How Does Pipe Diameter Affect Water Pressure and Flow Velocity?

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The discussion focuses on calculating the flow velocity and gauge pressure of water in a tapered pipe using Bernoulli's equation. The initial flow velocity is 0.80 m/s at a diameter of 5.4 cm, and the diameter narrows to 2.6 cm at the top floor, resulting in a calculated flow velocity of approximately 3.45 m/s. The user attempted to find the gauge pressure at the top floor, initially arriving at 1.99 atm but noted this answer was incorrect. The conversation emphasizes the importance of unit tracking and proper application of Bernoulli's equation in fluid dynamics problems. Accurate calculations and understanding of pressure changes due to pipe diameter are crucial for solving such scenarios.
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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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