This lesson covers the concept of transient axisymmetric Poiseuille flow and the evolution of velocity profiles over time. It explains how to solve one-dimensional transient problems using the separation of variables method. The lesson also discusses the solution of Hagen Poiseuille flow, which is an axisymmetric Poiseuille flow with a parabolic velocity profile. The instructor further explains how to choose the sign of the constant depending on the homogeneous and non-homogeneous direction. The lesson also covers the concept of superposition method and how to use it to solve complex problems. For instance, the lesson demonstrates how to decompose a problem into a steady solution and a transient term to make it easier to solve.

- The separation of variables method is useful in solving one-dimensional transient problems.
- The sign of the constant in a problem is chosen based on the homogeneous and non-homogeneous direction.
- The superposition method can be used to decompose complex problems into simpler ones for easier solving.
- The solution of Hagen Poiseuille flow is an axisymmetric Poiseuille flow with a parabolic velocity profile.
- The evolution of velocity profiles over time can be studied using the concept of transient axisymmetric Poiseuille flow.

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