ATP document for environment engineering

atp

1. BITSPilani
Pilani Campus
20
th
Jan 2023
Lecture Class-I
Applied Transport Phenomena
(EEZG513) Dr. Sarbani Ghosh
Department of Chemical Engineering
B.I.T.S-Pilani, Pilani Campus
Contact: [email protected]

2. BITS Pilani, Pilani Campus
Introduction
⚫A Fluid may be defined as a substance that does not permanently resist distortion and hence, will change its shape
⚫a) If we place a specimen of either substance between two plates
⚫b) then apply a shearing force F, each will initially deform
⚫however, whereas a solid will then be at rest (assuming the force is not large enough to go beyond its elastic limit),
⚫c) & d) a fluid will continue to deform as long as the force is applied.
⚫It is very important to become familiar with the principles that govern the flow of fluids
⚫The amount of deformation of the solid depends on the solid’s modulus of rigidity
⚫rate of deformation of the fluid depends on the fluid’s viscosity μ.
⚫We refer to solids as being elastic and fluids as being viscous.

3. BITS Pilani, Pilani Campus

4. BITS Pilani, Pilani Campus
Introduction
⚫Flow and behaviour of fluids is important in many of the unit operations in chemical process engineering
⚫In the process industries, many of materials are in fluid form and must be stored, handled, pumped and
processed
⚫It is very important to become familiar with the principles that govern the flow of fluids
⚫Incompressible Fluid: If a fluid is insignificantly affected by changes in pressure
e.g., most liquids
⚫Compressible fluid: if the fluid flow is significantly affected by change in pressure
e.g., most gases
⚫Head of a Fluid: In fluid dynamics head is a concept that relates the energy in an incompressible fluid to
the height of an equivalent static column of that fluid
Pressure Head = in m or ft of a given fluid will exert the same pressure as the pressure it represents
height of the fluid column that would extert that amount of pressure at its baseP
ρg

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Fluid Mechanics

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various types of fluid flow problems in practice

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Chemical Plants

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Environmental and Energy

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Aerodynamics and automobile

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Fluid as a continuum
⚫The concept of a continuum is the basis of classical fluid mechanics.
For example, if (about the size of a grain of
sand), there will on average be 2.5x10
13
molecules present.
If density was measured simultaneously at an infinite
number of points in the fluid, we would obtain an
expression for the density distribution as a function of
the space coordinates,
The density at a point may also vary with time (as a
result of work done on or by
the fluid and/or heat transfer to the fluid). Thus the
complete representation of density
(the field representation) is given by

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Velocity Field
When the velocity field is invariant with time, the flow is said to be steady.
1D flow: Only one velocity component is required (Scalar).

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Steady Flow

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Newton’s law of viscosity is given for one-dimensional
flow
❑ Common fluids, e.g., water, air, mercury obey Newton's law of viscosity and are
known as Newtonian fluid.
❑ Other classes of fluids, e.g., paints, polymer solution, blood do not obey the
typical linear relationship of stress and strain. They are known as non-Newtonian
fluids.
Newton’s law of viscosity:Stressα train (deformation)
du du
=
dy dy
   
S : coefficient of viscosity(Dynamicviscosity) : coefficient of viscosity(Dynamicviscosity)

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Rheological Properties of Fluids
⚫The relationship between shear stress and shear rate in a real fluid are part
of the science of rheology (study of the deformation of flowing fluids)
⚫Newtonian: fluids for which the shear stress is linearly proportional (stress
proportional to strain rate)
⚫to the shear strain rate.
Gases and most liquids are newtonian
⚫Non-newtonian: Fluids for which the shear stress is not linearly related to
the shear strain rate are called non-Newtonian fluids. Examples: slurries and
colloidal suspensions, polymer solutions, blood, paste, and cake batter.
⚫Some non-Newtonian fluids are called shear thinning fluids or
pseudoplastic fluids, because the more the fluid is sheared, the less
viscous it becomes. A good example is paint.
⚫In some fluids a finite stress called the yield stress is required before the fluid
begins to flow at all; such fluids are called Bingham plastic fluids.
⚫shear thickening fluids or dilatant fluids: the more the fluid is sheared, the more viscous it becomes. The best
example is quicksand, a thick mixture of sand and water.
power law
model

17. BITS Pilani, Pilani Campus
n, is called the flow behavior index and the coefficient, k, the consistency index
⚫This equation reduces to Newton’s law of viscosity for n = 1 with k = μ.
⚫(n < 1) are called pseudoplastic (or shear thinning) fluids
⚫(n > 1) the fluid is termed dilatant (or shear thickening)
⚫A “fluid” that behaves as a solid until a minimum yield stress, τ y , is exceeded and
subsequently exhibits a linear relation between stress and rate of deformation is referred to
as an ideal or Bingham plastic. The corresponding shear stress model is
Rheological Properties of Fluids
power law
model

