Two-dimensional flow

Fluid motion can be said to be a two-dimensional flow when the flow velocity at every point is parallel to a fixed plane. The velocity at any point on a given normal to that fixed plane should be constant. Fluid motion can be said to be a two-dimensional flow when the flow velocity at every point is parallel to a fixed plane. The velocity at any point on a given normal to that fixed plane should be constant. Considering a two dimensional flow in the X − Y {displaystyle X-Y} plane, the flow velocity at any point ( x , y , z ) {displaystyle (x,y,z)} at time t {displaystyle t} can be expressed as – Considering a two dimensional flow in the r − θ {displaystyle r- heta } plane, the flow velocity at a point ( r , θ , z ) {displaystyle (r, heta ,z)} at a time t {displaystyle t} can be expressed as – Vorticity in two dimensional flows in the X − Y {displaystyle X-Y} plane can be expressed as – Vorticity in two dimensional flows in the r − θ {displaystyle r- heta } plane can be expressed as – A line source is a line from which fluid appears and flows away on planes perpendicular to the line. When we consider 2-D flows on the perpendicular plane, a line source appears as a point source.By symmetry, we can assume that the fluid flows radially outward from the source.The strength of a source can be given by the volume flow rate Q {displaystyle Q} that it generates. Similar to a line source, a line sink is a line which absorbs fluid flowing towards it, from planes perpendicular to it. When we consider 2-D flows on the perpendicular plane, it appears as a point sink.By symmetry, we assume the fluid flows radially inwards towards the source.The strength of a sink is given by the volume flow rate Q {displaystyle Q} of the fluid it absorbs. A radially symmetrical flow field directed outwards from a common point is called a source flow. The central common point is the line source described above. Fluid is supplied at a constant rate Q {displaystyle Q} from the source. As the fluid flows outward, the area of flow increases. As a result, to satisfy continuity equation, the velocity decreases and the streamlines spread out. The velocity at all points at a given distance from the source is the same.