Solve Garden Hose Problem: 19.6s to Fill 24L Container

[Alex Wiseman]

Homework Statement

A garden hose is used to fill a large metal container which can hold 24.0 L of liquid. If the radius of the garden hose's nozzle is 1.2 cm, and the speed of the water at this point is 272.0 cm/s, how long (in seconds) would it take to fill the container with water, assuming that none of it splashes out?
Hint: Use the fact that 1 L = 1000 cm3

Placing all relevant data in SI;
24L = 24,000cm³
= 0.024m³

V = 272cm/s
= 2.72 m/s

Homework Equations

ΔV/Δt = Av
Δt = ΔV/Av

The Attempt at a Solution

ΔV(metal container) = 0.024m ³
Δt = ?
A(nozzle) = ∏(0.012)² = 0.00045m²
v(water) = 2.72m/s

Δt = ΔV/Av
Δt = 0.024/(0.00045)*(2.72)
Δt = 19.6s

Now that I've figured it out, I suppose this doesn't really belong in advanced physics - even though it is part of my undergraduate.

 

[SteamKing]

How many centimeters in 1 meter?

24L = 24000 cm^3 (OK)
24L = 24 M^3 (?)

272 cm/s = .272m/s (?!)

What is the formula for the area of a circle given the radius?

(Hint: it's not 2 pi r)

 

[Vadar2012]

Check your units and formulas, you got some major mistakes in there. This question is easy and mistake proof if you use dimensional anaylsis.

 

[Alex Wiseman]

Check your units and formulas, you got some major mistakes in there.

I am aware I have some major mistakes, which is why I posted it. I need help getting started, I only posted what I had to show I made an attempt.

Edit: Oh I see what you are talking about, yes. This is rather embarrassing. Never trust a friend with conversions...

 

[Alex Wiseman]

How many centimeters in 1 meter?

24L = 24000 cm^3 (OK)
24L = 24 M^3 (?)

272 cm/s = .272m/s (?!)

What is the formula for the area of a circle given the radius?

(Hint: it's not 2 pi r)

I fixed up the silly mistakes, it is 1:00am and I've been reviewing for nearly 14 hours now. I just need help finding the correct formulas for solving this problem.

 

[SteamKing]

You still have a major problem:

24L = 24000 cm^3 OK

24L = 240 m^3 (?!)

I trust you know that if I have a cube which measures 10 cm on each side, the volume of the cube is 10 cm * 10 cm * 10 cm = 1000 cm^3 = 1.0 L

 

[Alex Wiseman]

You still have a major problem:

24L = 24000 cm^3 OK

24L = 240 m^3 (?!)

I trust you know that if I have a cube which measures 10 cm on each side, the volume of the cube is 10 cm * 10 cm * 10 cm = 1000 cm^3 = 1.0 L

As stated, it's 1:00am
Thanks for pointing that out, any idea where I can start to look for the correct equation? I looked at continuity (as suggested), but I am getting a massive amount of time for that.

Edit: I think I figured it out, it was entirely conversions that threw me off. Wow, how embarrassing.I posted my final answer.