Force & Velocity Homework: Ratios & Solutions

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The discussion revolves around calculating the ratio of water flow speeds in two hoses connected to a faucet. The first hose is 1 meter long with an 8 cm diameter, while the second is 4 meters long with a 4 cm diameter, and water flows out of the second hose at 8 cm³/s. The initial assumption that velocity is proportional to area was challenged, leading to the realization that the correct relationship is based on the conservation of mass, expressed as A1v1 = A2v2. Participants encouraged revisiting the principles of fluid dynamics to clarify the confusion regarding the flow rates. Understanding these concepts is essential for solving the problem accurately.
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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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Welcome to PF!

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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