An incompressible fluid that flows through a cylindrical pipe of radius '2r' at point A having radius 'r' at point B further along the direction of flow if the velocity at point A is v then velocity at point B is?

Explanation

The principle of continuity for incompressible fluids states that the mass flow rate must remain constant from one cross-section of a pipe to another. Mathematically, this is expressed as A1 * V1 = A2 * V2. Here, A1 and A2 are the cross-sectional areas at points A and B, respectively, and V1 and V2 are the corresponding velocities. At point A, the radius is 2r, so the area A1 = π(2r)^2 = 4πr^2. At point B, the radius is r, so the area A2 = πr^2. Substituting these into the continuity equation gives 4πr^2 * v = πr^2 * V2, simplifying to V2 = 4v. Therefore, the velocity at point B is 4V. The other options do not correctly apply the relationship between the area and velocity as dictated by the continuity equation.