What Is the Force on a Square Roof During High Winds with Bernoulli's Equation?

In summary, Bernoulli's equation is a fundamental principle in fluid dynamics that explains the relationship between pressure, velocity, and potential energy in a fluid. It is derived from the principles of conservation of mass and momentum and has various real-life applications such as in aerodynamics, carburetors, and meteorology. It can be applied to both liquids and gases, but has limitations such as assuming non-viscous and incompressible fluids and not accounting for external forces.
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During high winds, the atmospheric pressure inside a house may blow off the roof because of the reduced pressure outside. Calculate the force on a square roof of side 22.0 m if the wind speed over the roof is 29.0

i used bernoulli's equation and got an answer of... 246356N
i used 1.21 as the density of air. could someone check my work please?
 
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anyone care to try?
 
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Pi = Po + 0.5d V^2
F = (Pi-Po)A = 0.5 d V^2 ; d is the density = 1.293 kg/m^3
 

1. What is Bernoulli's equation and how does it relate to fluids?

Bernoulli's equation is a fundamental principle in fluid dynamics that describes the relationship between the pressure, velocity, and potential energy of a fluid. It states that as the speed of a fluid increases, its pressure decreases, and vice versa. This equation is based on the conservation of energy in a fluid system.

2. How is Bernoulli's equation derived?

Bernoulli's equation is derived from the principles of conservation of mass and momentum. It is based on the idea that the total energy of a fluid remains constant as it flows through a system, and that this energy can be transferred between the different forms (pressure, velocity, and potential energy).

3. What are some real-life applications of Bernoulli's equation?

Bernoulli's equation has many practical applications, including in the design of airplanes and other aerodynamic objects, the functioning of carburetors in engines, and the flow of water in pipes and channels. It is also used in meteorology to predict air flow and pressure patterns.

4. Can Bernoulli's equation be applied to both liquids and gases?

Yes, Bernoulli's equation can be applied to both liquids and gases, as long as they are in motion and the flow is steady (i.e. not changing over time). However, it is important to note that the equation does not account for any effects of compressibility in gases.

5. Are there any limitations to Bernoulli's equation?

While Bernoulli's equation is a powerful tool in fluid dynamics, it does have some limitations. It assumes that the fluid is non-viscous (i.e. there is no friction or resistance between layers) and incompressible (i.e. density does not change). It also does not take into account any external forces acting on the fluid, such as gravity or surface tension.

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