CE: Fluid

Steady and Unsteady Flows

*Steady flow* is defined as that type of flow in which the fluid characteristics like velocity, pressure, density, etc., at a point *do not change with time*. where (x₀, y₀, z₀) is a fixed point in fluid field *Unsteady flow* is that type of flow, in which the velocity, pressure or density at a point *changes with respect to time*.

Compressible and Incompressible Flows

Compressible flow is that type of flow in which the density of the fluid changes from point to point or in other words the density (ρ) is not constant for the fluid. *ρ ≠Constant* *Mach number* is generally taken as a measure of the relative importance of compressibility, Mach number *< 0.3*, the compressibility effects are ignored Incompressible flow is that type of flow in which the density is constant for the fluid flow. Liquids are generally incompressible while gases are compressible *ρ =Constant*

Laminar and Turbulent Flows.

Laminar flow is defined as that type of flow in which the fluid particles move along well-defined paths or stream line and all the stream-lines are straight and parallel. Thus the particles move in laminas or layers gliding smoothly over the adjacent layer. Thistype of flow is also called stream-line flow or viscous flow. Turbulent flow is that type of flow in which the fluid particles move in a zig-zag way. Due to the movement of fluid particles in a zig-zag way, the eddies formation takes place which are responsible for high energy loss. For a pipe flow, the type of flow is determined by a non-dimensional number*VD/v called the Reynold number, D = Diameter of pipe V = Mean velocity of flow in pipe v = Kinematic viscosity of fluid. *flow of fluid in a pipe* Re<2000→ laminar 2000<Re<4000→ transition Re>4000→Turbulent *flow b/n parallel plates* Re<1000→laminar Re>2000→Turbulent *flow in wide open channel* Re<500→laminar RE>1000→Turbulent *flow around a sphere* Re<1 laminar

Rotational and Irrotational Flows

Rotational flow is that type of flow in which the fluid particles while flowing along stream-lines, also rotate *about their own axis*. And if the fluid particles while flowing along stream-lines, do not rotate about their own axis then that type of flow is called irrotational flow. A Vortex or whirlpool which develops around a drain in the bottom of stationary tank represents an irrotational motion

TYPES OF FLUID FLOW

The fluid flow is classified as : ( i ) Steady and unsteady flows ( ii ) Uniform and non - uniform flows ; ( iii ) Laminar and turbulent flows ; ( iv ) Compressible and incompressible flows ( v ) Rotational and irrotational flows ; and ( vi ) One , two and three -dimensional flows

Streamlines, streaklines, and pathlines

The red particle moves in a flowing fluid; its pathline is traced in red; the tip of the trail of blue ink released from the origin follows the particle, but unlike the static pathline (which records the earlier motion of the dot), ink released after the red dot departs continues to move up with the flow. (This is a streakline.) The dashed lines represent contours of the velocity field (streamlines), showing the motion of the whole field at the same time. *a steady flow, the path lines, streak lines and streamlines are identical*.

The fluid motion is described by two methods .

They are ( i ) Lagrangian Method , and ( ii ) Eulerian . *Lagrangian method* , a *single fluid particle* is followed during its motion and its velocity , acceleration , density .. etc . .are described is a way of looking at fluid motion where the observer follows an *individual fluid parcel as it moves through space and time*. Plotting the position of an individual parcel through time gives the pathline of the parcel. This can be visualized as sitting in a boat and drifting down a river. this approach is *very accurate*, it is very difficult to keep track of a single fluid particle. *Eulerian method* , the velocity , acceleration , pressure , density etc . , are *described at a point in flow field* . The Eulerian method is commonly used in fluid mechanics . is a way of looking at fluid motion that focuses on *specific locations* in the space through which the fluid flows as time passes. This can be visualized by *sitting on the bank of a river* and watching the water pass the fixed location. we take a finite volume, called *control volume* through which fluid flow in and out

Uniform and Non-uniform Flows.

Uniform flow is defined as that type of flow in which the velocity at any given time *does not change with respect to space* Non-uniform flow is that type of flow in which the velocity at any given *time changes with respect to space*.

Streamlines

are a family of curves that are instantaneously *tangent to the velocity vector of the flow*. These show the direction in which a massless fluid element will travel at any point in time. .different streamlines at the same instant in a flow do *not intersect*, because a fluid particle cannot have two different velocities at the same point

Streaklines

are the *loci of points* of all the fluid particles that have passed continuously through a particular spatial point in the past. *Dye steadily injected* into the fluid at a fixed point extends along a streakline. .Streakline concentrates on fluid particles that have gone through a fixed station or point. At some instant of time the position of all these particles are marked and a line is drawn through them

Pathlines

are the trajectories that individual fluid particles follow. These can be thought of as *"recording" the path* of a fluid element in the flow over a certain period. The direction the path takes will be determined by the streamlines of the fluid at each moment in time.

Kinematics

is defined as that branch of science which deals with *motion of particles without considering the forces causing the motion* . The velocity at any point in a flow field at any time is studied in this branch of fluid mechanics . Once the velocity is known , then the pressure distribution and hence forces acting on the fluid can be determined .

One-dimensional flow

is that type of flow in which the flow parameter such as velocity is a function of time and one space coordinate only, say x. For a steady one-dimensional flow, the velocity is a function of one-space-co-ordinate only. The variation of velocities in other two mutually perpendicular directions is assumed negligible. Hence mathematically, for one-dimensional flow u = f(x), v = 0 and w = 0 where u, v and w are velocity components in x, y and z directions respectively

Three-dimensional flow

is that type of flow in which the velocity is a function of time and three mutually perpendicular directions. But for a steady three-dimensional flow the fluid parameters are functions of three space co-ordinates (x, y and z ) only. Thus, mathematically, for three-dimensional flow u=f₁(x, y, z ), v = f₂( x, y, z ) and w = f₃( x, y, z )

Two-dimensional flow

is that type of flow in which the velocity is a function of time and two rectangular space co-ordinates say x and y. For a steady two-dimensional flow the velocity is a function of two space co-ordinates only. The variation of velocity in the third direction is negligible. Thus, mathematically for two-dimensional flow u = f₁( x, y), v = f₂(x, y) and w = 0.