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 ?

Explanation

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`