Friday, November 23, 2012

The Physics Behind Dams

I live in San Francisco CA, where I think out tap water tastes much better than the tap water in upstate NY. This made me think about where that water in coming from and the physics behind where my drinking water is coming from – the physics behind a dam.
The O'Shaughnessy Dam at Hetch Hetchy:

Basic Aspects of a Dam:
-       A river flows into a dam – backs up water
-       Dams are thicker at the bottom, where the Pressure is greater
First Let’s look at what exactly the pressure is at the bottom of the backed-up water:
P = σgh
Height of dam = 130 m
Assume the density of the water is 1000 kg/L
P = (1000 kg/L)(9.8 m/s2)(130 m) =  1.3 x 106 Pa
This is a lot of force! The dam is made of concrete that is thicker at the bottom to accommodate this pressure
The strength at the bottom of the dam:
P/A = stress
The Dam is 270m wide – I am going to use this as the area at the bottom of the dam
Stress = (1.3 x 106 Pa)/(270m) = 480 N
The water then flows into a smaller gateway where water can flow in and out
σ1 v1 A1 =  σ2 v2 A2 à v1 A1 =  v2 A2
The water being backed up is barely moving = 0.05 m/s
I could not find the area of the tunnel, but I will guestimate it to be 150 m2
v2 = (v1 A1)/(A2) = (0.05 m/s * (130*270)m2) / (150 m2) = 12 m/s = 27 mph
Will Contain a lot of Power (Hydroelectric Turbine)
Power = F*v = (480 N)(12 m/s) = 5800 W
o   No depletion of natural resources from this process, and is automatically renewed – can be a good form of alternative energy, maybe even preferable. However, does not produce enough energy to supply all the energy we need. Ex Hoover Dam

1 comment:

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