What happens to all that water?

 

On Christmas Eve the wind was blowing hard from the south creating large waves on Coniston Water. If you enlarge the pictures you might see the waves. You can see the raised water level in the second picture. It made me wonder what happens to the water. If the surface water is all being pushed to the northern end of the lake, what happens? Does that mean that the water level is higher at the northern end and that the lake acts as a sort of pumped storage scheme? Or is there a counter current below the surface moving water back south in a manner akin to a convection current? I've been considering how to make lab models to check these hypotheses.

White water

 

The weather has been miserable recently - one big Atlantic storm after another. We got the edge of the awful pre-Christmas storm that battered the south. There were high winds and a lot of rain. If you enlarge the picture you'll see the prominent white water in the waterfall on this outlier of Wetherlam at Coniston. It got me thinking: why is turbulent water white? The water is full of bubbles and split into lots of drops. There are many reflecting surfaces and light is reflected in many directions, a form of scattering. White means that all colours are being reflected equally in our direction. This is a sketch of an answer - what I've been thinking about the issue.

The final quarter

 

This was the final quarter waning Moon taken on Christmas Eve at breakfast time. The evenings were much darker in the last week or so with the Moon rising after midnight. This morning we were back to the final crescent which was the first photo graph in this series, taken a month ago. I think the New Moon is New Year's Eve.

Oxford's Christmas Light Festival

Oxford was geared up for Christmas. Many religions use the metaphor of light in the darkness. So Oxford hosted what they called a "Christmas Light Festival". As a physicist I'm programmed to study things dispassionately - objectively, we like to say. But human animals are also programmed to respond to things emotionally. So in the pictures below you see scenes in which photons are travelling towards you at 300,000,000 m/s - or you might prefer to say that you are seeing the result of self-sustaining sinusoidal electric and magnetic fields that are perpendicular to each other. You might also just say that it is very pretty. I'm sure I've quoted Bertrand Russell's remarks about light already this autumn. He pointed out that someone blind from birth could experience a wave motion on a ship and learn the Physics of light waves. But they would have no idea of our experience of light.

 

Coniston Hydro-electric Power

We climbed up to Copper Mines Valley at Coniston on Christmas Day.

 

 

At the top of the stream we found the feed for the Coniston Hydro-electric Power Station. I found the details of the scheme on-line http://www.gilkes.com/case-studies/Coniston It's actually an old scheme from the 1930s which fell out of use and was then restored. 



 
 

 

The water travels 700m and falls through a height of 72m to reach turbines that generate 300kW of electrical power. It says that it takes the water 25 seconds to fall that distance. If it fell vertically in a vacuum, my calculations show that it would take only 3.8 seconds. The drag in the pipe means that it won't reach its theoretical maximum speed.  

 

Waning gibbous Moon

 

Not the world's greatest photograph but note that the whole Moon is no longer illuminated. More than half but less than whole = gibbous. It is the right hand side that fades away - or wanes. I had to wait until gone 10 o'clock to see the Moon last night and this picture was taken at 8 o'clock in the morning facing west. The waning Moon is seen late at night.

Santa in space

If you didn't see the story in the newspapers, do yourself a favour and follow this link to watch the film http://www.stratodean.co.uk/ It's very similar to the project by students from a neighbouring school up here. I love the flight data at the bottom of the screen.

Winter solstice on the M6 Toll

 

It was the shortest day of the year in the northern hemisphere - or to be more precise, the shortest number of hours of sunlight. We say that the Sun has reached its most southerly declination - ie it is not very high in the sky at midday. I took this picture at 3pm GMT from the services on the M6 Toll motorway near Birmingham. The Sun is already near the horizon and ready to set. It won't be quite as early tomorrow. Summer is on the way!

Dry ice bubbles

When we had the dry ice a couple of weeks ago we found an experiment in a book which said to add water and washing up liquid. The water heats the dry ice causing it to sublime and turn directly from solid into carbon dioxide gas. The gas then blows bubbles in the washing up liquid. We even added food colouring for effect. I realise now that I missed a trick: I should have added a burning match and watched it go out because carbon dioxide is a fire extinguisher. We noticed an odd phenomenon in that the bubbles stopped after a while. The water got so cold in contact with the dry ice that it turned into familiar water ice right around the dry ice pellets. This stopped the carbon dioxide escaping and occasionally there were odd sounds as it forced its way out.