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Rheological Properties of Fluids
power law
model

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Surface Tension
⚫a liquid as “wetting” a surface when the contact angle θ < 90
⚫Example: the car’s surface was wetted before waxing, and
not wetted after due to surface tension.
⚫Whenever a liquid is in contact with other liquids or gases,
or in this case a gas/solid surface, an interface develops
that acts like a stretched elastic membrane, creating surface
tension.
⚫There are two features to this membrane: the contact angle,
θ, and the magnitude of the surface tension, σ
⚫the most important effect of surface tension is the creation
of a curved meniscus that appears in manometers or
barometers, leading to a (usually unwanted) capillary rise
(or depression)
small water insects are
able to walk on the
surface of the water

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Hydrostatic Equilibrium

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Fluid Flow Phenomena
⚫The behaviour of a flowing fluid depends strongly on whether the fluid is under the influence of solid
boundaries
⚫Influence of wall is small → shear stress may be negligible → fluid behaviour may approach that of an
ideal fluid → called potential flow → is described by the principles of Newtonian mechanics &
conservation of mass
⚫Potential Flow
⚫Irrotational flow: Neither circulations nor eddies can form within
the stream
⚫Frictionless: Friction cannot develop → there’s no dissipation
of mechanical energy into heat
⚫Boundary Layer: Except for fluids moving at low velocities or
possessing high viscosities, the effect of the solid boundary on
the flow is confined to a layer of the fluid immediately adjacent to
the solid wall. This layer is called boundary layer.
⚫Outside the boundary layer potential flow survives

23. BITS Pilani, Pilani Campus
Description and Classification of
Fluid Motions
Fluid mechanics deal with: (1) the fluid’s viscous nature (2) its compressibility.
In engineering we subdivide fluid mechanics in terms of whether or not viscous effects and compressibility
effects are present. Also shown are classifications in terms of whether a flow is laminar or turbulent, and internal
or external.

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Viscous and Inviscid Flows
We can estimate whether or not viscous forces, as opposed to pressure forces, are negligible by simply
computing the Reynolds number
where ρ and μ are the fluid density and viscosity, respectively, and V and L are the typical or
“characteristic” velocity and size scale of the flow respectively. If the Reynolds number is “large,” viscous
effects will be negligible, at least in most of the flow; if the Reynolds number is small, viscous effects will
be dominant. Finally, if the Reynolds number is neither large nor small, no general conclusions can be
drawn.

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Viscous and Inviscid Flows

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Laminar and Turbulent Flows
At low flow rate the water will flow out very smoothly—almost “glass-like.” If you increase the flow rate,
the water will exit in a churned-up, chaotic manner.
A laminar flow is one in which the fluid particles move in smooth layers, or laminas.
A turbulent flow is one in which the fluid particles rapidly mix as they move along due to random three-
dimensional velocity fluctuations.
In most fluid mechanics problems—for example, flow of water in a pipe—turbulence is an unwanted but
often unavoidable phenomenon, because it generates more resistance to flow; in other problems—for
example, the flow of blood through blood vessels—it is desirable because the random mixing allows all of
the blood cells to contact the walls of the blood vessels to exchange oxygen and other nutrients.

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Laminar and Turbulent Flows

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Compressible versus Incompressible Flow
Incompressible flow: If the density of flowing fluid remains nearly constant throughout
(e.g., liquid flow).
Compressible flow: If the density of fluid changes during flow (e.g., high-speed gas
flow)
When analyzing rockets, spacecraft, and other systems that involve high-speedgas
flows, the flow speed is often expressedby Mach number
Ma = 1 Sonic flow
Ma < 1 Subsonic flow
Ma > 1 Supersonic flow
Ma >> 1 Hypersonic flow

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Internal versus External Flow
Externalflow:The flow of anunbounded fluid over a surface such
as a plate, a wire, or a pipe.
Internalflow: The flow in a pipe or duct if the fluid is completely
bounded by solid surfaces.
•Water flow in a pipe is internal
flow, and airflow over a ball is
external flow .
•The flow of liquidsin a duct is
called open-channel flow if the
duct is only partially filled withthe
liquid and there is a free surface.
External flow over a tennis ball, andthe
turbulent wake region behind.

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Basic Equations of Fluid Flow

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THANK YOU