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$1,000,000 if you can move 1000 liters of water from Sydney to Los Angeles in 21 days. How do you do it? (lemmy.world)
submitted 2 weeks ago by to c/asklemmy@lemmy.world
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You have 1000 kilograms of clean, fresh water in a single IBC container in Sydney at the Opera house. You will be paid 1 million dollars if you can deliver it to Los Angeles McArthur Park within 3 weeks, or 21 days, or 504 hours. You can split the water into as many containers as you want, and the IBC doesn't need to make it to LA, just the water inside. If you deliver 2000 bottles each containing 500ml of undiluted, clean, fresh water, or like, 99% of it to account for evaporation and some spillage, that counts as a win. You can assume that any partial water deliveries that remain in Sydney or arrive in LA won't be stolen in your absence so you don't need to hire guards. There are no consequences for failing, but if you do fail or succeed, any money you spend on the project, you don't get refunded. Normal consequences for breaking laws apply.

How do you do it, or do you even bother trying?

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[–] 1 point 1 week ago*

I've been a bit busy at work, but I'll deliver on my promise of numbers :D

I've used the Darcy-Weisbach equation for the pressure drop / flow rate relationship, and assumed

  • We have laminar flow in the hose (which is reasonable)
  • You're delivering water at 1 bar (can't go below that without suction on the receiving side)
  • Viscosity of water: 1.0518 mPa s
  • Viscosity of air: 18.03 micro Pa s
  • Your hose is indestructible, and can therefore tolerate arbitrarily large pressures.
  • You have the pump ready at day 0, and the hose is already stretched out at day 0.

The biggest pumps I could find (1, 2, 3) can deliver water at 400 MPa, with pretty high flow rates (much larger than what we can support with our hose). We're talking about pumps that draw on the order of 1 MW of power.

We start pumping water into the air-filled hose at 4 000 bar on day 0.

After two days, the water front has moved about 1000 km along the hose. Flow rate is at about 1.2 L/s, and pressure at the water front is at a solid 450 bar. This is looking good.

After one week, the water front has moved about 2000 km along the hose. Flow rate is now at about 0.6 L/s, and pressure at the water front has fallen to 200 bar. You begin to worry.

After two weeks, the water front is now at 3100 km. Flow rate has further fallen to 0.4 L/s, and pressure is at 150 bar. The pressure on you to deliver is substantially higher.

After three weeks, water has been pumped 3900 km, and is moving at a speed of 1.15 m/s. Pressure at the water front is around 100 bar. The guys that loaned you money for the massive pump and indestructible hose are lurking around your house.

About 100 days later, the first water starts flowing out of the hose in LA at a flow rate of about 0.5 L/s. It would take you about half an hour to fill the 1000 L tank at this rate. Too bad the tank was impounded by the guys that loaned you the pump and indestructible hose. You have gone into hiding.

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