The Full Moon

 

We've reached the Full Moon. I took the photographs early evening and the Moon was low down in the east. I got my telescope out which is really for watching wildlife. It is a refracting telescope but does get to 40x magnification. At first the camera was over-exposing as in the first image. Far too many photons were hitting the CCD in the camera which removed any detail. I shortened the exposure time to get this image with better contrast.

The human wind speed measurer

It was incredibly windy yesterday. A tree even blew over on Lowmoor Road so we had to make a diversion going home. However, we made the most of the day before the rain came. Here is the author of this blog on top of Latrigg. It was one of those days when it was possible to lean into the wind and not fall over. So I've done some Physics to measure the wind speed.

 

Essentially we need to consider two forces. The red arrow shows my weight acting through my centre of gravity. It causes anticlockwise turning around the pivot so my weight would make me fall forwards. The green arrow is a representation of the force of the wind. This will act all over the front of me but I have assumed that it can be averaged in such a way as to act through my centre of gravity. It produces clockwise turning around the pivot. Provided the clockwise and anticlockwise moments (technical term for turning) are equal, then I won't fall over.

 

Anticlockwise moment = weight x distance from pivot = 65kg x 10 x 0.15m roughly = 100 Nm roughly.

 

To calculate the force of the wind I'm going to use Impulse = change in momentum.

I am assuming that the air stops dead when it hits me.

Momentum = mass x velocity.

If I take a time of one second, a volume of air hits me that I will assume is rectangular in area and cuboid in shape. It's area will be my area, roughly 1.8m x 0.30m. It's depth will be the distance the air travels in 1 second ie the velocity of the wind v. Volume of air stopped in 1 second = 1.8 x 0.30 x v. The density of air is about 1.2 kg per cubic metre so mass of air stopped in 1 second = 1.2 x 1.8 x 0.30 x v = 0.65v roughly.

So change in momentum = mv = 0.65 x v-squared.

Impulse = force x time but time was 1 second so finally

Force of wind = 0.65 x v-squared. This is the green arrow

 

Clockwise moment due to wind = force x distance from my feet to my middle = 0.65 x v-squared x 0.9 = 0.6 x v-squared to 1sf

 

Set the two moments equal to each other:

0.6 x v-squared = 100

v-squared = 170 ish

v = 13 metres per second

This is about 30 mph.

 

It's impressive that this rough method gives a not unreasonable answer. Consulting the Beaufort Scale suggest it might have been nearer 40 mph.

 

 

A gibbous Moon

We went to Watchtree last night to hear a talk about astronomy by the Border Astronomical Society http://www.astronomyclubs.co.uk/ Sadly Comet Ison has vanished but we did look at Jupiter and the Moon. The Moon didn't reach its zenith until mid-evening and 3/4 of it was lit up. It's called a gibbous Moon. The Moon is said to be waxing for the first half of the month when more and more of the surface is being lit up.

First quarter Moon

 

The Moon is waxing at the moment. That's an old fashioned term that means that the Moon is getting more and more lit up as the days go by. I posted about the first crescent last Thursday. Technically the New Moon is when you can't see anything I think. Today we have reached the first quarter. Oddly named because half of the face is lit up.

 

The New Moon coincided with awful flooding on the east coast - a tidal surge. At the New Moon, the Moon and Sun are in line on the same side of the Earth. They pull together on the sea and produce bigger tides. This coincided with a major storm to cause flooding.

Making "smoke" with dry ice

I had some dry ice to use up before it melted. For those who've missed the concept, dry ice is solid carbon dioxide. It is at about -80 degrees Celsius. However, when it melts it turns straight into a gas. You don't get liquid carbon dioxide at normal pressures. We say that the dry ice sublimes - the technical term for turning straight from a solid to a gas. A favourite trick is to pour water onto the dry ice. The water might be at 5 degrees Celsius at this time of year but that is considerably warmer than the dry ice. The dry ice sublimes and releases the carbon dioxide gas. Look at the picture. Carbon dioxide is invisible so why is there a white gas? The answer is that the carbon dioxide gas is still very cold. This make the water vapour in the air condense to form clouds. We've made fog! It was how they used to make "smoke" on stage.

