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Question

# A rectangular vessel when full of water, takes 10 min to be emptied through an orifice at its bottom. How much time will it take to be emptied when it is half filled ?

A
9 min
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B
7 min
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C
5 min
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D
3 min
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Solution

## The correct option is B 7 minGiven, time taken to empty fully filled vessel, t1=10 min To find: Time taken to empty half filled vessel, t2=? We know, time taken to empty a tank is given by - T=Aa√2hg, where A→ area of cross-section of tank a→ area of cross-section of hole h→ height of water in the tank ⇒T∝√h So, T1T2=√h1√h2 ⇒10 minT2=√h√h2 [ assumed, height of fully filled water to be h ] ⇒T2=10√2=7 min

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