Calculating Fill Time for Inflatable Pool Using Garden Hose

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In summary, the conversation discusses how to calculate the time it will take to fill a circular inflatable wading pool to a depth of 32 cm using a garden hose with a diameter of 2.8 cm and a water flow speed of 1.1 m/s. The equations used are delta m=p1 A1 v1 delta t, (p=density, A=area, v=velocity, t=time), A1 v1=A2 v2, and Q=A v. The conversation also mentions the importance of using the correct measurements for volume and cross sectional area, as well as converting mass to volume using density. Overall, the summary highlights the process of finding the volumetric flow rate and mass flow rate to determine the
  • #1
iseidthat
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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...
 
Last edited:
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  • #2
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.
 
  • #3
my typing is terrible this morning, sorry for the spelling mistakes. going to get some more coffee :smile:
 
  • #4
redargon said:
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.
 
  • #5
i figured it out. thanks :)
 
  • #6
pensity was a spelling mistake for density, sorry. Glad you got it, no prob.
 

1. How long does it typically take to fill a pool?

The time it takes to fill a pool can vary depending on the size of the pool, the water pressure, and the size of the hose or pump being used. On average, it can take anywhere from 6-48 hours to fill a pool.

2. Can the time it takes to fill a pool be affected by weather or temperature?

Yes, weather and temperature can affect the time it takes to fill a pool. For example, if it is very hot outside, more water may evaporate from the pool, meaning it will take longer to fill. Additionally, colder temperatures may result in slower water flow, increasing the time it takes to fill the pool.

3. How can I calculate the time it will take to fill my specific pool?

To calculate the time it will take to fill your pool, you will need to know the volume of your pool in gallons and the flow rate of your hose or pump in gallons per minute. Then, divide the volume of your pool by the flow rate to determine the number of minutes it will take to fill your pool.

4. Are there any factors that can speed up or slow down the filling process?

Yes, there are several factors that can affect the filling process. These include the size and shape of the pool, the water pressure, the size of the hose or pump, and any obstructions or obstacles that may impede the flow of water into the pool.

5. Is it possible to fill a pool too quickly?

Yes, it is possible to fill a pool too quickly. If the water is added too quickly, it can cause the pool to overflow, which can lead to damage to the pool and surrounding area. It is important to monitor the filling process and adjust the flow rate as needed to avoid this issue.

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