Fluid Mechanics Question

Question

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 = (6000X10X6)+(2000X10X2) = 400,000 J When height in both tanks reaches 4 m, flow stops. Thus, final energy stored in the system = (4000X10X4)+(4000X10X4)=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.

Answer 1

The energy of a tank of water is the sum of energy of all drops of water. Some are on the bottom some are on top-level, so we can average the total energy to the volume of water multiplied by the height of its center of mass, respectively 3 and 1 meters.

$$ (6000*10*3)+ (2000*10*1)=200,000 \ J \rightarrow \text{: initial energy.}$$

$$ ( 8000*10*2= 160000 \ j) \rightarrow \text{: final energy.}$$

$$ 200000-160000=40000 \ j$$