Physics of an amusement park "Ocean Park".

Single aspect with physics principles discussed in detail

I chose to discuss the water pressure exerted on the glass at the Atoll Reef.

The aquarium has a circular cross-section with a radius of 10 meters, and a depth of 9 meters. It consists of 3 viewing levels for visitors: ground level, Lower 1 (L1), and Lower 2 (L2).

The panels are 2 meters high each and each level is separated by 1 meter of concrete ground. As there are three different levels, the pressure is different for each level, resulting to panels of different thickness. On ground level, the glass is 2.54 cm (1 inch) thick, 5.08 cm (2 inches) thick on L1, and 7.62 cm (3 inches) thick on L2. The increasing thickness of the glass panels which are placed lower is due to the increasing pressure of water as you get deeper into the water.

Without the right thickness of glass, the difference of pressure outside the aquarium and inside the aquarium might cause the less thick glass panel to crack, endangering both the fish and visitors. The glass must be able to exert an equal and opposite force to keep in equilibrium. The maximum force the glass can withstand must be around 10 times more than it's usual load for obvious safety reasons; visitor like children hitting the glass panel, fish hitting the panel, and other unusual accidents which might occur which results to the glass panel withstanding an extra force.

I am modeling this problem with air pressure and water pressure acting oppositely each others as vectors. I will work out the pressure on the very bottom of the panel of each level, which means I am using the depth readings 2 m, 5 m, and 8 m.

I believe the glass of the aquarium is made of silica (SiO2), which has a Young's Modulus of 94 GPa.

P = gph

Where P is the pressure exerted, g is gravitational acceleration, p is the density of the liquid, and h is the depth.

Pressure at ground level:

P = 9.8 x 1000 x 2

P = 1.96 x 104 Pa (2 s.f.)

Pressure at L1:

P = 9.8 x 1000 x 5

P = 4.9 x 104 Pa (2 s.f.)

Pressure at L2:

P = 9.8 x 1000 x 8

P = 7.84 x 104 Pa (2 s.f.)

Now that we have the pressure exerted on the glass, we can work out by how much the glass is compressed by using Young's Modulus. Using the information that the area of the glass is 2 x 1:

For ground level:

Young's Modulus = Stress / Strain

?l / l = Stress / Young's Modulus

?l / 0.0251 = (1.96 x 104 / 2) / 9.4 x 1010

?l = 2.6 x 10-9 m (2 s.f.)

For L1:

?l / l = Stress / Young's Modulus

?l / 0.0508 = (4.9 x 104 / 2) / 9.4 x 1010

?l = 1.3 x 10-8 m (2 s.f.)

For L2:

?l / l = Stress / Young's Modulus

?l / 0.0762 = (7.84 x 104 / 2) / 9.4 x 1010

?l = 3.2 x 10-8 m (2 s.f.)

As you can see, because of silica glass being a strong, hard and inelastic material, the ?l is negligible. There is not yet enough force to even take the glass towards it's height of elastic regime, which is an advantage because it wouldn't be safe if it was. Other materials which constructors would have thought about using might have been using yet another material which is colourless and transparent, like plastic. But plastic isn't as strong, even if it may be cheaper. The downside of glass is when glass shatters, it breaks into random shards due to its random molecular structure.

The limitation to using silica glass is the aquarium cannot be built much deep, because the glass would reach its elastic limit and shatter. There is not yet a material stronger than glass which has the same properties as glass made yet, so silica is the best material available.

I think a development to the silica glass panels is the have them laminated. A laminated silica glass panels is having a sheet of pure plastic between two sides of silica glass. This is commonly used by car manufacturers to create a car's windshield which doesn't shatter when smashed. This won't increase the panel's Young's Modulus much, but it does increase safety by far.

Another use of working out the pressure and Young's Modulus of a material can be applied on the engines of vehicles. Fuel pipes, air pipes, and the cylinder where the combustions take place, are all under very high pressures when working. In that context, we can also work out the pressure exerted on the cylinder and pipes, and use this information, along with the Young's Modulus and properties of materials, to work out which materials and of what thickness is needed to make a safe and powerful engine.

Bibliography

http://www.hk-phy.org/oceanpark/

http://www.walter-fendt.de/ph11e/hydrostpr.htm

http://www.mse.cornell.edu/courses/engri111/modulus.htm

Nuffield Advanced Science: Revised book of data

Salter Horners' Advanced Physics