Study the geometric properties of fluid motion, without addressing the specific role of hydrodynamics forces branch.

Description of the flow of fluid motion analysis described in two ways, namely, the Lagrangian method and Eulerian methods. Lagrange's method focuses on fluid particles, try to describe the location of each fluid particle variation with time. Usually use the initial moment of the fluid particle in Cartesian or curvilinear coordinates a, b, c as a sign to distinguish between different fluid particles. The movement of fluid particles can be expressed as r = r (a, b, c, t), where r is the radius vector of fluid particles; t is time; a, b, c, t collectively referred to as Lagrangian variables. Euler's method focus on the space points, each point in space trying to describe the fluid motion on the change in status over time. The movement of the fluid particle velocity vector can be v = v (r, t) that, where r, t is called Euler variables. Euler method is widely used, less use of the Lagrangian approach, as determined by Euler variable speed function is defined point in time and space, so is the velocity field, called the flow field, knowledge of field theory can be used to solve ; Secondly, the Euler method, because the acceleration is a derivative, so the motion equations are first-order partial differential equations, than the Lagrangian method of second order partial differential equations easier to handle.

Geometric description of the flow of fluid particle movement in space as depicted in curve traces; every point in the flow field with the velocity vector on the tangent of the curve is called flow lines. Trace is the same fluid particle formation at different times of the curve, it is the physical point in the Lagrangian approach mid-stream movement of the geometric representation; flow time line is the same fluid particles composed of different curves, which is Euler's method the geometric law of motion of fluid particles, said. Only in steady motion, only the two overlap together.

Flow analysis of complex fluid motion than the rigid body motion, which in addition to translation and rotation, but also deformed. Helmholtz decomposition theorem states that the speed, fluid movement of micro-groups can be decomposed into translation, rotation and deformation, and 3 parts

Kinematics (see mechanical movement). Rigid body velocity decomposition theorem speed decomposition theorem with an important difference as follows: ? fluid than the rigid body movement of micro-groups more part of the deformation rate; ? speed decomposition theorem of rigid body established for the entire rigid body, so is the integrity of the theorem, while velocity decomposition theorem only micro-group set up in the fluid, so the theorem is localized.