 

The fog is much colder than the air around it. It contracts and is therefore more dense so it sinks. That explains the "waterfall" of fog over the lip of the tray. I have seen cloud do this between valleys on days when there is a cloud inversion.

The secret cave in Langstrath

We spent a day out in the rain looking for the secret cave in Langstrath. We knew roughly where to go but it took about 20 minutes to find the cave entrance. It's an unusual cave because it is really just a space under massive boulders from a crag which collapsed. As you can see, the entrance is very small. You have to crawl inside. You can stand up in there though. Someone has put down boards so that four or five people can sleep in there. There are metal supports and there used to be a metal door.

 

We tried to estimate the mass of the boulder above it. We estimated 5 metres long by 5 metres high by perhaps 4 metres deep means 100 cubic metres. The density of andesite, a common volcanic rock in these parts, is about 2.5 tonnes per cubic metre. So the rock will have a mass of maybe 250 tonnes. And you sleep underneath it! It was hard to take photos inside but here is one of the cooking shelf. There was even a dust pan and brush in the bag. We signed the visitors' book but it is full so if you go consider taking an empty exercise book.

 

So where is it? It's a secret. No one on the Internet tells you exactly where but we worked it out. All I'll add is that it is at the very bottom of the crag. I climbed too far up at first.

 

New Moon Over Wigton

 

Enlarge this picture and you'll see that as predicted, the crescent has moved from the left hand side lit up to the right hand side lit up. And the Moon has moved from the morning to the evening. It's the start of a new lunar cycle - a New Moon.

The Physics of Leo Houlding

We went to see Leo Houlding talking about two amazing expeditions last night in Lancaster. No photographs allowed but you really ought to watch the trailers to his new films to why I thought the mountains were awesome: http://www.youtube.com/watch?v=WzBaPd3OxmM and http://www.youtube.com/watch?v=IqkxeZza5mM

I noted down several bits of Physics.

He stated that a stone dropped from the top of El Capitan in Yosemite falls 1000m in 27 seconds. Simple calculation ignoring air resistance using the equation s = ut + 1/2 at(squared) suggest 14 seconds. There is the possibility that he has timed it but that would mean reaching terminal velocity very quickly. I'll need to think about the calculations involved to figure that out.

About the film of climbing on Ulvetanna he claimed that it went from -5 to -20 degrees Celsius in seconds when the shadow of the mountain moved across the climbers as the day wore on. What a marvellous example of radiant heat - that the heat from the Sun comes as infra-red at the speed of light, even in Antarctica.

He also said that the most efficient way to melt ice for drinking water was to constantly boil 3 litres from below with two stoves and then add a few snowballs at a time. This sounds like a do-able but tricky calculation for the Upper Sixth after Christmas!

No Moon This Morning

 

No sign of the Moon this morning at roughly the same time as Saturday. As predicted the time for the Moon's zenith will have moved forward about an hour a day. It will be highest in the sky at around midday. The shadow side will be facing us so we won't see a Moon. Note that the dim light needed a longer exposure time with the shutter open for a longer time than usual to let in enough light. I couldn't hold the camera perfectly still so the photograph is slightly blurred.

Sliding away in Wigton

 

There was an ice rink on the car park over the weekend. I didn't go on but I'm told that it wasn't really ice. In fact, I've found the Wikipedia page for "synthetic ice" http://en.wikipedia.org/wiki/Synthetic_ice The Physics issue will be that the surface has a low coefficient of friction. The skates have a very small surface area and a polished metal surface also has a low coefficient of friction. If it had been real ice I could have written about the high pressure under the blade causing the ice to melt and you sliding along on a sheen of water which refreezes behind you. 

Luminites and the Wigton lights

It was the switching on of the Wigton Christmas lights tonight. Here's our MP Rory Stewart counting down to the moment that the lights came on.

 

He was followed by the Luminites. I thought they were great on BGT and they were great again this evening. They were very nice about Wigton. And RESPECT to everyone who put on a great event that brought so many people out.

 

Here comes the Physics: Light is an odd thing. I'll tell you that it is an electromagnetic wave. It consists of a moving electric field wave with a moving magnetic field wave at 90 degrees. Each field generates the other so light can be self-sustaining through a vacuum. It does not need particles. However the philosopher Bertrand Russell made a good point. He said that you could take a person who was born blind and put them onto a boat. They could feel the waves moving the boat up and down and you could tell them that light is like that: light is a wave. But he pointed out that they would have no idea what light is really. We don't define it; we just experience it. Physics take note.

