A liquid of density \(600\) kg/m\(^3\) flowing steadily in a tube of varying cross-section. The cross-section at a point \(A\) is \(1.0\) cm\(^2\) and that at \(B\) is \(20\) mm\(^2\). Both the points \(A\) and \(B\) are in same horizontal plane, the speed of the liquid at \(A\) is \(10\) cm/s. The difference in pressures at \(A\) and \(B\) points is ________ Pa.

Using the equation of continuity:

\(A_A v_A = A_B v_B\)

\((1.0 \times 10^{-4}) \times 0.1 = (20 \times 10^{-6}) \times v_B\)

\(v_B = \dfrac{10^{-5}}{2 \times 10^{-5}} = 0.5\) m/s

Using Bernoulli's equation for a horizontal tube:

\(P_A + \dfrac{1}{2} \rho v_A^2 = P_B + \dfrac{1}{2} \rho v_B^2\)

\(P_A - P_B = \dfrac{1}{2} \rho (v_B^2 - v_A^2)\)

Substituting the given values:

\(P_A - P_B = \dfrac{1}{2} \times 600 \times (0.5^2 - 0.1^2)\)

\(P_A - P_B = 300 \times (0.25 - 0.01)\)

\(P_A - P_B = 300 \times 0.24 = 72\) Pa

Answer: \(72\)