UREA INDUSTRY

Presentation Topic: Fluid flow phenomenon,

One dimensional flow, Velocity field

Presented to: Engr . M Tariq

Presented by: Makhdoom Ibad Ullah hashmi

Usman tariq

PRESENTATION ON FLUID FLOW PHENOMENA

CONTENT Fluid Behaviour of fluid Potential Flow Behaviour of fluid stated Boundary layer For incompressible fluid For compressible fluid RHEOLOGICAL PROPERITIES OF FLUIDS

FLUID FLOW PHENOMENA Fluid: In physics a fluid is a substance that continuously deforms under an applied

shear force. OR

A fluid is a substance that doesn’t permanently resist distortion. An attempt to change the shape of mass of a fluid results in sliding of the layer of the fluid over one another.

Behaviour of fluid: Behaviour of fluid depend upon either the fluid is under the fluid

under the influence of solid bounderies

In the region where the influence of wall is small shear stress is neglible.

Fluid behaviour approach to that of an ideal fluid The flow of such an ideal fluid is called potential flow and is completely described by

1. Newtonian mechanics2. Conservation of mass

FLUID FLOW PHENOMENA Potential Flow:

The flow of incompressible fluid with no shear is known as Potential flow

It has some important characteristics- 1. Neither circulation nor eddies forms

within the stream. Hence the potential flow is known as irrotational flow. 2. Friction cannot develop since there is no

existence of shear stress & hence there is no dissipation of mechanical energy into heat energy.

Potential flow can exist since at distance not far from solid boundries

Behaviour of fluid stated by:A fundamenrtal behaviour of of fluid mechanics is stated by pandtl in 1904 is

that of fluid move at low velocities and high viscoties

FLUID FLOW PHENOMENA Boundary layer : The effect of solid boundary on the flow is confined

to the layer of the fluid immediately adjacent to the solid boundary.

This layer is called Boundary Layer & also the shear stress are confired to this part of the fluid only.

Outside the boundry layer potential flow survives

Outside the boundry layer potential flow survives:

Most technical fluid process are studied by considering e the fluid stream as two parts

Parts of fluid: (1)Boundary Layer (2)Remaining fluidThe flow converging to boundry layer is neglected The flow through pipes and channel fills the

entire channel and there is no potential flow

FLUID FLOW PHENOMENAFor incompressible fluid

Within the current of incompressible fluid under the influence of solid boundries four proper affect appear1) The coupling of velocity gradient and shear field2) The onset of turbulence3) The formation and growth of boundry layer4) The separation of boundry layer from contact with

solid boundries

For compressible fluid :In the flow of compressible fluids past solid boundaries, additional effects appear, arising from the significant density changes that are charactetistic of compressible fluid

RHEOLOGICAL PROPERITIES OF FLUIDS

Newtonian fluid – Fluid flow in simple linearity are called Newtonian fluid. In a Newtonian fluid the shear stress is proportional to the shear rate , and the proportionality constant is called the viscosity.

where μ = co-efficient of viscosity

Exmp- Water , Gasses etcNon-Newtonian fluid-

1. The curve starts from origin & concave downwards represents Pseudoplastic fluid & this type of fluid is said to be shear rate –thinning.

Exmp – Polymer solutions , starach suspensions etc.

2. The curve starts from origin & concave upwards represents Dilatant fluid & this type of fluid is said to be shear rate –thickening.

Exmp – Wet beach sand , starch in water etc

3. The straight line having some intercepts in y – axis represents Bingham plastic . This type of fluid do not flow at all until a threshold shear stress attained & then flow linearly at shear stress greater than Exmp – Sludge

dydu

gc

dydu

gc

FIGURE : Shear stress vs shear rate for Newtonian & Non-Newtonian fluid

Newtonian & Non-Newtonian fluid:-

0 0

Reynolds stresses :- The stress is much larger in turbulent flow than the laminar flow . Since the shear stress is higher in turbulent flow Turbulent shear stress are called Reynolds stresses

Eddy viscosity :- By analogy , he relationship between shear stress and velocity gradient in a turbulent stream is used to define an eddy viscosity EV . where E v =

eddy viscosity Also we know , μ = co-

efficient of viscosity

The above two expression is almost similar .Hence eddy viscosity is analogous to μ .

