How Does Pipe Diameter Affect Water Pressure and Flow Velocity?

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SUMMARY

The discussion focuses on the relationship between pipe diameter, water pressure, and flow velocity, specifically using Bernoulli's equation. The initial conditions include a gauge pressure of 3.8 atm and a flow velocity of 0.80 m/s through a 5.4 cm diameter pipe, tapering to 2.6 cm at a height of 20 m. The calculated flow velocity at the top floor is approximately 3.45 m/s, while the gauge pressure calculated using Bernoulli's equation was initially found to be incorrect at 1.99 atm due to unit tracking errors.

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  • Understanding of Bernoulli's equation and its applications
  • Knowledge of fluid dynamics principles
  • Ability to perform unit conversions, particularly between pascals and atmospheres
  • Familiarity with flow velocity calculations in tapered pipes
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  • Review Bernoulli's equation and its derivation
  • Learn about the continuity equation for fluid flow
  • Study the effects of pipe diameter on flow rate and pressure
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Students in engineering or physics, fluid mechanics enthusiasts, and professionals involved in hydraulic systems will benefit from this discussion.

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1. Homework Statement
Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.80 m/s through a pipe 5.4 cm in diameter. The pipe tapers down to 2.6 cm in diameter by the top floor, 20 m above (see figure here http://www.uploadgeek.com/share-85DD_49B54943.html ). Assume no branch pipes and ignore viscosity.
A). Calculate the flow velocity in the pipe on the top floor.
I have this, its 3.450887574 m/s

B).Calculate the gauge pressure in the pipe on the top floor.
*****Figured it out, I wasn't tracking units.*****

2. Homework Equations
I have been trying to use Bernoulli's equation. P1+(.5 pv12)+(pgy1) = P2+(.5 pv22)+(pgy2)

3. The Attempt at a Solution
So far solving for P2 in Bernoulli's equation and dividing by 101300(pa/atm). I have come up with 1.990429541 atm. for my answer. Unfortunately this is wrong, help would be greatly appreciated.
 
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So far solving for P2 in Bernoulli's equation and dividing by 101300(pa/atm). I have come up with 1.990429541 atm. for my answer. Unfortunately this is wrong, help would be greatly appreciate

Show your calculations.
 

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