Estimating Weight of 6.5m x 15m Flat Roof in Wind

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In summary, the weight of the roof can be estimated by using Bernoulli's equation and calculating the force needed to lift the roof. This force can then be assumed to be equal to the weight of the roof.
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itryphysics
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Homework Statement



A 190 km/h wind blowing over the flat roof of a house causes the roof to lift off the house.
If the house is 6.5m x 15m in size, estimate the weight of the roof. Assume the roof is not nailed down.

Homework Equations



Bernoulli's equation : P1 + 1/2pv^2 +pgy = P2 + 1/2pv^2 + pgy

The Attempt at a Solution



i reduced the equation down to 1/2pv^2 to get pressure which numerically was 1671.3 and then i multiplied that by the area which i calculated to be 97.5 m^2, to get the force.

I was clueless on how to approach this problem, but I am even more confused now. please help.
 
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  • #2
You are done, aren't you? The problem asked for the weight of the roof. In order to lift something, you must apply a force (at least) equal to its weight. If the force you calculated was just enough to lift the roof, then that is the weight of the roof!
 

1. How do you calculate the weight of a 6.5m x 15m flat roof?

The weight of a flat roof can be estimated by multiplying the area of the roof by the weight per unit area. For example, if the weight per square meter is 25 kg, then the weight of a 6.5m x 15m flat roof would be 6.5m x 15m x 25 kg = 2,437.5 kg.

2. What factors affect the weight of a flat roof in wind?

The weight of a flat roof in wind is affected by various factors such as the type of roofing material, the design and construction of the roof, the wind speed, and the location of the building. For example, a flat roof with a heavier roofing material and a higher wind speed will have a higher weight in wind compared to a flat roof with a lighter material and lower wind speed.

3. How do you determine the weight per unit area of a flat roof?

The weight per unit area of a flat roof can be determined by dividing the total weight of the roof by its area. This can be done by weighing the roof using a scale or by using the weight information provided by the manufacturer of the roofing material. For example, if a flat roof weighs 2,437.5 kg and has an area of 97.5 square meters, then the weight per unit area would be 2,437.5 kg / 97.5 m² = 25 kg/m².

4. How does wind affect the weight of a flat roof?

Wind can increase the weight of a flat roof by exerting a force on the roof and causing it to deflect or bend. This increased weight can put additional stress on the roof and its supporting structure, potentially leading to damage or collapse. Wind can also cause debris or objects to impact the roof, adding to its weight and potentially causing damage.

5. What is the importance of estimating the weight of a flat roof in wind?

Estimating the weight of a flat roof in wind is crucial for ensuring the safety and stability of the building. It helps engineers and architects determine the appropriate design and construction of the roof to withstand wind forces. It also allows for proper maintenance and repair of the roof to prevent potential damage or collapse. Additionally, estimating the weight of a flat roof in wind is important for insurance purposes and compliance with building codes and regulations.

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