A tank is filled with water to a depth of 1m. A hole of cross section 1 cm^2 at the bottom allows the water to drain out. At what distance below the hole the cross sectional area of the stream is 0.9 times the area of the hole.
Applying Bernoulli's Theorem to the cross section of water stream just outside the hole to a depth 'x'
Patm + Ïgh + 1/2 Ïv12 = Patm + 1/2 Ïv22
h=1m v1= (2gh)1/2
v2=v1/0.9 (from equation of continuity)
On solving I got x as 0.46 m (app)
But the answer is 0.23 m
What is wrong?
Any ideas appreciated.
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1 Answers
1let me use simple kinematics....
From eqn of continuity,
(1)√(2g1) = (0.9)v
or v = √200.9
Now v2 - u2 = 2gh
=> 200.81 - 20 = 20h
=> h = 0.23 m
