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(II)A58in. (inside) diameter garden hose is used to fill a round swimming pool 6.1 m in diameter. How long will it take to fill the pool to a depth of 1.4 m if water flows from the hose at a speed of 0.40 m/s?

Short Answer

Expert verified

The time taken to fill the pool is 5.88days.

Step by step solution

01

Understanding the of volume flow rate

In this problem, the volume flow rate can be calculated by using the product of area as well as velocity of fluid.

02

Given data

The diameter of garden hose is d=58in.

The diameter of the round swimming pool is D=6.1m.

The depth of the pool is h=1.4m.

The speed of water flows from the hose is v=0.40m/s.

03

Evaluating the volume of swimming pool and area of hose

The volume of swimming pool is calculated as:

V=ฯ€4D2h

Substitute the values in the above equation.

=ฯ€4(6.1m)2(1.4m)=40.91m3

The area of hose is calculated below:

A=ฯ€4d2

Substitute the values in the above equation.

=ฯ€4(58inร—0.0254m1in)2=2.01ร—10โˆ’4m2

04

Evaluating the time taken by hose to fill the pool

The time taken by hose to fill the pool is calculated below:

Vฮ”t=Aโ‹…vฮ”t=VAโ‹…v

Substitute the values in the above equation.

=40.91m3(2.01ร—10โˆ’4m2)(0.40m/s)=508674.1sร—(1day86400s)=5.88days

Hence, the time taken by hose to fill the pool is 5.88days.

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