Hydropower session notes 1

first meet was at the Vale on Tuesday 2nd May 2023 here's some of the background to the discussion we had the primary objective of this meeting was to familiarise ourselves with the very basics of energy use, measurement and generation, and the concepts of work, energy power, potential energy.

the aim here is to get more familar with measuring energy, its storage and use, and clarify the language we use around all that

Key concepts

work. energy and power:

To do work requires energy.

An example of work is lifting bucket of water, against the force of gravity, from the floor onto a table. This is work and it requires energy to do it.

Work done has the same units as energy - joules.

Power is the rate of doing work. Power is the amount of work done, divided by time taken to do it. Power = work / time

Lifting a bucket of water slowly requires less power than lifting it quickly. The amount of work done and the energy used is the same in each case. But to do the same amount of work more quickly you need more power. A fitter and more powerful cyclist can get to the top of the hill before a less fit and powerful cyclist.

The energy you put into lifting the bucket of water is stored as potential energy in the water, by virtue of it's increased height. This potential energy can be released by allowing the water to flow back down to the floor.

Throughout our discussions we are going to measure energy in Joules, power in Watts, time in seconds. We might measure longer times in hours, just be aware there are 3600 seconds in an hour. ( 1 hour = 60 minutes x 60 seconds = 3600 seconds ). And we often use the x 1000 prefix "kilo" when numbers are large. So we can have kW or kiloWatt to mean 1000 Watts, or kJ or kilo Joule to mean 1000 Joules. Also we will often see kWh, to mean kilo Watt hour.

Something to be clear about is the equation linking energy transferred, power and time.

The formula which links energy transferred, power and time, and the formula which helps you calculate the energy transferred is as follows:

Energy transferred = power x time. This can also be presented in the following format: E = P t

so 1 Joule = 1 Watt x 1 second etc.

discussion: why and how do we measure energy use ?

suggestions and some relevant ideas;

initially purely commercial and for resource sharing if resources are limited

at first (way way back) 1000's of years before any industrialisation, energy was needed only for domestic cooking and in cold climates heating of dwelling place

later we needed enrgy for making utensils (clay, bronze, iron require wood or charcoal for prodction, charcoal being preferable to wood)

an energy economy begn to grow, where one group of people, a family unit perhaps, would gather wood and make charcoal, (whence the surname collier is derived) which they would provide to artifact makers (artisans) in exchange for artifacts and utensils, which they could then exchange for food or livestock etc. and so an economy of specialised roles and skills evolved.

Eventually the notion of money was accepted and instead of direct barter ( a bundle of wood for some eggs) a common currency enabled more flexible trade. (later of course money itself became a commodity in it's own right... and then later still came derivative trading etc. and out of that the financial crisis was invented, but that's another story)

up until recently most enegy use in homes, offices, factories, vehicles, etc. was measured purely for commercial reasons; from the energy provider's (the seller) point of view to enable them to quantify what they had delivered to the customer and charge enough to make profit, from the users point of view in order that they can find ways to economise and reduce unnecssary expenditure

detailed energy monitoring in the home is quite a recent thing, it's always been present though, householders being mindful of what they could afford and how to keep within their budget measured in sacks of wood or coal, "dont put so much coal on the fire, we only have 3 buckets-full left to last the week etc." and the quarterly electricity bill "make sure you switch the light off" etc

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what is energy anyway ?

a discussion with the aim to get a feel for what energy is and comparisons between different types of energy storage and energy usage

work energy and power introduce the concepts of work, energy and power as used in maths and physics (assume no prior experience of work energy and power in maths/physics, just get a general feel for what the coincepts mean, and how they are useful)

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what is work ? (doing something useful is a pretty good answer)

we tend in general conversation to refer to work as something tiring, exhausting or even diagreable, (as opposed to play), but for our puposes (our aim here is measuring energy and its storage and use) anything that requires effort for a period of time is what we will define as "work" so play also is "work" in the purely physical sense

what is needed to do work ? 2 things; energy and time

"i don't have any energy, i am full of energy etc.

everyday examples of work from a personal perspective;

writing a book playing a musical instrument climbing the stairs lifting a bucket of water onto a chair driving to the cinema ( this is also an example of leverage) walking to the top of Alphin, and walking down again (but, notice the difference !) etc.etc.

to do work we need fuel;

what is fuel ? ( fuel is stored energy is a pretty good answer)

an example of fuel is chocloate, choclolate is full of calories, everybody knows that don't they.. calorie is a measure of energy ( 1 calorie = the amount of energy needed to heat up 1 gram of water 1 degree C ) so a chocolate bar is an example of energy storage

how do we measure energy stored in fuel ?

if you look on the label it might have an energy amount per 100 grammes, usually in calories (small c) or Kilocalories (large C)

calories is a measure of how much energy is contained in the chocolate an indication of how much work it will help you achieve

you can also use calories to measure the energy stored in a bag of coal, a gallon of petrol etc

but we don't use calories any more
( we did until around 1960 in UK. Some other places, USA for example, still do use calories, feet, inches, pounds, gallons as measurement units)

calories and Joules are both measurements of energy, just have different scales, like inches and centimeteres

approx conversions: 1 kJ = 0.2 Calories 1 Calorie = 4.2 kJ One kilocalorie equals 4 kilojoules (rounded to the nearest whole number).

