# An Initial and Boundary Value Problem of Fluid Mechanics - the Navier Stokes equations - Lesson 10

A boundary value problem for fluids will be discussed in this lesson. The flow of an incompressible viscous fluid at a steady state is discussed. The mathematical expression for the flow of this fluid and the relevant boundary conditions for the fluid are shown. Navier Stoke’s equation is used here.

Continuing from the mass balance shown in the previous lesson, momentum balance will be used next. The final equations that need to be solved are arrived at and will be solved in the next lesson.

The lesson starts with recalling that the problem to be solved at hand is the flow of an incompressible fluid at a steady state. The parameters and the variables derived so far for this problem are discussed. Poisson’s equation is shown, and the terms derived so far are plugged into this equation. Pressure drop with viscosity is explained. The use of the equation of Continuum Mechanics and solving PDE is the more general way in which the problems will be solved in this course.