A pipe 2cm in diameter has a constriction of diameter 1cm. Find the velocity of flow at the constriction and the rate at which water is discharge through the pipe if the velocity of flows in the broader region og the pipe is 5cm/s.

Explanation

For horizontal flow of water, we have from Bernoulli's theorem
`P_1 + (1)/(2)p v_1^2 = P_2 + (1)/(2)p v_2^2` therefore `P_2 = p_1 + (1)/(2) p (v_1^2 - v_2^2)`
` p_1 and p_2` are pressure where the velocities are `v_1 and v_2` respectively. On substituting the given value `P_2 = 1400 + (1)/(2) xx 1000 (0.3^2 - 0.3^2) = 1265 N/ m^2`.