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A cylindrical vessel open at the top is 20 cm high and 10 cm in diameter. A circular hole of crosssectional area 1 cm 2 is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate of 10 4 cm 3 /s. The height of water in the vessel uder steady state is ? (take g = 10 m/s 2 )

A cylindrical vessel open at the top is 20 cm high and 10 cm in diameter. A circular hole of crosssectional area 1 cm2 is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate of 104 cm3/s. The height of water in the vessel uder steady state is ? (take g = 10 m/s2)

Grade:12

7 Answers

Mallikarjun Maram
50 Points
9 years ago
p { margin-bottom: 0.25cm; line-height: 120%; }

At steady state the flow through the hole = incoming flow.

ie., Av = 104 cm3/s = 10-2 m3/s

A = 1 x 10-4m2, and v =

Substituting the values and solving for h, we get h = 500 m,

which is very high compared to height of the cylinder.

Hence cylinder will fill and overflow.

Himaja
40 Points
9 years ago
The answer is 5 cm.
Mallikarjun Maram
50 Points
9 years ago
Dear Student, please check the data provided in the problem.  To get the answer 5 cm, you need to have incoming flow to be 102 cm3/sec not 104 cm3/sec.
Himaja
40 Points
9 years ago
Actually this is a question from D C Pandey mechanics part-2 (understanding physics series) there may be a printing mistake in the book
Mallikarjun Maram
50 Points
9 years ago
Dear Student, You probably have the older version of the book.  I have a new copy and verified in it.  Incoming flow is correctly printed as 102 cm3/s, as I mentioned.  Hope this helps.
 
Himaja
40 Points
9 years ago
thank you sir
Ahmet
13 Points
6 years ago
Mallikarjun Maram 
You considered that the flow rate of incoming and outcoming fluid is the same SO How will be a height of water? 
the same amount of water added to the vessel in a given time is equal to the same amount out !!! Am I missing something? 
 

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