A `16cm^3` volume of water folws per second through a capillary tube of radius r cm and of length 1 cm, when connected to a pressure head of h cm of water. If a tube of the same length and radius r/2 is connected to be same pressure head, find the mass of water flowing per minute through the tube.

Explanation

Here, `V_1 = 16cm^3//"sec" , P_1 = h rho g, r_1 = r , l_1 = l , r_2 = r//2 , P_2 = h rho g`,
So `P_1 = P_2 ,` Now `V_1 = (pi P_1 r_1^4)/(8eta l_1) and V_2 = (pi P_2 r_2^4)/(8 eta l_2) , (V_2)/(V_1) = (P_2)/(P_1) xx (r_2^4)/(r_1^4) xx (l_1)/(l_2) = ((r//2)^4)/(r^4) xx l/l = (1/2)^4 = 1/(16)`
`V_2 = (16)/(16)= 1 cm^3//s` , volume of water flowing per minute `=1 xx 60 = 60 cm^3//"min"`
`therefore ` Mass of water flowing per minute `= 60 xx 1 = 60 ` gram/min