Web programming Module 1webprogramming.pptx

Dr. Suman Pawar
Assistant Professor
Dept of Chemical Engineering, SIT.

Fluid Statics and Its Applications
 Concept of unit operations, Concept of Momentum Transfer, Variation of
pressure with height – hydrostatic equilibrium, Barometric equation, Devices
of measurement of pressure.
 Fluid Flow Phenomena: Nature of fluids, Types of fluids – shear stress and
velocity gradient relation, Newtonian and non – Newtonian fluids, Types of
flow – laminar and turbulent flow, Reynolds number.
MODULE - I

 Fluid statics deals with the study of fluids at rest which involves the study
of pressure exerted by a fluid at rest and the variation of fluid pressure
throughout the fluid.
 Fluid dynamics deals with the study of fluids in motion relative to
stationary solid walls or boundaries.

Concept of unit operations
 Bioprocesses treat raw materials and generate useful products. Individual operations or steps in
the process that alter the properties of materials are called unit operations.
 Although the specific objectives of bioprocesses vary from factory to factory, each processing
scheme can be viewed as a series of component operations that appear again and again in
different systems.
 For example, most bioprocesses involve one or more of the following unit operations:
adsorption, centrifugation, chromatography, crystallisation, dialysis, distillation, drying,
evaporation, filtration, flocculation, flotation, homogenisation, humidification, microfiltration,
milling, precipitation, sedimentation, solvent extraction, and ultrafiltration.

Typical unit operations used in the manufacture of enzymes.

Generalised downstream processing schemes for cells as product, products
located inside the cells, and products located outside the cells in the
fermentation liquor.

Concept of Momentum Transfer
 In physics, momentum transfer is the amount of momentum transferred from one particle to
another during particle collision or interaction.
 This phenomenon can be utilized in various areas of physics and optics including condensed
matter physics and diffraction on the atomic scale.
 Fluid mechanics is an important area of engineering science concerned with the nature and
properties of fluids in motion and at rest.
 Fluids play a central role in bioprocesses since most of the required physical, chemical, and
biological transformations take place in a fluid phase.

 Because the behaviour of fluids depends to a large extent on their physical characteristics,
knowledge of fluid properties and techniques for their measurement is crucial.
 Fluids in bioprocessing often contain suspended solids, consist of more than one phase,
and have non-Newtonian properties; all of these features complicate the analysis of flow
behaviour and present many challenges in bioprocess design.
 In bioreactors, fluid properties play a key role in determining the effectiveness of
mixing, gas dispersion, mass transfer, and heat transfer.
 Together, these processes can exert a significant influence on system productivity and the
success of equipment scale-up.

Fluid Flow Phenomena
 A fluid is a substance which is capable of flowing if allowed to do so.
 A fluid is a substance that has no definite shape of its own, but conforms to the shape of
the containing vessel.
 A fluid is a substance which undergoes continuous deformation when subjected to a
shearing force/shear force. Since liquids and gases / vapours possess the above cited
characteristics, they are referred to as fluids.

 Ideal Fluid : It is a fluid which does not offer resistance to flow / deformation /
change in shape, i.e., it has no viscosity. It is frictionless and incompressible.
However, an ideal fluid does not exist in nature and therefore, it is only an imaginery
fluid.
 An ideal fluid is the one which offers no resistance to flow/change in shape.
Real Fluid : It is a fluid which offers resistance when it is set in motion. All naturally
occurring fluids are real fluids.
CLASSIFICATION OF FLUIDS
1. Based upon the behaviour of fluids under the action of externally
applied pressure and temperature, the fluids are classified as :
(a) Compressible Fluids (b) Incompressible Fluids.

 2. Based upon the behaviour of fluids under the action of shear stress, the fluids are
classified as : (a) Newtonian Fluids (b) Non-Newtonian Fluids.
 A fluid possesses a definite density at a given temperature and pressure.
 Although the density of fluid depends on temperature and pressure, the variation of
density with changes in these variables may be large or small.
Compressible Fluid : If the density of a fluid is affected appreciably by changes in
temperature and pressure, the fluid is said to be compressible.
If the density of a fluid is sensitive to changes in temperature and pressure, the fluid
is said to be compressible.

