Ever wondered how much energy is in a hurricane? Let\'s figure it out! First, we
ID: 109069 • Letter: E
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Ever wondered how much energy is in a hurricane? Let's figure it out! First, we are going to ignore the energy in the winds and simply look at how much energy is contained in the clouds that form within a hurricane. Below is an image of Hurricane Matthew (2016) as it slammed into Haiti at Category 4 strength (145 mph winds). Matthew's cloud field stretched across the Western Atlantic Ocean and extended 10 km into the troposphere. Use the following assumptions to find how much energy is contained in this clouds field. Finally, compare this energy to energy released in the "Fat Man", 21-kiloton bomb dropped on Japan during WWII Your final answer should be expressed as the number of bombs worth of energy in Hurricane Matthew Assumptions: 1. Assume Matthew's cloud field looks like a cylinder 10 km tall with a diameter that can be estimated from the image below. 2. The liquid water content of these clouds = 1 g/m^3. 3. Latent heat of vaporization = 2260 J/g This is the amount of energy in each gram of water in Hurricane Matthew's cloud field. 4. 1 kiloton = 4.184*10^12 JExplanation / Answer
Hurricanes can be thought of as a heat engine; obtaining its heat input from the warm, humid air over the tropical ocean, and releasing this heat through the condensation of water vapor into water droplets in deep thunderstorms of the eyewall and rain bands, then giving off a cold exhaust in the upper levels of the troposphere (~12 km/8 mi up).
The energetics of a hurricane in two ways:
-the total amount of energy released by the condensation of water droplets or ...
-the amount of kinetic energy generated to maintain the strong swirling winds of the hurricane
It turns out that the vast majority of the heat released in the condensation process is used to cause rising motions in the thunderstorms and only a small portion drives the storm's horizontal winds.
Total energy released through cloud/rain formation:
An average hurricane produces 1.5 cm/day (0.6 inches/day) of rain inside a circle of radius 665 km (360 n.mi). (More rain falls in the inner portion of hurricane around the eyewall, less in the outer rain bands.) Converting this to a volume of rain gives 2.1 x 1016 cm3/day. A cubic cm of rain weighs 1 gm. Using the latent heat of condensation, this amount of rain produced gives 5.2 x 1019 Joules/day or 6.0 x 1014 Watts.
This is equivalent to 200 times the world-wide electrical generating capacity - an incredible amount of energy produced
Total kinetic energy (wind energy) generated:
For a mature hurricane, the amount of kinetic energy generated is equal to that being dissipated due to friction. The dissipation rate per unit area is air density times the drag coefficient times the wind speed cubed One could either integrate a typical wind profile over a range of radii from the hurricane's center to the outer radius encompassing the storm, or assume an average wind speed for the inner core of the hurricane. Doing the latter and using 40 m/s (90 mph) winds on a scale of radius 60 km (40 n.mi.), one gets a wind dissipation rate (wind generation rate) of
1.3 x 1017 Joules/day or 1.5 x 1012Watts.
This is equivalent to about half the world-wide electrical generating capacity - also an amazing amount of energy being produced, approximately the amount of energy liberated by the explosion of a 10-megatone nuclear bomb every 20 minutes, or 200 times the production capacity of electric power around the world.
Either method is an enormous amount energy being generated by hurricanes. However, one can see that the amount of energy released in a hurricane (by creating clouds/rain) that actually goes to maintaining the hurricane's spiraling winds is a huge ratio of 400 to 1.
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