How to Solve a Fluid Dynamics Problem with Bernoulli’s Equation?

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SUMMARY

The discussion centers on solving a fluid dynamics problem using Bernoulli's equation, specifically calculating the speed of water supplied from a large tank through pipes of differing diameters. The problem states that a 50 cm diameter output pipe is connected to a 6 cm diameter water main, with a gauge pressure of 9.8 E4 Pa. The expected speed of water is 0.5 m/s, but participants express confusion regarding the application of Bernoulli's equation, particularly in relation to pressure changes and pipe geometry. Key considerations include the height difference between the pipes and the potential impact of pipe fullness and flow rates across the outlet cross-section.

PREREQUISITES
  • Understanding of Bernoulli's equation and its applications in fluid dynamics
  • Knowledge of fluid pressure concepts, including gauge pressure and hydrostatic pressure
  • Familiarity with the principles of fluid flow through pipes of varying diameters
  • Basic geometry related to pipe configurations and height differentials
NEXT STEPS
  • Study the derivation and applications of Bernoulli's equation in various fluid dynamics scenarios
  • Learn about the continuity equation and its role in fluid flow through pipes
  • Research the effects of pipe diameter on flow rate and velocity, including the concept of flow rate conservation
  • Examine case studies involving gauge pressure calculations in fluid systems
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Students in engineering or physics, educators preparing fluid dynamics curriculum, and professionals involved in hydraulic system design or analysis.

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Homework Statement



A very large open water tank has a 50 cm diameter output pipe connected 10 m above the water main which is 6 cm in diameter. If the gauge pressure in the water main reads 9.8 E4 Pa what is the speed at which the water is supplied?
The answer should be 0.5 m/s but I can't see how with Bernoulli's equation. The gauge pressure given is exactly what the pressure change would be (roh g h) when height is the only factor. If the velocity term drops because of no velocity change tho, how can the pipe diameters be different?

Homework Equations



Bernoulli's

The Attempt at a Solution



The gauge pressure given is exactly what the pressure change would be (roh g h) when height is the only factor. If the velocity term drops because of no velocity change tho, how can the pipe diameters be different?
 
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fysics4fun said:

Homework Statement



A very large open water tank has a 50 cm diameter output pipe connected 10 m above the water main which is 6 cm in diameter. If the gauge pressure in the water main reads 9.8 E4 Pa what is the speed at which the water is supplied?
The answer should be 0.5 m/s but I can't see how with Bernoulli's equation. The gauge pressure given is exactly what the pressure change would be (roh g h) when height is the only factor. If the velocity term drops because of no velocity change tho, how can the pipe diameters be different?

Homework Equations



Bernoulli's

The Attempt at a Solution



The gauge pressure given is exactly what the pressure change would be (roh g h) when height is the only factor. If the velocity term drops because of no velocity change tho, how can the pipe diameters be different?

Hmm. As you say, the pressure in the inlet pipe corresponds to a head of water that is the same as the supposed elevation of the outlet pipe above it. Perhaps the precise geometry becomes significant. Is the 10m pipe separation center to center? Top of one to the bottom of the other? Is the outlet pipe actually full? Does it empty into free air, or an open pond at the same level? Is the pressure change with depth across the face of the outlet pipe significant (different flow rates across its cross-section)?
 
We are not provided any details other than the problem stated just as it is. I am a teacher, and I put this question on Friday's exam (as extra credit) without looking at it very closely, unfortunately (it looks easy at first glance!) Now I have to explain it tomorrow and I don't know how :P
I'm starting to think it's just a badly written problem, but I'd like a few more responses to give me confidence that I'm not missing something.

I REALLY appreciate your input- I've been dying waiting to hear from people...
 

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