The radius of the circular duct varies as r = [0.06(1 )] m, where x is in meters. The flow of water at A is Q = 0.003 m3/s at t = 0, and it is increasing at dQ/dt = 0.003 m3/s2. If a fluid particle...

The radius of the circular duct varies as r = [0.06(1

)] m, where x is in meters. The flow of water at A is Q = 0.003 m³/s at t = 0, and it is increasing at dQ/dt = 0.003 m³/s². If a fluid particle is originally located at x = 0 when t = 0, determine the time for this particle to arrive at x = 0.3 m. Use average velocities at the cross section for the solution.