Two capillary tubes of length 15 cm and 5 cm and radii 0.06 cmand 0.02 cm respectively are connected in series. If the pressure difference across the end faces is equal to pressure of 15 cm high water column, then find the pressure difference across the (i) first tube and (ii) second tube.

Answer

(i) 0.54 cm of water column; (ii) 14.46 cm of water column

Explanation

Rate of flow of liquid through each tube in series will be the same. If h is the height of the water column at the junction of two tubes in series, then `V = (pi xx (15- h)rho gxxr_1^4)/(8 eta l_1) = (pi (h rho g)xxr_2^4)/(8eta l_2)`
`or (15 - h)(r_1^4)/(l_1) = (hxxr_2^4)/(l_2)`
`or (15-h) ((0.06)^4)/(15)= (hxx(0.02)^2)/(5)`
On solving, h = 14.46 cm. :. Pressure difference across first tube = 15 - 14.46 = 0.56 cm of water column Pressure difference across second tube = 14.46 cm of water column