Find the speed of fluid using bernoulli

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SUMMARY

The discussion focuses on applying Bernoulli's equation to determine the velocity of fluid in a pipe. The user correctly simplifies the equation by assuming atmospheric pressure at both ends and setting the initial velocity and height to zero, leading to the conclusion that the fluid velocity can be expressed as v = √(2gh). The user confirms their understanding of the concepts involved, including the equation of continuity, which justifies the assumption of zero velocity at the water surface due to its larger cross-sectional area compared to the pipe.

PREREQUISITES
  • Understanding of Bernoulli's equation
  • Knowledge of fluid dynamics principles
  • Familiarity with the concept of pressure in open systems
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of Bernoulli's equation in fluid mechanics
  • Learn about the equation of continuity and its applications
  • Explore real-world applications of Bernoulli's principle in engineering
  • Investigate the effects of viscosity on fluid flow
USEFUL FOR

This discussion is beneficial for students studying fluid dynamics, engineers working with fluid systems, and anyone seeking to understand the practical applications of Bernoulli's equation in real-world scenarios.

songoku
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Homework Statement


untitled-7.jpg


Find v


Homework Equations


Bernoulli


The Attempt at a Solution


Here's what I've done

I took the surface of water as first reference and the right-end of the pipe as second reference, so:

P1 + 1/2 ρV12 + ρgh1 = P2 + 1/2 ρV22 + ρgh2

P1 = P2 = Patm and I assumed v1 = 0 and h1 = 0, then the equation became:
0 = 1/2 ρV2 - ρgh
v = √(2gh) ---> ta daa, I'm finished with degree of confidence 0.5 % that my answer is correct.

Do I get it right? Thanks
 
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It is 100% correct.

However to build up your confidence let's just clear up how we got here.

After applying the equations, we realized two things.Pressure at surface and Pressure at exit are same as they are open to atmosphere.

Then we made velocity zero.
That was using equation of continuity as surface area of water is much greater than that of pipe.
 
Ah I get it. Thanks for the help :smile:
 

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