Chapter 4 Fluid Kinematics
Steady & unsteady flow If the fluid and flow characteristics (such as density, velocity, pressure etc.) at a point do not change with time, the flow is said to be steady flow. If the fluid and flow variables at a point may change with time, the flow will be unsteady.
Uniform and Non-uniform flow If the velocity vector at all points in the flow is same at any instant of time, the flow is uniform flow. If the velocity vector varies from point to point at any instant of time, the flow will be non-uniform laminar flow generally occess at low velocities while turbulent flow occurs at high velocities.
Laminar and Turbulent flow In laminar flow, the particles moves in layers sliding smoothly over the adjacent layers while in turbulent flow particles have the random and erratic movement, intermixing in the adjacent layers.
Streamline
A streamline is an imaginary line drawn in a flow field such that a tangent drawn at any point on this time represents the direction of velocity vector at that point.
There is no velocity component normal to stream lines.
Pathline A pathline is a curve traced by a single fluid particle during its motion. The path can cross each other.
Streakline When a dye is injected in a liquid or smoke in a gas so as to trace the subsequent motion of liquid particles passing a fixed point, the path followed by the dye or smoke is called the streakline.
In a steady flow streamline, pathline & streak lines are same.
Stream tube Stream lines are drawn through a closed curve, they form a boundary surface across which fluid cannot penetrate.
Stream-line equation in 3- D
Fluid Acceleration
Tangential acceleration (a_{s} ) = V/t (local acceleration) +V (convective acceleration)
Normal acceleration (a_{n}) = Vn/2 (local acceleration) + (convective acceleration)
Type of flow | Convective Acceleration | Temporal Acceleration |
Steady & uniform | 0 | 0 |
Steady & non-uniform | Exists | 0 |
Unsteady & uniform | 0 | Exists |
Unsteady & non-uniform | Exists | Exists |
Acceleration in three dimensional-flow
Above equations are valid for steady & unsteady flows uniform & non uniform flow. Continuity Equations For incompressible and steady 3 dimensional flow
For compressible and 3 dimensional unsteady flow
For compressible one dimensional flow
r_{1} A_{1} V_{1} = r_{2} A_{2} V_{2}
One dimensional differential form
For incompressible one dimensional flow A_{1}V_{1} = A_{2}V_{2}
Circulation Circulation is defined as the summation of the product of velocity along the element of curve and element length ds.
G = òv cos qds
Vorticity at a point, x =
x_{Z} =circulation/area
W = 1/2 N Hence, w = 0
For irrotational flow in 3 – D Ñ ´ V = 0