Running Grisly Numbers

As I have noted earlier, I've not made much in the way of comments about the Gaza war, because I have very little to add.

Then there was a discussion of plans by IDF to bring in large pumps and flood the Gaza tunnel complexes with seawater at the Stellar Parthenon BBS, and someone said that they should use desalinated water to minimize the damage.

And then I got to go all, "Guardian of Forever," because I got to run numbers. Someone gave me a problem to solve, and by Spock's pointy ears, once you do that, there is no stopping me.

Just ask Sharon*, when I said early in our marriage that I was neither of us were the divorcing kind, we were the murdering kind, and she asked me, "So how would you kill me?"

Give me a problem, and I will look for a solution.  It makes me happy to figure stuff like this out.

My solution, rather upset Sharon* for a few days, but as the chicken said, "You knew the job was dangerous when you took it.

So back to the flooding problem.

Point 1 which should be obvious to everyone, is that flooding the tunnels will do enormous damage regardless of the salinity of the water , because pumping that much water into a cave complex does a f%$# tonne of damage.

So, let's assume that the IDF has about 20 so pumps to flood the Tunnel.

The first question is, "How much water will they move?"

Well, given that the Three Gorges dam has a flow rate of about 600–950 cubic metres per second with a water head of 86m through through its generators, and you are looking for flow rate, and not pressure (head), we can say that about 20 pumps could likely put out about 100 m3/s, (26,417 gallon/s) probably with about a 10m (32.8 feet) head.

Each pump would put out 5m3/s (1321 gallon/s).

By way of comparison, the one of the larger fire boats out there the Warner L. Lawrence  can put out about 38,000 gallon/minute. (633 Gallon/S or 2.397 m3/s).

OK, so we would probably be looking at more pumps, or less water, but comparative numbers are the same.

The equation for the energy required for pumping is:

P = q h ρ / (6116 103 μ) (3)

where

P = power (kW)
q = flow (liter/min)
h = head (m)
ρ = density (kg/m3) (water 1000 kg/m3)
μ = pump efficiency (decimal value)

100 m3/s equals 6 million liters per minute, we've got a head of 10 feet, and I am assuming a pump efficiency of 80%, which is probably a bit low.

Crunching those numbers, we get 12,263 kW, which is a lot of power, about ⅓ of the shaft horsepower of a Virginia Class SSN.

So for 100 m3/s of water desalination, how much power does it take?

Well, it takes between 3 and 9 kWh/m3 of water using reverse osmosis, generally considered the most efficient method. Taking the low end, 3kWh = 10,800,000 Joules, so to desalinate 100 m3/s of water, you would need, 1,080,000,000 Joules/s = 1,080,000,000 W = 1,080,000 kW = 1,080 mW = 1.08 gW.

That is roughly 88 times more power than involved in just pumping sea water, and about 5% of Israeli generation capacity of 21.5 gW.

As such it is likely not viable.

Now this is all just spitballing, and I am not considering the humanitarian and moral issues, because this serves as a way for me to avoid the potential humanitarian and moral issues.

Please, feel free to check my math.  It is late at night, and I am still recovering from whatever variant of the Plague that I caught from my wife, so my mind is no where as clear as it should be.

Feel free to castigate me for running these numbers as a way to avoid looking at the moral dimensions here.  I just can't do that yet.

^*Love of my life, light of the cosmos, she who must be obeyed, my wife.