how long will it take to fill a 50 m^3 pool with water and what will be the fina

Question

how long will it take to fill a 50 m^3 pool with water and what will be the final temperature of the water, if we use a garden hose to fill it and its inner diameter is 2.5 cm, and the average velocity of the water in the hose is 2.5 m/s. Knowing the pool initially contains 28 m^3 of 36 celsius water and the water from the hose is 15 celsius? how long will it take to fill a 50 m^3 pool with water and what will be the final temperature of the water, if we use a garden hose to fill it and its inner diameter is 2.5 cm, and the average velocity of the water in the hose is 2.5 m/s. Knowing the pool initially contains 28 m^3 of 36 celsius water and the water from the hose is 15 celsius? how long will it take to fill a 50 m^3 pool with water and what will be the final temperature of the water, if we use a garden hose to fill it and its inner diameter is 2.5 cm, and the average velocity of the water in the hose is 2.5 m/s. Knowing the pool initially contains 28 m^3 of 36 celsius water and the water from the hose is 15 celsius?

Explanation / Answer

Solution :-

Lets first calculate the volume of the water hose

Diameter = 2.5 cm

Radius = 2.5 cm / 2 = 1.25 cm

1.25 cm * 1 m / 100 cm = 0.0125 m

Assume its length is 2.5 m

Therefore now lets calculate the volume

V= pi r^2 * h

= 3.14 * (0.0125 m)^2 * 2.5 m

= 0.00123 m3/s

Therefore in 1 second it delivers 0.00123 m3 of water

Now lets calculate the amount of needed to be delivered in pool

50 m3 – 28m3 = 22 m3

Now lets calculate time needed to deliver this amount of water

22 m3 * 1 s / 0.00123 m3 = 17886 s

So it will take 17886 second.

Now lets calculate the final temperature of the water

Initial temperature pool = 36 C

Initial temperature of hose = 15 C

Final temperature = ?

-qhot = q cold

-28m3 *4.184*(T2-36C) = 22 m3 *4.184* (T2-15C)

-117.152(x-36)=92.048(x-15)

4217.47-117.152x=92.048x-1380.72

X=26.76 C

Therefore the final temperature is 26.76 C

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