Calculating Fill Time for Inflatable Pool Using Garden Hose

[iseidthat]

Homework Statement

To fill a child's inflatable wading pool you use a garden hose with a diameter of 2.8 cm. Water flows from this hose with a speed of 1.1 m/s. How long will it take to fill the pool to a depth of 32 cm if it is circular and has a diameter of 2.7 m?

Homework Equations

delta m=p1 A1 v1 delta t
(p=density, A=area, v=velocity, t=time)

A1 v1=A2 v2

Q=A v

idk if there is another equation that deals with time, i can't find any.

The Attempt at a Solution

since everything is dealing with water, i didn't really consider density.

the amount of water needed:
V= pi r^2 h=pi (1.35)^2 (.32)= 1.83 m^3

the area of the hose is:
A= pi r^2= pi (.014)^2= 6.16e-4 m^2

Q=A v=6.16e-4 (1.1)=6.78e-4 m^3/s

mass flow rate= .6776 kg/s

i don't really know where to go from here...

 

[redargon]

first, your volume of pool measurement is a little wrong. You've used the diameter as a radius in your equqtion.
You've also made the sam mistake in calculating the cross sectional area of the hose.
delta m over delta t will give you your mass flow rate. But you need your volumetric flow rate. so how do you turn mass in a volume (hint: pensity is required)

keep trying and le tme know.

 

[redargon]

my typing is terrible this morning, sorry for the spelling mistakes. going to get some more coffee

 

[iseidthat]

first, your volume of pool measurement is a little wrong. You've used the diameter as a radius in your equqtion.
You've also made the sam mistake in calculating the cross sectional area of the hose.
delta m over delta t will give you your mass flow rate. But you need your volumetric flow rate. so how do you turn mass in a volume (hint: pensity is required)

keep trying and le tme know.

i fixed the problems and hopefully they are right. i found the mass flow rate and also the volumetric flow rate. we haven't learned about pensity in our class yet...so there has to be a different way.

 

[iseidthat]

i figured it out. thanks :)

 

[redargon]

pensity was a spelling mistake for density, sorry. Glad you got it, no prob.