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since mid 1800s scientists and astronamers have been trying to get everyone to agree on some standard measures for basic stuff (further interest SI units https://physics.nist.gov/cgi-bin/cuu/Info/Units/history.html )

so we now use metres, grams, litres, joules, watts instead of the older and more confusing system of feet/inches, pounds/ounces, pints/gallons, calories, horsepower

the unit of energy we will use is the Joule
the unit of power we will use is the Watt
(1 watt of power equals 1 joule of energy for 1 second)

the Joule is part of standard/universal system of measurments, the basis of which is centimetre, gram, second (three dimensional CGS system, from which everything else is derived)

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aside note: Joule has a capital letter, because it is named after a person James Prescott Joule, (born December 24, 1818, Salford, lancashire, died October 11, 1889, Sale, Cheshire) a physicist who established that the various forms of energy—mechanical, electrical, and heat—are basically the same and can be changed one into another.

note kilojoule, Megajoule kJ MJ , the abbreviation "J" has a capital letter, the word "joule" doesn't

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some potential energy storage comparisons:

one litre of petrol or similar refined fossil fuel (petrol or diesel)

so about 36 MJ/litre

36 000 000 J

one of our 12v batteries

12V, 2.2Ah , i.e. 26.4 Wh
(Ah means "Amp hour", 1 Ah means the battery can supply one Amp for one hour)
(Wh means "Watt hour", this is equivalent to the Amp hour capacity x the battery voltage)

1 hour = 3600 seconds,
1 watt = 1 joule for 1 second, 26,4 Wh = 26.4 x 3600 Joules = 95000 joules

energy is the capacity to do work, the standard unit used for energy (and work) is the Joule.
A joule of energy is defined as the energy expended by one ampere at one volt, for one second. 

so 12V x 2.2A x 3600 seconds = 95000 Joules

95 000 J

10 (10kg) litre bucket of water at 1000 metres

The potential energy of anything falling from a height is given by U = mgh, where:

   • U is the potential energy in joules 
   • m is the mass in kilograms 
   • h is the height in meters 

1 liter of water has a mass 1 kg and the value of g is 9.8 m/s^2. U = 10(1000)9.8 = 98000 J

The amount of energy 10 L of water would have after falling 1000 m is,

98 000 J

a medium-sized electric car battery

( a 50kWh battery is good for about 220 miles before it needs recharging, giving an efficiency figure of 4.38 miles per kWh. 50 kWh in joules= 50000 x 3600 = 180 000 000 joules )

180 000 000 J

1 kilogram of coal

29 000 000 J

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work. energy and power: Key concepts

so we might now have an idea of the concept of energy, energy is the capacity to do work work done is when something useful is done, e.g. moving something, this requires force over distance

Connection Between Energy and Work Done

If energy is not conserved, then it is used to do work.  In other words, the work done is equal to the change in energy. energy and work are measured in joules ( J)

so what is power then ?

Power is the rate at which work is done (measured in watts (W)), in other words the work done per second. 

It turns out that:

in the mechanically realm:

Power = Force × Velocity ( newton x metres/second )

in the electrical realm:

Power = current x voltage ( amps x volts)

a key concept is that energy can be converted from one form to another, and stored in many different ways

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where are fossil fuels from ? where does the energy stored in a fossil fuel come from ?

( sunlight, organic chemistry, carbon locked up and stored underground from carbon which was fixed by organic processes millions of years ago)

btw; the carbon itself most likely came from a planetery collision, there is just too much carbon in the earths crust that would be accounted for without such an event

how does this relate to hyrdro power generation?

How much energy can I extract from 1 litre of water falling for 1 meter? 9.8 joules.

