A pipe is running full of water. At a certain point A It tapers from 60 cm diameter to 20 cm at B. The pressure difference between A and B is 1 m of water column. Find the rate of flow of water through the pipe.

A pipe is running full of water. At a certain point A It tapers from 6

1.	A pipe is running full of water. At a certain point A It tapers from 60 cm diameter to 20 cm at B. The pressure difference between A and B is 1 m of water column. Find the rate of flow of water through the pipe.
Answer» Solution :Let ` P_1 andP_2` be the pressure at A and B respectively and `v_1 and v_2`be the corresponding velocities Rate of flow = Velocity `xx` area of cross - section ` "" v_1 a_1= v_2a_2` ` v_1 pi r_1^(2)= v_2pi r_2^(2)` ` v_1 xx pi (0.3) ^(2)= v_2xx pi xx (0.1)^(2)` ` "" v_2 = 9 v_1` The gravitational potential energy remains constant By Bernouli.s theorem, ` P_1+(1)/(2)rho v_1^(2)= P_2+(1)/(2)rho v_2^(2)` `P_1- P_2 = (1)/(2)rho ( v_2^(2) - v_1^(2))` ` "" = (1)/(2)xx 1000 (8l v_1^(2)- v_1^(2))` But ` "" P_1 - P_2 =1 m " of water " ` ` ""9800 = 500 xx 80 v_1^(2)` `""v_1 ^(2) = ( 9800)/(500 xx 80 ) ` ` "" v_1 = 0. 495ms ^(-1) ` Rate of flow `"" a_1 v_1 = pi ( 0.3) ^(2) xx 0. 495` ` ""= 0. 1399 m ^(3)` per s