The end of the Moon

Never mind Comet Ison, the Moon has almost gone! Well, for this month at least. The Moon has nearly finished its monthly journey around the Earth. This picture was taken at 8am looking almost due South. In other words, it is highest in the sky at perhaps 9am. If it takes 27 days to go round the Earth, this high point in the South must be about an hour later every day. That means in 3 days time the Moon will be due South at around midday. It will be on the same side of the Earth as the Sun. The Sun will be lighting up the side that we can't see and the side facing us will be in shadow. In other words, in a couple of days we won't be able to see the Moon at all. Then after that there will be a faint sliver of a crescent on the right hand side this time - a New Moon. If the sky is clear I'll try to photograph it!

Cows need water

We were out on Hadrian's Wall the other month and found this water trough for cows. Our house doesn't have a water tank like this in the loft because the advent of the combi-boiler has removed the need for a hot water tank. But the ballcock is a fabulous invention. The plastic ball is less dense than water so it floats. The upthrust force on it pushes it up against the valve in the pipe, closing the valve. As the water level drops, the floating ball drops with it. Eventually there is so little upwards force on the valve that water pushed through to fill the tank. The floating ball rises to close the valve and cut off the water. An example of feedback!

 

An piece of art about waves

 

We went to Tullie House on Monday to see the Roman helmet but we also found a brilliant work of art. They would let me photograph it so you'll have to make do with a photograph of the leaflet. Alternatively you can go to http://www.artfund.org/what-we-do/art-weve-helped-buy/artwork/11956/ocean

It is about 1000 small ceramic pots laid out to be like a wave on the ocean. Waves are a transient thing. They are hard to pin down. Do you draw a graph of them frozen in one moment in time or draw a graph of how a single point on the wave moves with time? I suppose Natasha Daintry has chosen the former. I like its simplicity. I should have measured the wavelength. The amplitude decreases. What would we give for the wave speed? The exhibition is in Carlisle until March - plenty of time to go to see it.

DNA security at the substation

 

Substations are very dangerous but we were intrigued by the DNA sign. The yellow sign is obvious. Will need to find out about the DNA security system.

Kelvin Wake on Walla Crag

I always like climbing up above Derwent Water because you can look down on the wave patterns. Yesterday we were looking down from Walla Crag when the passenger boat came past. If you enlarge the photograph you can see the characteristic wave pattern behind the boat. It is called a Kelvin Wake after Lord Kelvin the Scottish physicist who first did the analysis. I haven't had time to read the mathematics in detail - I'll need to get back to you - but it seems that the angle may be just over 19 degrees whatever speed in deep water. I need to check this claim. I got my information from http://www.wikiwaves.org/Ship_Kelvin_Wake

 

 

When we were on the summit another bloke pointed out the marking in the rocks shown below. He said he thought it was a benchmark, which was a topic on this blog in September. I have checked the benchmark listing website and it's not recorded, so the jury is out. It doesn't look natural but it is flat, not vertical. It has no top line.

 

Red like a Spindle Tree

We found a Spindle Tree at Watchtree Nature Reserve. We surprised to find one so far north. Note the lovely red flowers. I teach that things are red because they reflect red but absorb the other colours of the spectrum that fall on them. The combination of the colours makes up white light. Quantum theory leads to some uncomfortable thinking for me. What do I mean by absorb? I'd normally mean that the photon energy matches an electron energy level jump so an electron jumps up. But that's what happens with the red. Then the electron falls and re-emits a red photon as far as I understand it. I'd say that the other photons are ignored by the atom as their energies don't match electron level jumps. So where do they go? They don't go though the object or else it would seem somewhat translucent. This needs working on.

 

Measuring the flow in Wigton

They put a depth measurement scale into the Wiza by the factory in the summer.

 

 

This followed the disastrous flood one Saturday afternoon in May. Here's what Station Road looked like. And, yes, that is someone canoeing down the road.

 

 

The study of fluid flow has its place in Physics. I hope someone will be able to find a solution. Perhaps data from the new pole will help.

