Force & Velocity Homework: Ratios & Solutions

[FauxNews]

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!

 

[tiny-tim]

Welcome to PF!

Hi FauxNews! Welcome to PF!

At first I assumed v1/A1 = v2/A2 …

hmm … so you think velocity is proportional to area?

why? ​

 

[FauxNews]

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. :(

 

[JDHalfrack]

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!

 

[tiny-tim]

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!

(just got up :zzz: …)

Hint: conservation of mass. ​