Water

Maximum water load
6x1.5+1x1+2x0.5+1x0.75=11.75 litres! 

No topic here is more important than Water.

In the bundle of files (see under Download) there is a document called "Hiking the desert Arad to Eilat.pdf". It may be worth carrying this with you if you decide that this is a method that suits you. The bulk of the text in this post can be found in that document.

Overview

The Shvil Israel divides into three stages going from North to South.
1 Dan to Tel Aviv (20 days - 17 stages)
2 Tel Aviv to Arad (20 days - 11 stages)
3 Arad to Eilat (27 days - 20 stages)
Note: My count of days includes rest days.

The North and the Middle

The first two stages are relatively straightforward with the second a bit tougher than the first. The third is where it gets interesting and much more challenging.

That said there are places where I carried between 2 and 4 litres of water, and others where I filled with enough to camp overnight some distance before actually needing it. It gave me a sense of security and independence, and allowed me to pick a spot as soon as I found something suitable, knowing that I had sufficient food, water and fuel with me. That added flexibility at a cost of some effort. Overall this was good training for later on. I couldn't help noting how much easier cycle touring is than hiking in this regard.

However there are sufficient sources (springs and taps) as well as settlements such that you will survive and gradually acquire experience if you lack it at the outset.

Water quality

In all cases I drank tap water directly with no ill effect. Where I took water from Springs I invariably boiled it for tea or in cooking. I carried a few strips of tablets but used these rarely and only if I wanted cold water. I dispensed with my Steripen before the South as a weight saving measure, although generally I am much in favour of this method. Only once on the entire trip did I buy bottled water.

The South

Important qualifications
I did this hike in winter. I started on the 11th November in Dan and reached Eilat on the 16th January.

The feasibility of doing this the way that I did depends on three factors none of which may be the same for anyone else. So please take this as a description of what I did not as a guide to what you should do. You will need to work out your own program but it might help to have some ideas from this experience.

There are three factors that may differ considerably for you.

The weather
Even if you do it over exactly the same dates you weather may differ considerably. Most especially it could be hotter at critical moments. Or there could be flash floods. Beware!

Your capacity
To do it this way you need to carry heavy loads for many days. Your capacity to do this may be greater than mine or less.

Your consumption
Your body is not my body. You may drink less but eat more or eat less and drink more. Either way what you require will differ from what I needed even under identical circumstances.

That said here is a description of what I did.

Section by section details

I broke the third Stage into 7 Sections.

1 Arad to Sde Boqer
I left Arad in the late afternoon after eating well in town so I didn't need to cook that night. I had food for 6 days and 10.25 litres of water, which was my carrying capacity as well as about all I could manage (un)comfortably.

It took 6 nights to reach Sde Boqer and my food supply was perfect.

I had enough water to reach the quarry near where the road crosses to Dimona (approximately N 31.027639, E 35.24522).

My initial plan was to hitchhike to Dimona but they kindly let me fill up. The sign (in Hebrew which I couldn't read) forbids entry. I ignored this and while initially a bit put out that I had walked in they ended up being very friendly. The benefit of being a foreigner.

I then used that water to reach Oron plant. I refilled there and used that until Sde Boqer.

During this time I found one bottle of 1.5 litres neatly full (and cold!) and a 750ml bottle partially filled. This was a bonus and you can't count on it. But I would have still been ok without it.

Please also note that the most technically demanding part occurs towards the end of this section when descending a canyon. You may still be carrying several litres and a day's food at this point which means taking it very carefully.

2 Sde Boqer to Mizpe Ramon
This is a short section (3 nights) and I simply carried sufficient water and food for the entire section.

There is a small (expensive but adequate) supermarket in Sde Boqer. I stayed on the campus with a friend.

There was one spring (Ein Aqev) near the start with reliable water but I didn't take any.

There was just enough water in a couple of pools later on to help with washing up. But not really useful for drinking.

3 Mizpe Ramon to Tzofar
I camped about 6km before MR so only had about a 90 minute walk into town in the morning. It was the coldest morning of the entire trail (4°C).

In MR I drank coffee and recharged my phone at the gas station cafe, then ate at a little cafe behind the front row of shops.

