Calculating Pressure Outside a Box: Bernoulli's Equation

In summary, Bernoulli's equation is a fundamental equation in fluid dynamics that describes the relationship between pressure, velocity, and height of a fluid. It can be used to calculate pressure outside a box by knowing the velocity, height, and density of the fluid. This equation has many practical applications in fields such as aerodynamics, hydraulics, and plumbing. It also relates to the conservation of energy in a fluid system. However, there are limitations to using Bernoulli's equation, such as assuming an incompressible and non-viscous fluid with no energy loss due to friction or turbulence.
  • #1
subopolois
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Homework Statement


Calculate pressure outside the box- ATM pressure is 101325 Pa, air moving outside the box is 45 m/s, air density is 1.3 kg/m^3

Homework Equations


P + 1/2(roe)(v)^2 = Patm

The Attempt at a Solution


P + 1/2 (1.3kg/m^3)(45m/s)^2 = 101325 Pa
P + 1316.25 Pa = 101325 Pa
P= 100008.75 Pa
 
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  • #2
I guess the problem is an open box with static air inside and air blowing over the open end, in which case your computation is right.
But you need to define problems more fully.
 
  • #3
Bernoulli's equation is an express of energy conservation. All terms have energy density dimensions and your calculation is correct.
 

FAQ: Calculating Pressure Outside a Box: Bernoulli's Equation

1. What is Bernoulli's equation?

Bernoulli's equation is a fundamental equation in fluid dynamics that describes the relationship between the pressure, velocity, and height of a fluid. It states that as the velocity of a fluid increases, the pressure decreases, and vice versa.

2. How do you calculate pressure outside a box using Bernoulli's equation?

To calculate pressure outside a box using Bernoulli's equation, you will need to know the velocity of the fluid, the height of the fluid, and the density of the fluid. The equation is P + 1/2ρv^2 + ρgh = constant, where P is pressure, ρ is density, v is velocity, g is the acceleration due to gravity, and h is the height. You can rearrange the equation to solve for pressure.

3. What are the applications of Bernoulli's equation?

Bernoulli's equation has many practical applications, including in aerodynamics, hydraulics, and plumbing. It is used to calculate the lift force on an airplane wing, the flow of water through pipes, and the pressure in a fluid-filled container.

4. How does Bernoulli's equation relate to the conservation of energy?

Bernoulli's equation is a statement of the conservation of energy in a fluid system. It shows that the total energy of a fluid remains constant as it flows, with the energy being distributed between pressure, velocity, and height.

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

Yes, there are some limitations to using Bernoulli's equation. It assumes that the fluid is incompressible, non-viscous, and that there is no energy loss due to friction or turbulence. In real-world situations, these assumptions may not hold, so the calculated pressure may not be entirely accurate.

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