As I said last night I would follow up on more details of this.
I am a little further advanced than I think I indicated but as I have found out in the last 24 hours there are a lot more things to consider.
I obtained from the Internet a design book which is the most detailed set of equations that I have been able to lay my hands on. It is an FAO document on designing fish farms and has a chapter on hydraulic procedures that may be relevant to that. Section 3.7 of Chapter 8 is entitled Design formulas for Siphons. The full document is located at:
and it is by J. Kövári of Food and Agriculture Organization of the United Nations, Rome, Italy
It includes calculations for atmospheric pressure at various heights which I have parameterised, vapour pressure of water vs temperature, pipe losses, bend losses, suction heads, downstream heads and minimum flow rates for various pipe sizes. I have built this into an Excel spreadsheet and it seems to give meaningful numbers.
However, some other reading on the subject suggests that cavitation may be a limiting design criterion and I am keen to get independent confirmation that the figures for the siphons created will work.
From the comments from this forum I see I have to add two parameters to the model - liquid density which will reduce the atmospheric pressure head compared to pure water, and mole fraction of the liquid which will have a slight lowering effect on the vapour pressure. The latter can probably be ignored as it will only make the design a little more conservative but the former is important. It is easy to add this.
There are three aspects of the design which are given without comment and which cause me concern.
- I think the calculation of the allowable pressure head before velocity terms are added is rather conservative? They use 90% of the atmospheric pressure head less the vapour pressure head less 1m. Thus at sea-level and with 20degreeC water the allowable pressure head is 90% * 10.3m - 0.24m - 1m which is just over 8m. Is this a good rule to ensure no problems with cavitation etc.
- They have a mysterious Minimum flow as a function of pipe diameter.
1m/sec at 120mm, 1.5 at 200mm, 1.7 at 400mm etc up to 2.6m/sec at 1200mm. I cannot find the logic behind this. Plotting the function shows it to be very strangely shaped with a rapid rise, then a slow rise then a sort of asymptotic rise again. I wonder if this is the rate that will tend to flush out entrapped air at the top of the pipe?
- They insist on a minimum depth for the intake. There are various formulae for this and my guess is that it is to prevent air being drawn into the intake by (in my layman's terms) a whirlpool. This is not too much of a worry though as it does not affect the design and builds in more flexibility.
So I would be interested in the groups comments on the first two points above, and any other on the overall design concept if anybody is interested in going there.
Now the lake situation.
The Ruapehu Crater lake (See the google images using those three words) is at an altitude of 2530m, is some 400m by 500m in size, and has a catchment of about 1km2. An average of 5000m3/day flows into the lake. The water has pH about 1,is muddy brown in colour and ranges from 20 to 40 degrees C in temperature.
At its outlet is a 7m deep tephra (volcanic ash) dam over a more solid base. If the lake got to the top of the dam and started to erode it, the whole top
7m of the lake could take off down the valley in about 15 to 45 minutes, picking up on its way 3 to 5 times its volume in "mud" i.e. about
2000m3/sec. It would be fun to watch.
The lake is not in an area that is easy to reach. A good walker could get there in just over an hour if the skifield chairlifts were running, and two hours otherwise. It is in a National Park (I think the second one created in the world), it is a World Heritage site, and is of considerable importance to all New Zealanders particularly our Maori people. Bulldozers are out.
To date siphons have (apparently) been considered but rejected for vague reasons that they "don't work at that altitude" or are "too hard to maintain so far from base". These are the points that I am considering.
Would a siphon work there and would it work well?
My initial calculations say yes and I have passed my spreadsheet to the people concerned. They want the calculations checked by someone with expertise. Read - not an amateur scientist electrical engineer in his mid
It seems to me that with 60m of 200mm pipe buried in a shallow hand made trench to minimise visual impact and maximise working head one could slow the rate of rise of the lake level and allow the water to infiltrate the tephra and break it down. A lahar from 3-4 metres below the top of the dam would be a much smaller event than the 7m one above and would have much less effect downstream.
The effect of the water downstream is already accounted for. This river does not pass through any power schemes etc. All its neighbours do though. It does not need piping down the hill - spilling down the valley is fine.
Meanwhile all aspects of safety downstream are being dealt with well. And yes people ski there (including myself), people hike there (including myself), and people climb there. It is a wonderful place. And yes I will ski there this coming winter!
At the last eruption (1995 and 1996) we could see the plume from Hamilton where I live 180km away - that¹s about 110miles.
So that is the situation. I wonder if anybody has comments to make on this scenario, in particular to the questions I raise. You have already offered a lot of very useful pointers. Some need more thought from me. Starting, bleeding, keeping it going, density, materials, etc. etc.
Thanks for your efforts so far - it is appreciated.