An incompressible fluid flows steadily through a cylindrical pipe having radius R at point A and ( R 3 ) at point B further along the direction of flow of liquid. If the velocity at point A is ' V ' then that at point B is

Step-by-step solution

The equation of continuity for an incompressible fluid in steady flow requires that the mass flow rate remains constant, thus A_A V_A = A_B V_B . The cross-sectional area varies with the square of the radius: A_A = R^2 and A_B = ( R 3 )^2 = R^2 9 . Substituting into the continuity equation gives R^2 V = R^2 9 V_B . Solving for V_B by canceling R^2 yields V_B = 9V . Final answer: 9V