(You can extract the reduction in potential energy of the water, which is given by mgh , where m is the mass of the water, g the acceleration due to gravity at the surface of the Earth, and h the drop in height. In MKS units, water is 1 gram/cc hence 1 kg/liter, so m=1 kg, h=1 m, g=9.8m/s2, hence you can extract 9.8 kg-m2/s2 = 9.8 joules. )

calculating the amount of electricity (kilowatt hour) produced from 1000 liters of water per hour falling from a 20 meter fall through a hydro electric generator turbine? The potential energy of anything falling from a height is given by U = mgh, where:

   • U is the potential energy in joules 
   • m is the mass in kilograms 
   • h is the height in meters 

1000 liters of water has a mass 1000 kg and the value of g is 9.8 m/s^2. The amount of energy 1000 L of water would have after falling 20 m is, U = 1000(20)9.8 = 196,000 J 1000 L of water falls 20 m every hour the amount of power available is, 196,000/3600 = 54.444 W There are 3600 seconds in an hour & watts is the joules per second. Allowing for friction and efficiency of a turbine, say 20 percent of the available power is converted to electricity - turbine manufacturers will be able to give a more accurate number. The power generated would be, Electrical power generated = 0.2(54.444) = 10.888 watts per hour.

back to practicalities, walk round the building and check some power usages with a power meter, or the online power monitors: guess, measure write it down

What uses energy here at The Vale? Which items here do you think use the most? how much energy do we use in our buildings ?how can we find out ( bills, energy monitor, awareness)

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how much energy to boil a kettle ?

guess =

test = (look for the power rating, how long does it take? time it for say 1 litre)

calculate= can calculate from specific heat capacity of water : specific heat of water = 4200 J kg-1 K-1 so from 10 degrees to 100 degrees is 90 K, thats 4200 x 90 per litre (37800 J per litre) kettle is 2.2kW (?) thats 2200 Joules per second, shoulkd take 171 seconds for 1 litre in a 2.2kW kettle .... thats 37.6 kJ

measure= ( use the power meter)

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any thoughts on how much energy to:

heat a sinkfull of hotwater ?

anything else? we can measure using the meters and the plug thingy

to drive 20 mile round trip in small car ?

to fly to canary islands and back ?

to fly to brazil and back ?

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from all the above can be have a stab at how much water falling from what height would be the same energy as boiling a kettle ?

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at our first meet on 2nd May we tried 3 different ways to find out how much energy it takes to boil the kettle,

in the kettle, electric energy from mains power is converted to heat energy in the water, using a heating element.

to do this calculation, first we needed to know the specific heat capacity of water, which is 4184 J⋅kg⁻¹⋅K⁻¹. ( this is a simple fact, just like the fact that one litre of water weighs 1 kilogram ) Find this sort of information in a text book, or via internet search.

so, the specific heat capacity of water is 4184 J⋅kg⁻¹⋅K⁻¹. more simply put, that's 4184 J per kilogram per degree

which, in plain english, means: one kilogram of water has to absorb 4184 Joules of energy for it's temperature to increase by 1°C

just to make the maths easier, rather than use 4184 we will round it up to 4.2 kJ per kg per deg C,

starting conditions of the experiment:

• we made sure the kettle was cold by rinsing it out first with cold tap water

• we put in 1.5 litres of cold water from the tap

• we estimated the water from the tap to be 10 deg C

• we know water boils at 100 deg C
• we know the specific heat capacity of water is 4.2 kJ per kg per deg C
• we know the power rating of the kettle, about 2.7 kW, from the power rating label on the bottom of the kettle (this is very approximate, within 20% perhaps)
• and kW = kilo Watt , i.e. a thousand Watts, 1 Watt = 1 Joule for 1 second ( power = energy x time)

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first method; using the power rating and a timer,

it took 2min 20 sec, that's 200 seconds to bring to the boil

the kettle's pwer rating is approx 2700 Watts

Energy transferred = power x time

2700 x 200 = 540 kJ

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second method; using a plug-in power meter,

the power meter registered 0.165 kWh ( kilo Watt hours)

0.165 kWh = 165 Wh ( Watt hours)

there are 3600 seconds in an hour, so

165 Wh = 165 x 3600 Watt seconds, that's 594000 Watt seconds

we want the answer in Joules, , and we know Energy transferred = power x time i.e. 1 Joule = 1 Watt x 1 second

so the answer here is 594 kJ

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third method; theoretical calculation,

start temperature = 10 deg, finish temperature = 100 deg

so the temperature rise = 90 degrees

amount of water = 1.5 kg

specific heat capacity of water = 4.2 kJ per kg per degree

energy used = amount of water x temperature rise x specific heat capacity

so, energy used in kJ = 1.5 kg x 90 deg x 4.2 kJ per kg per degree ( or more scientifically written; energy kJ = 1.5 x 90 x 4.2 k J⋅kg⁻¹⋅K⁻¹ )

doing the maths; energy used = 1.5 x 90 x 4.2 = 576 kJ

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so all three methods come out with similar results,

first method; using the power rating and a timer, 540 kJ

second method; using a plug-in power meter, 594 kJ

third method; theoretical calculation, 576 kJ

of course we wouldn't expect the results to be exactly the same because some of the measurements such as amount of water, starting temperature, etc. were estimates or guesses, but the similarity shows we got some meanigful answers

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