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24 cm3 of water flows per second through a capillary tube of radius r cm and length l cm, when connected to a pressure head h cm of water. If a tube of the length l/2 cm and radius r/2 cm is connected to the same pressure head, then volume of water flowing per second through the tube is
  • a)
    3 cm3−s⁻1
  • b)
    6 cm3−s⁻1
  • c)
    12 cm3−s⁻1
  • d)
    24 cm3−s⁻1
Correct answer is option 'A'. Can you explain this answer?
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24 cm3 of water flows per second through a capillary tube of radius r ...
B)6 cm3
c)12 cm3
d)24 cm3

The volume of water flowing per second through a capillary tube is given by the formula:

V = πr^4h/8ηl

where V is the volume of water flowing per second, r is the radius of the tube, h is the pressure head, η is the viscosity of water, and l is the length of the tube.

When we connect a tube of length l/2 and radius r/2 to the same pressure head, the volume of water flowing per second is given by:

V' = π(r/2)^4h/8η(l/2)

Simplifying this equation, we get:

V' = (π/16) r^4h/ηl

Therefore, the volume of water flowing per second through the smaller tube is (π/16) times the volume of water flowing through the original tube. Substituting the given values, we get:

V' = (π/16) * 24 = 3 cm3

Therefore, the answer is (a) 3 cm3.
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24 cm3 of water flows per second through a capillary tube of radius r ...
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24 cm3 of water flows per second through a capillary tube of radius r cm and length l cm, when connected to a pressure head h cm of water. If a tube of the length l/2 cm and radius r/2 cm is connected to the same pressure head, then volume of water flowing per second through the tube isa)3 cm3−s⁻1b)6 cm3−s⁻1c)12 cm3−s⁻1d)24 cm3−s⁻1Correct answer is option 'A'. Can you explain this answer?
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