Water is flowing with a speed of 2 ms^(-1) in a horizontal pipe with cross-sectional area decreasing from 2 xx 10^(-2) m^(2) to 0.01 m^2 at pressure 4 xx 10^4 Pa. What will be the pressure at small cross-section ?

Water is flowing with a speed of 2 ms^(-1) in a horizontal pipe with c

1.	Water is flowing with a speed of 2 ms^(-1) in a horizontal pipe with cross-sectional area decreasing from 2 xx 10^(-2) m^(2) to 0.01 m^2 at pressure 4 xx 10^4 Pa. What will be the pressure at small cross-section ?
Answer» Solution :Here , `v_1 = 2 ms^(-1) , a_1 = 2 xx 10^(-2) m^2, a^2 = 0.01 m^2 , P_1 = 3 xx 10^(4) Pa, P_2 = ? , rho = 10^3 KG m^(-3)` `v_2 = (a_1v_1)/(a_2) = (2 xx 10^(-2) xx 2)/(0.01) = 4 ms^(-1)` As `"" P_1 + 1/2 rho v_1^2 = P_2 + 1/2 rho v_2^2` `"" P_2 = P_1 - 1/2 rho (v_1^2 - v_2^2)` `= 4 xx 10^4 - 1/2 xx 10^3 (2^2 - 4^2)` `P_2 = 3.4 xx 10^(4)Pa`