The issue is flow rate. This means how fast the volume of water is shifted so it will be measured in cubic metres per second. At this point in Wigton, the Wiza is constrained in a narrow but deep channel. Water cannot be compressed into a smaller volume. In a liquid, the atoms are basically touching each other. If the new shape of the channel doesn't have a big enough volume for the water pouring into it there will be flooding. One way round the problem is to get the water flowing faster, or to pour the water in slower at the start. The other problem is that the water has a tight corner to turn at the factory so momentum will tend to make it carry straight on and out onto the road by the fire station.

Lower Sixth Estimation Question #3

Here are 2 pictures of a radiant heater showing it before and after it is turned on. It is made of 2 heating elements that are wired in parallel. Each element is rated at 1kW. It is connected to mains voltage. If you click on the top picture to enlarge it, you'll see that each element is made of reasonably thick wire wound around a cylinder. Ignore the central cylinder - it's the wire that spirals around it that carries the current and heats up.

 

I want you to

1. Calculate the resistance of one of the heating elements.
2. Estimate the length and cross-sectional area of one spiral of heating wire.
3. Calculate the resistivity of the wire.
4. See if you can find a metal with that resistivity.

 

Biomass

We found this sign on the door of a hotel shed in the Lake District. Biomass is a word that seems to have changed its meaning.

 

Biomass has a strict meaning in Biology. It is the mass of the living tissue in an organism. Water isn't alive so it can't be counted. When you stand on the scales you are weighing both your biomass and the mass of water. To find your true biomass we'd have to dry you out in an oven before weighing you. In Biology the movement of biomass in a food chain is important. The higher up the food chain the lower the total biomass because some is lost by living.

But biomass is now often used for fuel that has come from living things as opposed to fossil fuels. It seems to me that this shed is really just a wood store with a fancy name!

On the front line in Silloth

We drove through rain from Wigton to Silloth to have our lunch. The sky was just clearing over the sea as we arrived. Looking south west along the coast there was this long bank of cloud. According to the weather maps it's a cold front. At our latitude, cold air front the Arctic runs into warm air from the Equator. The air masses don't easily mix to give medium temperature air. Where a block of warm air meets a block of cold air you get a weather front. What happens is that as the cold air moves into the back of a mass of warm air, the warm air moves up because it is less dense. A wedge of more dense cold air moves in underneath it. There is more water vapour dissolved in the warm air but as that air rises it cools down. The water vapour can't be held invisible in the air anymore so it condenses out to form clouds. So the boundary between warm and cold air is marked by a line of cloud. These were first drawn on weather maps just after the First World War. They looked like maps of the Western Front battle lines, so they became called weather fronts. It takes about 6 to 8 hours for a frontal system to clear the UK, hence my dad's old weather saying: Rain before 7, fine before 11.

 

 

Looking north east. The weather front curls away to the right.

 

Looking over to Criffel in Scotland. This is looking into the cold air mass. There is less convection to distort the visibility in cold air so the view was very clear.

A real radiant heater

I couldn't resist photographing this radiant heater. This type of heater was always used as an example in Physics text books. The bright bits are tightly wound coils of thick wire. They must have high resistance because the current heats the wire until it glows at the red end of the spectrum. As well as the visible light, a lot of infra-red must also be released. It is reflected in our direction by the concave silver backing. Silver is a bad absorber of infra-red. These heaters are great because they heat a room most quickly. The infra-red travels at the speed of light. The other issue is that the metal case would conduct electricity in the event of a fault. Thus there is an earth wire soldered onto the case to conduct away stray electric current and blow the fuse. The case can't be made of insulating plastic because it would melt.

 

 

Finding fault near the Priest's Hole

We climbed up to the Priest's Hole, a rock shelter high on Dove Crag. Some people sleep there and it even has its own log book to record your visit.

 

 

Caves in the Lake District cannot be like those in limestone areas that are due to acidic water wearing the rock away. This is because the rocks are volcanic. I suspect this enlarged overhang is probably the result of ancient earth movements - ie a fault. The cave is situated near the top of the crag just left of centre in the picture below. If you enlarge it you can probably make out a diagonal grass shelf sloping from left to right. This is evidence of a fault.

 

We found this amazing boulder nearby. The ash layers in the tuff are clearly visible.

 

Look at the small scale fault in the rock. It has only slipped a few centimetres.