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Bernoulli's Principle and Storms
Bernoulli's principle, which results from conservation of energy, relates the elevation, pressure, and speed of a fluid (liquid or gas). Without elevation changes, high speed fluids have a lower pressure.
During violent storms, such as hurricanes or tornados, high speed winds blowing over a house roof cause a pressure difference. Is the pressure difference enough to lift the roof? Let's do the math. Work it yourself, follow along, or just skip to the answer.
Pressure Difference
Bernoulli's principle gives the pressure difference between the inside and outside of the roof, rather than the force directly. Pressure is force divided by area, so the force is the pressure times the area of the roof. The equation for Bernoulli's principle is in most college physics books.
The air inside the house is still, there are no elevation differences, and the wind is blowing over the roof. Bernoulli's equation tells us the pressure difference between the inside and outside of the roof is one half the air density multiplied by the wind speed squared. If the air density is 1.3 kilograms per cubic meter, and the wind speed is about 67 meters per second (=150 miles per hour - a strong hurricane), the pressure difference between the inside and outside of the roof is 3000 Newtons per square meter or 0.4 pounds per square inch.
Tornados can have faster wind speeds. For wind speeds of 260 miles per hour (=115 meters per second), Bernoulli's equation gives a pressure difference of 1.2 pounds per square inch. Minor et al. (1977 in NOAA Tech memo ERL-NSSL_82) find a pressure difference of 1.4 pounds per square inch for a tornado with 260 mile per hour winds. The result of this approximate calculation is very close to their detailed engineering analysis.
Upward Force on Roof
This pressure sounds insignificant, but the total force is the pressure times the area. A modest home might have a roof area of 1000 square feet. There are 144 square inches in a square foot. Multiplying 1000 by 144 by 0.4 pounds per square inch gives a lifting force of about 60,000 pounds (30 tons!). Higher wind speeds will produce even greater lifting forces.
Weight of Roof
Is this lift enough? What does the roof weigh? More math. We can very roughly estimate the mass of the roof by assuming it has about the same density as water (1000 kilograms per cubic meter). Wood is less dense (so it floats), and nails, roofing materials, etc. are more dense, so this is an approximate average. Mass is density times volume. If the 1000 square foot (90 square meter) roof is about 0.1 meters thick, its volume is 9 cubic meters, which rounds to 10 cubic meters. Multiplying gives an approximate mass of 10,000 kilograms or a rounded weight of 20,000 pounds.
The net upward force on the 1000 square foot roof, the lifting force minus the weight, is about 40,000 pounds or 20 tons! This force is greater for a larger roof or higher wind speed.
Approximate calculations show that the Bernoulli effect can lift roofs from houses, unless they are very firmly anchored. Good engineering and construction helps the roof resist the lifting effect.
Other Damage
If the roof lifts from the house, the wind blowing under the roof equalizes the pressure below and above. With no lifting force, it crashes down. In the brief time the roof is suspended, entering winds can blow the walls outward. So it looks like the house exploded.
This effect is of course not the only way that a tornado or hurricane can destroy a house. Direct winds and flying projectiles also cause plenty of damage.
There is a myth that opening a window before a tornado can prevent a house from exploding. The NOAA does not recommend this practice however. Opening a window won't help. Most houses are already ventilated, and there are plenty of other ways for the wind to damage the house. Just get to safety as quickly as possible.
More Examples of Bernoulli's Principle
Airplane Wings and Curve Balls
Bernoulli Effect While Driving
Bernoulli's Principle and Storms
Bernoulli's principle, which results from conservation of energy, relates the elevation, pressure, and speed of a fluid (liquid or gas). Without elevation changes, high speed fluids have a lower pressure.
During violent storms, such as hurricanes or tornados, high speed winds blowing over a house roof cause a pressure difference. Is the pressure difference enough to lift the roof? Let's do the math. Work it yourself, follow along, or just skip to the answer.
Pressure Difference
Bernoulli's principle gives the pressure difference between the inside and outside of the roof, rather than the force directly. Pressure is force divided by area, so the force is the pressure times the area of the roof. The equation for Bernoulli's principle is in most college physics books.
The air inside the house is still, there are no elevation differences, and the wind is blowing over the roof. Bernoulli's equation tells us the pressure difference between the inside and outside of the roof is one half the air density multiplied by the wind speed squared. If the air density is 1.3 kilograms per cubic meter, and the wind speed is about 67 meters per second (=150 miles per hour - a strong hurricane), the pressure difference between the inside and outside of the roof is 3000 Newtons per square meter or 0.4 pounds per square inch.
Tornados can have faster wind speeds. For wind speeds of 260 miles per hour (=115 meters per second), Bernoulli's equation gives a pressure difference of 1.2 pounds per square inch. Minor et al. (1977 in NOAA Tech memo ERL-NSSL_82) find a pressure difference of 1.4 pounds per square inch for a tornado with 260 mile per hour winds. The result of this approximate calculation is very close to their detailed engineering analysis.
Upward Force on Roof
This pressure sounds insignificant, but the total force is the pressure times the area. A modest home might have a roof area of 1000 square feet. There are 144 square inches in a square foot. Multiplying 1000 by 144 by 0.4 pounds per square inch gives a lifting force of about 60,000 pounds (30 tons!). Higher wind speeds will produce even greater lifting forces.
Weight of Roof
Is this lift enough? What does the roof weigh? More math. We can very roughly estimate the mass of the roof by assuming it has about the same density as water (1000 kilograms per cubic meter). Wood is less dense (so it floats), and nails, roofing materials, etc. are more dense, so this is an approximate average. Mass is density times volume. If the 1000 square foot (90 square meter) roof is about 0.1 meters thick, its volume is 9 cubic meters, which rounds to 10 cubic meters. Multiplying gives an approximate mass of 10,000 kilograms or a rounded weight of 20,000 pounds.
The net upward force on the 1000 square foot roof, the lifting force minus the weight, is about 40,000 pounds or 20 tons! This force is greater for a larger roof or higher wind speed.
Approximate calculations show that the Bernoulli effect can lift roofs from houses, unless they are very firmly anchored. Good engineering and construction helps the roof resist the lifting effect.
Other Damage
If the roof lifts from the house, the wind blowing under the roof equalizes the pressure below and above. With no lifting force, it crashes down. In the brief time the roof is suspended, entering winds can blow the walls outward. So it looks like the house exploded.
This effect is of course not the only way that a tornado or hurricane can destroy a house. Direct winds and flying projectiles also cause plenty of damage.
There is a myth that opening a window before a tornado can prevent a house from exploding. The NOAA does not recommend this practice however. Opening a window won't help. Most houses are already ventilated, and there are plenty of other ways for the wind to damage the house. Just get to safety as quickly as possible.
More Examples of Bernoulli's Principle
Airplane Wings and Curve Balls
Bernoulli Effect While Driving
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