Bernoulli Principle of fluid question about velocity

The top open trough implies that the atmospheric pressure is equal to the water pressure. In summary, A dairy farmer notices a hole at the base of a rusty circular water trough. The hole is 0.11 m below the water level and the top of the trough is open to the atmosphere. The question asks for the speed of the water as it leaves the hole, assuming the trough is large enough for the velocity at the top to be 0. The Bernoulli equation can be used to solve for this velocity, taking into account the atmospheric pressure and the acceleration of gravity.
  • #1
DrunkApple
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Homework Statement


A dairy farmer notices that a circular water trough near the barn has become rusty and now has a hole near the base. The hole is 0.11 m below the level of the water that is in the tank.
If the top of the trough is open to the atmosphere, what is the speed of the water as it leaves the hole? Assume that the trough is large enough that the velocity of the water at the top is zero. The acceleration of gravity is 9.81 m/[itex]s^{2}[/itex]

Homework Equations


[itex]p_{1}[/itex] + [itex]\frac{1}{2}[/itex]ρ[itex]v_{1}[/itex]^2 + ρg[itex]y_{1}[/itex] = [itex]p_{2}[/itex] + [itex]\frac{1}{2}[/itex]ρ[itex]v_{2}[/itex]^2 + ρg[itex]y_{2}[/itex]


The Attempt at a Solution


In the question, it said I can assume that the certain velocity is 0. But I don't know which one. [itex]v_{1}[/itex] or [itex]v_{2}[/itex]? Even if one of the velocities is 0 because it is so insignificant, shouldn't that make the other velocity 0 as well?
 
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  • #2
Not necessarily. That is what the Bernoulli relationship explains.
 

Related to Bernoulli Principle of fluid question about velocity

1. What is the Bernoulli Principle of fluid velocity?

The Bernoulli Principle of fluid velocity states that as the velocity of a fluid increases, the pressure exerted by the fluid decreases, and vice versa. This principle is named after Swiss mathematician Daniel Bernoulli, who first described it in the 18th century.

2. How does the Bernoulli Principle relate to flight?

The Bernoulli Principle plays a crucial role in flight as it explains the generation of lift. As air flows over the curved surface of an airplane wing, it travels faster over the top of the wing than the bottom. According to the Bernoulli Principle, the faster-moving air exerts less pressure, creating a pressure difference that results in lift.

3. What factors affect the velocity of a fluid according to the Bernoulli Principle?

The velocity of a fluid is affected by several factors, including the shape and size of the object the fluid is flowing over, the density of the fluid, and the speed of the fluid. Additionally, changes in elevation or temperature can also impact the velocity of a fluid according to the Bernoulli Principle.

4. Can the Bernoulli Principle be applied to gases as well as liquids?

Yes, the Bernoulli Principle can be applied to both gases and liquids. The only difference is that gases are compressible, while liquids are not. This means that the density of a gas can change with pressure, while the density of a liquid remains constant.

5. Are there any limitations to the Bernoulli Principle?

While the Bernoulli Principle is a fundamental concept in fluid mechanics, it does have limitations. It assumes that the fluid is non-viscous (no internal friction) and incompressible. In reality, fluids do have viscosity and can be compressed, so the Bernoulli Principle is not always an accurate representation of fluid behavior.

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