Bernoulli's Principle(?) Problem

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SUMMARY

The discussion centers on a fluid dynamics problem involving Bernoulli's Principle and flow rate calculations. The main pipe has a diameter of 6.0 cm, while the faucet tap has a diameter of 2.0 cm, and the water fills a 25-liter container in 30 seconds. The calculated speed of water leaving the faucet is 2.7 m/s, derived from the flow rate formula. The user seeks assistance in determining the gauge pressure in the main pipe using Bernoulli's Equation.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Bernoulli's Equation.
  • Knowledge of flow rate calculations and area-velocity relationships.
  • Familiarity with gauge pressure concepts in fluid systems.
  • Basic algebra and physics skills for manipulating equations.
NEXT STEPS
  • Study Bernoulli's Equation and its applications in fluid mechanics.
  • Learn how to calculate gauge pressure using fluid height and density.
  • Explore the relationship between flow rate and cross-sectional area in pipes.
  • Investigate the implications of fluid dynamics in real-world plumbing systems.
USEFUL FOR

Students studying fluid dynamics, engineers working with hydraulic systems, and anyone interested in applying Bernoulli's Principle to practical problems.

sephirothrr
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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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I didn't want to do this, but...

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

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

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