Calculating Pressure in a Narrowed Pipe

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Homework Help Overview

The problem involves calculating the pressure difference in a horizontal pipe that narrows from a larger diameter to a smaller one, specifically focusing on the pressure readings at different sections of the pipe while water flows through it.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of Bernoulli's equation and the relationship between pressure and velocity in different sections of the pipe. There is an attempt to clarify the equations involved and their correct application.

Discussion Status

Some participants have confirmed the equations being used, and there seems to be a productive exchange regarding the understanding of the principles involved. However, there is no explicit consensus on the final approach to the problem.

Contextual Notes

The original poster expresses uncertainty about their attempts and seeks clarification on how to arrive at a specific answer, indicating a need for further exploration of the concepts rather than a straightforward solution.

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Homework Statement



Water flows at through a horizontal pipe that narrows smoothly from 10 cm diameter to 5.0 cm diameter. A pressure gauge in the narrow section reads 50 kPa.

What is the reading of a pressure gauge in the wide section

Homework Equations



A_1*F_1=A_2*F_2

The Attempt at a Solution



I tried to use this equation and it didn't work. I already know the answer is 5.34 x 10^4 but I need to know how to get that answer.
 
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Do you know bernoulli's eqn. I think that is what is needed here. Hint: in the narrow section the water must have 4 times the velocity as in the wide section. I'm off for now but maybe others can pick up if you need additional help.
 
Let me see if I have the equation correct.

P1-P2=1/2 (density) (V2^2-V1^2)

and

A1V1=A2V2

Is this what you are talking about?
 
Yes. Those are correct. You can see the derivation here -

http://en.wikipedia.org/wiki/Bernoulli's_principle
 
Thanks for your help this make sense now
 

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