a u shaped tube,both ends open, contains same liquid in it. If one arm of tube contains liquid upto 3m height, what will be height of liquid column in another arm? and why? Which property of liquid does it show?
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Answer:
When the levels equalize, the height of liquid in each arm is (h
1
+h
2
)/2.
We may then visualize that a length h
1
−(h
1
+h
2
)/2=(h
1
−h
2
)/2 of the liquid has been transferred from the left arm to the right arm.
Mass of liquid transferred =(h
1
−h
2
)/2Aρ, where A is area of hole and ρ is density.
Vertical distance through which it moves =(h
1
−h
2
)/2.
Loss in gravitational potential energy =[(h
1
−h
2
)/2]
2
Aρ.
Mass of the entire liquid =(h
1
+h
2
+h)Aρ
If this moves with velocity v,
kinetic energy =
2
1
(h
1
+h
2
+h)Aρv
2
Equating energies, we get v=(h
1
−h
2
)
2(h
1
+h
2
+h)
1
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