Force & Velocity Homework: Ratios & Solutions

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Homework Help Overview

The problem involves fluid dynamics, specifically the flow of water through hoses of different diameters and lengths. The original poster is tasked with finding the ratio of the speeds of water flowing in two hoses connected to a faucet.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use the relationship between velocity and area to find the ratio of speeds but expresses confusion about the validity of their assumptions. Some participants question the proportionality of velocity to area and suggest reconsidering the underlying principles of fluid flow.

Discussion Status

The discussion is ongoing, with participants exploring the relationship between area and velocity in fluid dynamics. Guidance has been offered to revisit the principle that relates area and velocity, hinting at the conservation of mass as a relevant concept.

Contextual Notes

The original poster expresses uncertainty about the equations applicable to the problem and has attempted various approaches that have not yielded correct results. There is a noted confusion regarding the assumptions made about velocity and area relationships.

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Homework Statement



A 1 meter long hose of 8 cm diameter is conneted to a faucet. The end of this hose is connected to a second hose which is 4 meters long and 4 cm in diameter. At the open end of the second hose water flows out at a rate of 8 cm cubed/s.

What is the ratio of the speed of the water flowing in the second hose to the speed of the water flowing in the first hose?


Homework Equations



P = F/A Not sure what other equations I could be using!


The Attempt at a Solution



At first I assumed v1/A1 = v2/A2, so (8 cm cubed/s)/(4pi) = (x)/(16pi), and thus the answer ought to be 1/4, but that is incorrect. I also tried to use squares, since I reasoned that a = (v^2)/r, but this gave me the equally incorrect ratio of 1/8. Help!
 
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Hi FauxNews! Welcome to PF! :wink:
FauxNews said:
At first I assumed v1/A1 = v2/A2 …

hmm … so you think velocity is proportional to area?

why? :smile:​
 
Thank you for the welcome!

Well, I know that F1/A1 = F2/A2...correct? But I suppose that would not hold true for velocity, now that I think about it! I'm completely confused. :(
 
tiny-tim's question is a hint to guide you on your way. The fact that A1v1 = A2v2 is only true because of the way the rate of flow of a fluid "works."

So, go back and figure out why A1v1 = A2v2, and see if that helps you find the solution.

Good luck!
 
FauxNews said:
Thank you for the welcome!

Well, I know that F1/A1 = F2/A2...correct? But I suppose that would not hold true for velocity, now that I think about it! I'm completely confused. :(

Hi FauxNews! :smile:

(just got up :zzz: …)

Hint: conservation of mass. :wink:​
 

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