fluid mechanics question

[Vander Waal]

Hi,
I am preparing for GATE(Chemical). I need the answer of this question part 2 (question 54) as I am not able to find the mistake in my logic.

I have applied the logic here as:

Initial energy stored in the system = energy stored in 1st tank when valve is closed + energy stored in 2nd tank when valve is closed
= (6000*10*6)+(2000*10*2) = 400,000 J
When height in both tanks reaches 4 m, flow stops.
Thus, final energy stored in the system = (4000*10*4)+(4000*10*4)=320,000 J
Thus, energy loss= 400,000-320,000=80,000 J

The answer for this question is 40,000 J while, mine as shown above is coming as 80,000 J.
Please advice where I am doing wrong.

 

[IRstuff]

Student posting is not allowed.

However, when dealing with transport of materials with height, you need to use the change in center of mass and not total height. However, your approach is rather long. The change in potential energy must come from the top 2m of the left tank moving 2 m downward to fit in the 4m ending height of the right tank.

Therefore m * g * delta_h = change_in_energy, which avoids thinking about the center of mass.

TTFN (ta ta for now)
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