A pathline is a curve traced by a single fluid particle during its motion. The path can cross each other.
Stream lines are drawn through a closed curve, they form a boundary surface across which fluid cannot penetrate.
Physically acceleration of any object is a measure of the change in its velocity. If the velocity vector of any fluid flow is a function of space and time, then it can change with space and as well as with time. Thus the acceleration, or change in velocity, experienced by the fluid particles can be due to the change of velocity with space and can be due to the change of velocity with time.
The acceleration of fluid particles due to change in velocity in space is called convective acceleration and acceleration due to change in velocity in time is called local or temporal acceleration. Acceleration of fluid particles can thus have two components: tangential and normal acceleration.
Tangential acceleration is due to the change in velocity along the direction of motion. This tangential change in velocity or the tangential acceleration of fluid particles is the sum of tangential convective (change with space) and tangential local (change with time) accelerations.
Normal acceleration of any particle is the component of the change in velocity normal to the direction of motion or the tangential velocity. Normal acceleration comes into picture when fluid particles move in curved paths. While moving in curved paths the velocity of the fluid particle changes in direction; it can also change in magnitude, too.
For compressible and 3 dimensional unsteady flow
For compressible one dimensional flow
r1 A1 V1 = r2 A2 V2
One dimensional differential form
For incompressible one dimensional flow
A1V1 = A2V2
The circulation, C, about a closed contour in a fluid is defined as the line integral evaluated along the contour of the component of the velocity vector that is locally tangent to the contour.
In continuum mechanics, the vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate, as would be seen by an observer located at that point and traveling along with the flow.
The vorticity equation of fluid dynamics describes evolution of the vorticity ω of a particle of a fluid as it moves with its flow, that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The equation is:
where Dt is the material derivative operator, u is the flow velocity, ρ is the local fluid density, p is the local pressure, τ is the viscous stress tensor and B represents the sum of the external body forces.
Irrotational and Rotational flow
Velocity potential (ϕ)
Streamline function ( y )
Construction of a flownet is often used for solving groundwater flow problems where the geometry makes analytical solutions impractical.