# Two capillary tubes AB and BC are joined end to end at B. AB = 12 cm long and of diameter 4 mm. whereas BC is 3 cm long and of diameter 2mm. The compo

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Two capillary tubes AB and BC are joined end to end at B. AB = 12 cm long and of diameter 4 mm. whereas BC is 3 cm long and of diameter 2mm. The composite tube is held horizontally with A connected to a vessel of water giving a constant head of 5 cm and C is open to the air. Find the pressure difference between B and C.

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Let h cm be the head of pressure at B over C. Then pressure difference between A and B,
p_(1) = (5-h)" cm of "H_(2)O
For tube AB : L_(1) = 12 cm,
r_(1) = 2mm -=0.2 cm,
p_(1) = (5-h)" cm of water"
= (5-h) xx 1xx 980 dyn e//cm^(2)
Rate of flow of water through AB is
Q_(1) =(pi p_(1)r_(1)^(4))/(8 eta l_(1)) = (pi(5-h) xx 1 xx 980 xx (0.2)^(4))/(8 eta xx 12) cm^(3) s^(-1)
For tube BC: l_(2) = 3 cm ,
r_(2) 1 mm = 0.1 cm,
p_(2)" h cm of water "= h xx 1 xx 980 dyn e//cm^(2)
Rate of flow of water through BC is
Q_(2) =(pi p_(2)r_(2)^(4))/(8 eta l_(2)) = (pi xx h xx 1 xx 980 xx (0.1)^(4))/(8 eta xx 3) cm^(3) s^(-1)
As flow through the two tubes in series is steady, so Q_(1) = Q_(2)
or (pi(5-h) xx 1 xx 980 xx (0.2)^(4))/(8 eta xx 12) = (pi h xx 1 xx 980 xx (0.1)^(4))/(8 eta xx 3)
3(5-h) xx 16 = 12 h
On solving, h = 4" cm of water column".

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