Two capillary tubes of radiir and 4r and lengths l, 3l are fitted horizontally to the bottom of the vessel with pressure head p in parallel with each other. Calculate the radius of the single tube of same length l which can replace the two capillaries such that rate of flow is not affected.

Two capillary tubes of radiir and 4r and lengths l, 3l are fitted hori

1.	Two capillary tubes of radiir and 4r and lengths l, 3l are fitted horizontally to the bottom of the vessel with pressure head p in parallel with each other. Calculate the radius of the single tube of same length l which can replace the two capillaries such that rate of flow is not affected.
Answer» SOLUTION :r = RADIUS of each capillary `V_1V_2` = rate of flow of liquids through two capillaries `l_1l_2` = lengths of capillaries Total rate of flow of liquid `V=V_1 + V_2` l= LENGTH of a single tube which can replace the two capillaries. `V=(pi pr^(4))/(8 ETAL) .........(ii)` Using (i) and (ii) `(pi pr^(4))/(8 etal)=(pi pr^(4))/(8 eta) [1/l_(1)+1/l_(2)]` `1/l=1/l_(1)+1/l_(2)` `l=(l_(1) l_(2))/(l_(1)+l_(2))`