We know, where ν=kinematic viscosity And also,

Where =Eddy diffusivity of momentum =

Here kinematic viscosity is analogous to eddy diffusivity.

dyduEg vct

dydu

gc

DVDVDVNRE

mvvRE

DVEDV

EDVN

m vE

BOUNDARY LAYERS

Here the flow of fluid is parallel to a thin plate . A boundary is define as the part of a moving fluid in which a fluid is influence by a solid boundary . The velocity of the fluid as solid-liquid interface is zero. The velocity increases with distance from the plate as shown in figure.

Each of the curve represents the velocity profile for definite value of x , the distance from the leading edge of the of the plate. The curves changes slope rapidly near the plate . Line OL represents an imaginary surface , which separates the fluid stream into two parts , one in which fluid velocity is constant and the other where the velocity varies from zero to a velocity substantially equal to that of un disturbed fluid.

LAMINAR & TURBULANT FLOW IN BOUNDARY LAYER

Flow near the boundary layer is laminar flow. Since velocity is very low as we move further from the solid boundary the velocity is fairly large and hence the floe become turbulance. There are three layers:- 1. Viscous sublayer 2. Buffer layer 3. Turbulent zone

BOUNDARY LAYER FORMATION IN STRAIGHT TUBUES

Considering a straight, thin-walled tube with fluid entering it at a uniform velocity. As shown in the above fig. A boundary layer begins to form at the entrance to the tube and as the fluid move to the first part of the channel , the boundary layer thickens. During this stage the boundary layer occupies only a part of the tube & total stream consists of a core of fluid moves like a road like manner . But the velocity of fluid is constant. In the boundary layer , the velocity varies from zero to constant velocity existing in the core . As we further move down to the tube , the boundary layer occupies an increasing portion of the cross-section of the tube. At this point , the velocity distribution in the tube reaches its final point & remains unchanged for the remaining part of the fluid . Such flow with an unchanging velocity distribution is called ‘Fully Developed Flow' .

VELOCITY FIELDWhen a stream of fluid is flowing in bulk past a solid at the actual interface adhere between solid and fluid.The adhesion is a result of the force field at the boundary, which are also responsible for the interfacial tension between solid and fluid.If the wall is at rest in the reference frame chosen for the solid system ,the velocity of the fluid at the interface is zero.

CON..But at the distance away from the solid velocity is not zero there must be variation in velocity from point to point in the flowing system.The velocity also vary with time

MATHEMATICALLY Velocity field implies a distribution of velocity in a given region .It is denoted in a functional form as V(x,y,z,t) . It is useful to recall that we are studying fluid flow under the Continuum Hypothesis which allows us to define velocity at a point. Further velocity is a vector quantity i.e., it has a direction along with a magnitude. This is indicated by writing velocity field as

Velocity may have three components, one in each direction, i.e, u,v and w in x, y and z directions respectively. It is usual to write   as

STEADY FLOWIf a flow is such that the properties at every point in the flow do not depend upon time, it is called a steady flow. Mathematically speaking for steady flows,

where P is any property like pressure, velocity or density. Thus

UN STEADY FLOWFlow is one where the properties do depend on time.

USES OF VELOCITY FIELDThe flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity

CON….For steady flow the representation will be

For incompressible the representation will be

For ir rotational flow

ONE DIMENSIONAL FLOWTerm one, two or three dimensional flow refers to the number of space coordinated required to describe a flow. It appears that any physical flow is generally three-dimensional. But these are difficult to calculate and call for as much simplification as possible. This is achieved by ignoring changes to flow in any of the directions, thus reducing the complexity. It may be possible to reduce a three-dimensional problem to a two-dimensional one, even an one-dimensional one at times.

EXAMPLE OF ONE DIMENSIONAL FLOW

Consider flow through a circular pipe. This flow is complex at the position where the flow enters the pipe. But as we proceed downstream the flow simplifies considerably and attains the state of a fully developed flow.

A characteristic of this flow is that the velocity becomes invariant in the flow direction as shown in Fig

Velocity for this flow is given by

It is readily seen that velocity at any location depends just on the radial distance   from the centre line and is independent of distance, x or of the angular position  . This represents a typical one-dimensional flow