A horizontal pipeline carries water in a streamlime flow, At a point along the pipe, where the cross-sectional area is `10cm^(2)`, the water velocity is `1ms^(-1)` and the pressure is `2000 Pa`. The pressure of water at another point where the cross-sectional area is `5cm^(2)`, is .....Pa. (Density of water `=10^(3)kg-m^(3))`.

Answer

500

Explanation

From continuity equation
` A_1v_1 = A_1v_2 therefore v_2 = ((A_1)/(A_2))v _ 1 = ((10)/(5))(1) = 2m//s `
Applying Bernoulli’s theorem at 1 and 2
` p_2 + (1)/(2) rho v_2 ^2 = p_1 + (1)/(2) rho v_1 ^2 `
` therefore p_2 = p_1 + (1)/(2) rho (v_1 ^ 2 - v _ 2 ^ 2 ) = (2000 + (1)/(2) xx 10^(3) (1-4 ) ) , therefore P_2 = 500 Pa `