Physics Investigation
Hydrostatic Pressure
One of the most important things in dam design is what force must the dam be designed to withstand. Let us start by looking at the pressure at the base of the dam. The depth of Lake Mead at the Hoover Dam is 600ft. Using the expression for pressure exerted by a fluid
pressure = density x depth
where the density of water is 62.4 lb/ft3 . Upon calculation we get a pressure of 37440 lb/ft2 or 18.72 tons/ft2. Now if we calculate the pressure half way up the height of the dam we find that the pressure is 9.36 tons/ft2. According to the quick fact page we see that the width of the base of the dam is 660ft, but the width of the top of the dam is 45 ft. Using the pressures we have just calculated can you explain why the dam is narrower at the top then it is at the bottom? Below are a pair of sketches of the design of the dam itself.
Courtesy of Water Power and Unites States Department of the Interior
Looking at the second sketch,one can see that the walls of the dam curve from one side of the canyon to the other. What is the purpose in this design?
Answers to these questions can be found at the Water Power Web Page.
Additional information and lessons for all age groups can be found at the Cracking Dams home page.
Power Generation
One of the benefits of dams is that they can provide electrical power. From an pollution standpoint this is generally viewed as clean power since there are no pollutants generated during the production of power. This is not to say that there are not ecological drawbacks from the dam itself. We will explore some of these in later sections.
Below is a sketch of what the typical layout is in a dam for power generation.
The electrical energy that is generated at the dams power plant is a result of the converting the potential energy of the water behind the dam in to electrical energy. Water from behind the dam is allowed to stream through pipes near the bottom of the dam. The pipes connect through turbines so that the water turns the turbines which produces the electricity. The 17 turbines at the Hoover Dam are capable of producing 2000 Megawatts of power. The amount of water required to power the generators can be calculated by considering the amount of potential energy that will converted in to electrical power. Assuming the water falls 600 ft we can use the expressions below for power and gravitational potential energy to calculate the rate of flow of water through the turbines.
power = energy/time
potential energy = mass x g x height
density = mass/volume
therefore
volume/time = power/(density x g x height)
where g is the acceleration due to gravity which is 32.2 ft/sec. Plugging in all the numbers we get 1220 ft3 /sec. This converts to roughly 10,000 gallons per second. Below are pictures of the generators used at the Hoover Dam.
Courtesy of United States Department of the Interior
By referring to the quick fact page we see that at peak output roughly 20,000 gallons pass through the dam in a second. What would account for the difference between the actual situation and calculation performed above?
For additional problems go to The Physics Education Research Group at The University of Maryland College Park.