One, Two and Three Dimensional Flows

One, Two and Three Dimensional Flows Fluid flow is three-dimensional in nature. This means that the flow parameters like velocity, pressure and so on vary in all the three coordinate directions.      Sometimes simplification is made in the analysis of different fluid flow problems by: Selecting the appropriate coordinate directions so that appreciable variation of the hydro dynamic parameters take place in only two directions or even in only one.         One-dimensional flow All the flow parameters may be expressed as functions of time and one space coordinate only. The single space coordinate is usually the distance measured along the centre-line (not necessarily straight)  in which the fluid is flowing. Example: the flow in a pipe is considered one-dimensional when variations of pressure and velocity occur along the length of the pipe, but any variation over the cross-section is assumed negligible. In reality, flow is never one-dimensional because viscosity causes the velocity to decrease to zero at the solid boundaries. If however, the non uniformity of the actual flow is not too great, valuable results may often be obtained from a "one dimensional analysis". The average values of the flow parameters at any given section (perpendicular to the flow) are assumed to be applied to the entire flow at that section.         Two-dimensional flow  All the flow parameters are functions of time and two space coordinates (say x and y).  No variation in z direction. The same streamline patterns are found in all planes perpendicular to z direction at any instant.         Three dimensional flow The hydrodynamic parameters are functions of three space coordinates and time.