I then bought 6 days food at the supermarket (and a couple of treats) and packaged these up into a cardboard box. I also bought 9 litres of water (6 bottles) in a pack with a handle.

After removing excess packaging I closed up the box and staggered with all this to the road leading out of town.

I hitched 58km to near Zihor junction (it's actually 2km before where the Shvil crosses the road: N 30.280512, E 35.001285). I walked about 300m and buried my cache in a hole covered with rocks. No digging tool was necessary.

I then hitched back to another point where the trail crosses the road about 13km before MR (N 30.583219, E 34.887446). I walked 1km or so to a place where I camped (about 2km before Wadi Gvanim camping).

I camped the night there and in the morning cached all my food, water and gear up the hill under a pile of rocks. I took with me an empty pack, jacket and the two water bottles that were by now empty.

I hitched back to MR to have coffee, recharge, do shopping (6 days food), buy a small gas canister (expensive and a little hard to locate the small shop) and have lunch.

Then I walked back to my camp, found my gear and cache and stayed a second night in the same spot.

This meant that I had enough water to reach Tzofar and food to last till Zihor.

4 Tzofar to Zihor junction
Having camped a few km before Tzofar I reached it before midday. There was a small supermarket, which also stocked gas canisters. I bought some treats to eat and a couple of extra supplies (flat bread and hummus).

I left with enough water (from a water cooler opposite) and food to reach my cache at Zihor (I arrived on the 3rd night).

5 Zihor to Shaharut
I left what I considered excess food, four litres of water (I had plenty in reserve when I arrived) and all my trash covered by rocks in my cache. I had sufficient food until Eilat and enough water until Shaharut.

Plan B in the event that my cache had been found and stolen was to camp overnight then hitchhike to MR, buy what I needed and return.

6 Shaharut to Be'er Ora
I replenished water in Shaharut where a very kind woman gave me a bag of fruit as well as filling my water bottles. Then I camped nearby. I had enough water to reach Timna Park.

Before Timna Park I met a tour group whose cook gave me three huge Pita breads made on an open fire with a lovely smokey taste. Very substantial.

At Timna Park the people were very friendly. I refilled water and they gave me a coffee and biscuits. I then had enough water to reach Be'er Ora.

7 Be'er Ora to Eilat
I refilled with water at Be'er Ora from the water cooler near the supermarket.

The small supermarket is good for a few food items and some on the spot treats. And a coffee. They also stock gas canisters at a decent price.

From here I had sufficient food and water for two nights till I reached Eilat in the afternoon of day 67.

Notes

What I would do differently
1 I needed less food in my main cache at Zihor campsite. After the trail I returned to collect the excess food and Trash. However I left 6 litres in the cache for a friend.

2 I would not take water from Ein Yetafim again. Didn't make me sick but it made terrible tea and was an unnecessary risk given that I had sufficient water with me.

3 I would carry a Sawyer mini water filter for some opportunistic refills from pools.

Water purification and treatment
In addition to filling water from reliable sources I carried two means of water purification.
1 Tablets (bought in Nepal). Cheap, effective and lightweight. It tastes less than ideal but good in an emergency. You need to wait 30-60 mins.

2 I also had sufficient fuel (gas) to boil extra water if needed.

Water carrying method
I opted for recycled Coke bottles and a Nalgene litre flask.

The advantages being that they are free, lightweight, robust, and provide redundancy. In addition it makes it easy to keep track of water consumption and rationing. I had one bottle with a sports top for drinking during the day.

I placed as much water as I could (5.25 litres max) under the lid of my pack. The remaining bottles were stored in an Ortlieb dry bag attached by shock cord to the back of the pack. This made it easy to manage, but did mean that at times the centre of gravity of the pack moved further away from my back than I would have liked. Still overall it worked and I felt it was a better solution than a single large water bladder.

Finally
It's a great feeling to be totally self dependent with the ability to survive for several days unaided. But it's hard work. It's quite possible that you may come across extra water either in natural pools or in bottles that people have dropped (or perhaps even left intentionally for others), but this water should be treated as a bonus and should not be relied upon.

Keep hydrated and stay safe. Good luck with your hike!