If you had 1,000 liters(1,000kg) of water and as much material, space, and time as you need to build a system.

Question

That system must be open to the atmosphere at the top. The contest is to see who can get the most pressure over an area of 10in^2 on the ground. The only thing you can use to get the pressure is gravity and the water. What shape would your system be and what would be the pressure on the 10in^2 area at ground level.

"The only thing you can use to get the pressure is gravity and the water."

What I mean to say is that the system can have no moving parts.

Answer 1

It would be shaped like a giant upside down golf tee. More accurately, it would be a flat disc shaped chamber at the bottom with a thin tube extending up out of it, very high into the sky.

It would be made of a very strong and rigid material like steel, but the inside would be coated with a water repellant material like teflon.

The principle is that at a point at a given depth within a column of liquid, the pressure is equal to the height of the column above that point times the density of the fluid:

height (cm) X density (gm / cm^3) = pressure ( gm / cm^2)

This relationship is independent of the WIDTH of the column.

Therefore you can exert the same amount of pressure using a thin tube of water as you can with a thick one. Since the thin tube contains less volume per linear distance, your fixed volume of water would stack up higher and exert more pressure!

Ignoring practical concerns such as the fact that water tends to stick to the walls of thin tubes and wick upward (this is why I suggest to teflon coat the inside of the mechanism - to minimize the capillary effect) you can basically calculate the gemoetry of the container to solve for any pressure you like. There is effectively no upper bound.

Let's do some practical examples:

I'm going to convert to cm's since you gave me water in liters.

10 in X 2.54 cm/in = 25.4 cm. 25.4^2 = 645.16 cm^2.

Lets construct a volume chamber at the base of our water pressure mechanism which holds very little volume. Let's make it a circle with an area of 645.16 cm^2 and 1 cm deep, completely enclosed. it now has a volume of 645.16 cm^3.

That's 0.64516 liters, we have 1000 - 0.64516 = 999.35 liters left.

Now lets construct a tube that enters into the top of our volume chamber. Let's make it a tube with a cross sectional area of exactly 1 cm^2 so that every 1 cm of height corresponds to exactly 1 cm^3 of volume (and exactly 1 gram of water weight).

Since we have 999.35 L = 999,350 cm^3 of water left, this tube will fill to a height of 999,350 cm.

999,350 cm X 1 g/cm^3 = 999,350 g/cm^2 at the bottom of the column. To be precise, add the remaining 1 cm of water height IN the volume chamber which we designed to be that deep.

This mechanism exerts a pressure at the base of 999,351 g/cm^2.

This isn't, strictly speaking, a correct answer. The unit "gram" is a unit of mass, unlike the unit "pound" which is a unit of force. The SI unit for force is actually the "newton" (N) which is the amount of force needed to accelerate 1 kg at 1 m/s. On earth, under the acceleration of gravity (g) 1 kg exerts a force of 9.8 N. Therefore this answer should be converted into the units N/m^2 which is "pascals" (Pa).

I don't think in "pascals", I think in PSI because everything I've ever built to withstand pressure has been metered out in PSI.

So, screw the SI units!! I'm converting to PSI.

1 pound is about 453.59 grams.

999,351 g X 1 lb / 453.59 g = 2203.2 lbs.

1 inch = 2.54 cm. 1 cm^2 is therefore 1 / (2.54^2) in^2 = 0.1550 in^2

2203.2 lbs / 0.1550 = 14,214 PSI

If you want to double the pressure, halve the diameter of the upright tube so that the column goes twice as high ... etc.

At the extreme, you could back-calculate. If you want 100,000 PSI at the bottom, you'd use the equation:

100,000 PSI = h inches, (height) X 0.036 lbs/in^3 (water density)

h = 100,000/0.036 = 2,767,976 inches

1 liter is about 61 in^3, 1000 L is about 61,000 in^3

61,000 in^3 / 22,767,976 in = about 0.022 in^2

So, using a column with a cross sectional area of 0.022 inches, you could raise your 1000 liter volume to a height of over 2.7 million inches, and exert a pressure at the bottom of 100,000 PSI.

Eventually, the surface characteristics of the thin tube starts to play a role in the way that water acts inside it. For this you'd have to incorporate some physical chemistry involving concepts of "surface free energy" and "capillary action" (which I don't remember how to do!)

However, the principle is that the pressure equalizes out throughout the water at a given depth, so that the column of water above does not need to be the same cross sectional area as the surface at the bottom in order to exert static pressure. All you have to do is raise a column to a given height and the pressure is determined by the height and the density of the fluid.

I hope that helps.

Answer 2

Water pressure varies based on height, and not on volume. So the higher you can get the water level, the more pressure there will be. 1000 L is 61023.8 in^3. If you have a tube with a base area of 10 in^2, this means you have a height of 6102.4 inches, or 508.53 feet of water. A foot of water gets .43 psi (lbs per square inch) of pressure, so at the base, there will be (508.53 ft*.43 psi/ft) = 218.7 psi of pressure.

Now theoretically, you could make a cone shape. This would force some of the water to expand upward past the 508 feet as the circumference gets smaller. At the top, it would have to be open, but theoretically you could get the water level much higher than 508 with a cone.

This can be taken even further with a very thin tube, that opens up at the base. You can make this tube extremely high, which would cause the pressure at the base to be extremely large. This would theoretically be the best design. The higher you can get the water to go, the more pressure there will be at the base.

Answer 3

You could create a pipette of a diameter just large enough to avoid capillary effects. This pipette could be quite high. If the cross section were 1 sqin, the height would approach one mile, and the pressure at the bottom would exceed 2000 psi. At the very bottom, just open this pipette up to a 10 sqin disk to transfer the pressure over the entire area.

This is how hydraulics work -- create a high pressure over a small area, and then transfer the high pressure to a large area.

Answer 4

You are going to have to keep the water cold to prevent its evaporation out of the top at those very, very high altitudes.