The Physics Behind Dams

By Farah Fouladi

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