suffice? Seeing it is in increments of 1000 gallons, I highly doubt you need such precision.

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My water company (South-Eastern) does understand litres and in its similar information on daily usage uses litres where appropriate.

The point of this discussion seems to be about using units that are of a sensible size. The anti-metric brigade sometimes suggests that metric units are of unsuitable size whereas imperial were designed around convenient sizes. However there are examples of non-metric units that do not seem to be of sensible size.

Most cars nowadays have a rev counter on the dashboard. A car engine revolves many times in a second – far faster than we can count, yet we spend a whole minute counting the revs, then calibrate the rev counter in revs x 100 or revs x 1 000 to get the figure down to a manageable size. I once worked in power stations. Generator speeds were in revs per minutes, electrical frequency was in cycles per second, latterly Hertz. Because there was a firm relationship between the two, conversion charts were provided. Why not count mechanical rotation in revs per second and avoid all this, I used to think. In aircraft jet engines, revs per minute can reach five digits.

Talking about aircraft, here is another figure that seems too large. The captain may tell the passengers that the aircraft is flying at 30 000 feet. A foot may seem to be a small unit to measure aircraft height. Why not miles or kilometres? The answer is that flight paths are set a certain levels, 1 000 feet apart, so that where paths cross aircraft are at different heights. Really these heights are in 1 000 feet units. If the pilot were to say they were flying at 30 kilofeet, that might sound a bit odd.

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A rev counter counts revolutions. It does not measure RPM, its a different device. I assume you mean tachometer.We have to stick to standard units like feet you mentioned, but you could say kilofeet for large distances,instead of yards. The imperial system had too many different units,for all the anti imperial posters!

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OK, Imperialyes, on a point of semantics you win! As you say, a rev counter counts revolutions – it makes a continuous record of how many revolutions take place. It does not indicate rotational speed in r.p.m. or whatever. That device, as you rightly say, is a tachometer, which can be calibrated in any units one likes, e.g. revolutions per second – I have even seen radians per second in laboratories.

A car speedometer is a type of tachometer. It measures the rotational speed of the wheels but is calibrated in mph or km/h, because that is what the driver is interested in. I was using the term “rev counter” loosely, as do most motorists, to avoid confusion with the tachometer that measures road speed.

But we are missing the point here. My point was that Severn Water was not the only example of using units apparently of unsuitable size – and neither of my examples is metric.

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I believe a cars speedometer today if they are digital are calibrated in metres per second and just mathematically converted to either kilometres per hour or miles per hour.

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Daniel: Fair comment on number of digits needed. It clearly needs to be rounded afterward. However, I preach “Convert exactly, round sensibly.” I prefer to remember one and only one conversion, the exact one, not various “adequate” rounded factors. My bill reports thousands only with no decimal places. The hundreds, tens, and units digits are masked and therefore truncated (but accumulating internal to the meter). Thus the integer (or possibly nearest tenth) number of cubic meters would represent sensible rounding at the end. You could round the conversion factor (as guard digits, I would recommend two more digits than you intend to retain) but then you have to round again afterward. With a computer or calculator, I always use the exact conversion. If I have to do it mentally, I would call it “about 4 L/gal” as I can’t multiply 10 digit numbers in my head.

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John,

“I prefer to remember one and only one conversion, the exact one, not various “adequate” rounded factors.”

This a problem, a very big problem. How many people can and do remember a 10 digit conversion factor? Almost no one. I don’t see the need for such definitions for simply, they can never be realised. The instruments to produce such precision either don’t exist or if they do would be very expensive and rare.

Filling machines today can only accurately fill in 5 g and 5 mL increments, making the need for multi-digit conversion factors moot and senseless. This puts the maintainers of these useless conversion factors out of step with the real world.

There needs to be a reanalysis and reevaluation of the conversion factors stated in law and have them altered to sensible factors that are no more than one or two digits.

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@Daniel: Any speedometer that works off the number of revolutions that a wheel makes has an inherent inaccuracy built in. New tyres have a tread depth of 8-9 mm. The minimum legal tread depth is 1.6 mm. Thus the radius of the wheel can vary by 6 mm. If we consider a 400 mm diameter wheel, that gives a radius of 200 mm. A change of 6 mm on 200 mm amount to 3%!

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I spent part of my working life in education. Like everyone else I had the issue of students giving answers to meaningless numbers of decimal places, because the pocket calculators gave them thus. I used to set this exercise.

A circle has diameter 10 cm. Calculate the length of its circumference.

They were to do the calculation to five decimal places three times using three approximations of π, viz:

22/7

3·14

3·141593

The answers they got were:

31·42857

31·40000

31·41593

If nothing else did not convince them that low input data accuracy with high output result accuracy generated little better than random numbers, nothing would. Yes, high accuracy data and calculation but round off to a sensible value every time.

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I trust that you followed up this exercise with another one – draw a line 40 cm in length, mark a zero point near one ond of the line and then mark off each of the calculated lengths usign the same zero point. (They would probably need 40 or 50 cm rulers to do the exercise)

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