Bernoulli's Principle(?) Problem

In summary, the conversation discusses the water supply of a building fed through a 6.0 cm diameter main entrance pipe and a 2.0 cm diameter faucet tap. The tap, positioned 2.0 m above the main pipe, fills a 25 liter container in 30 seconds. The first question asks for the speed at which the water leaves the faucet, which is found to be 2.7 m/s. The second question asks for the gauge pressure in the main pipe, which requires the use of Bernoulli's equation. The conversation ends with the asker in need of assistance on how to adapt Bernoulli's equation to find the pressure based on the height of the column.
  • #1
sephirothrr
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0

Homework Statement


The water supply of a building is fed through a main entrance pipe 6.0 cm in diameter. A 2.0 cm diameter faucet tap positioned 2.0 m above the main pipe fills a 25 liter container in 30 s.
(a) What is the speed at which the water leaves the faucet.
(b) What is the gauge pressure in the main pipe.
Assume that the faucet is the only outlet in the system.

Homework Equations


Flow rate = A/v (cross-section area / velocity)
Possibly(?) Bernoulli's Equation
Possibly(?) v = [tex]\sqrt{2gh}[/tex]

The Attempt at a Solution


Since the flow rate would be 50 *10[tex]^{3}[/tex] m[tex]^{-3}[/tex] / 60 S, I used that, which I know, and divided it by the area [tex]\pi[/tex]0.01[tex]^{2}[/tex], and I got the right answer of 2.7 m/s.

After that I'm lost as for what to do.
Help please!

Edit: Upon further analysis, I think that I need to convert this to the pressure based on the height of the column, but how would I adapt Bernoulli's equation to fit my needs?
 
Last edited:
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  • #2
I didn't want to do this, but...

BUMP!
 
  • #3
I really need this problem, so here goes the underhanded tactic again.

Bump...
(not that I needed to say that, but, whatever)
 

What is Bernoulli's Principle?

Bernoulli's Principle, also known as the Bernoulli Effect, states that as the speed of a fluid increases, its pressure decreases. This principle is named after Swiss mathematician and physicist, Daniel Bernoulli, who first described it in the 18th century.

How does Bernoulli's Principle work?

Bernoulli's Principle is based on the conservation of energy and the properties of fluid flow. As a fluid moves faster, its kinetic energy increases while its pressure energy decreases. This creates a lower pressure area, causing the fluid to move towards it, resulting in a higher speed and lower pressure.

What are some real-life applications of Bernoulli's Principle?

Bernoulli's Principle is used in many everyday applications, such as airplane wings, which are designed to create lift by creating a difference in air pressure. It is also used in carburetors, which use the principle to mix air and fuel for combustion in a car's engine.

Are there any limitations to Bernoulli's Principle?

Bernoulli's Principle is based on ideal fluid properties and assumes that the fluid is non-viscous and incompressible. In reality, most fluids have some degree of viscosity and compressibility, which can affect the accuracy of calculations using this principle.

How can I use Bernoulli's Principle to solve problems?

To solve problems using Bernoulli's Principle, you can apply the equation P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2, where P is pressure, ρ is density, v is velocity, and h is height. This equation can be used to calculate different parameters in a fluid flow system, such as pressure, velocity, and height, to solve for unknown values.

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