 Incompressible Fluid : If the density of a fluid is not appreciably affected by
moderate changes in temperature and pressure, the fluid is said to be
incompressible.
 If the density of a fluid is almost insensitive to moderate changes in
temperature and pressure the fluid is said to be incompressible.
 Thus, liquids are considered to be incompressible fluids, whereas gases are
considered to be compressible fluids.

PROPERTIES OF FLUIDS
 The properties of fluids are
(i) Mass density (specific mass) or simply density (ρ).
(ii) Weight density (specific weight) (w).
(iii) Vapour pressure.
(iv) Specific gravity.
(v) Viscosity.
(vi) Surface tension and capillarity.
(vii) Compressibility and elasticity.
(viii) Thermal conductivity.
(ix) Specific volume.

 Density : Density (ρ) or mass density of a fluid is the mass of the fluid per unit
volume. In the SI system, it is expressed in kg/m3
.
 The density of pure water at 277 K (4 o
C) is taken as 1000 kg/m3
.
 Weight Density : Weight density of a fluid is the weight of the fluid per unit volume.
In the SI system, it is expressed in N/m3
.
 Specific weight or weight density of pure water at 277 K (4 o
C) is taken as 9810
N/m3
.
 The relation between mass density and weight density is w = ρ g where g is the
acceleration due to gravity (9.81 m/s 2 ).
 Specific Volume : Specific volume of a fluid is the volume of the fluid per unit mass.
In the SI system, it is expressed in m3
/kg

 Specific Gravity : The specific gravity of a fluid is the ratio of the density of the fluid
to the density of a standard fluid.
 For liquids, water at 277 K (4 o
C) is considered/chosen as a standard fluid and for
gases, air at NTP (0°C and 760 torr) is considered as a standard fluid.
 Vapour Pressure : The vapour pressure of a pure liquid is defined as the absolute
pressure at which the liquid and its vapour are in equilibrium at a given temperature or
The pressure exerted by the vapour (on the surface of a liquid) at equilibrium
conditions is called as the vapour pressure of the liquid at a given temperature. Pure air
free water exerts a vapour pressure of 101.325 kPa (760 torr) at 373.15 K (100 o
C).
 Surface Tension : The property of liquid surface film to exert tension is called as the
surface tension. It is the force required to maintain a unit length of film in equilibrium.
It is denoted by the symbol σ (Greek sigma) and its SI unit is N/m.

 Viscosity : A fluid undergoes continuous deformation when subjected to
a shear stress.
 The resistance offered by a fluid to its continuous deformation (when
subjected to a shear stress/force) is called viscosity
 The viscosity of a fluid at a given temperature is a measure of its
resistance to flow.
 The viscosity of a fluid (gas or liquid) is practically independent of the
pressure for the range that is normally encountered in practice.
 However, it varies with temperature. For gases, viscosity increases with
an increase in temperature, while for liquids it decreases with an increase
in temperature.
Shear
stress, force
tending to
cause
deformation of
a material by
slippage along
a plane or
planes parallel
to the imposed
stress.

Consider two layers of a fluid 'y' cm apart as shown in Fig. Let the area of each of these layers
be A cm2
.
Assume that the top layer is moving parallel to the bottom layer at a velocity of 'u' cm/s relative
to the bottom layer.
To maintain this motion, i.e., the velocity 'u' and to overcome the fluid friction between these
layers, for any actual fluid, a force of 'F' dyne (dyn) is required.
Experimentally it has been found that the force F is directly proportional to the velocity u and
area A, and inversely proportional to the distance y. Therefore, mathematically it becomes

F u.A/y -----------------1
∝
Introducing a proportionality constant µ (Greek 'mu'), Equation (1) becomes
F = µ u A/y ---------------2
F/A = µ.u/y -------------------3
Shear stress, τ (Greek 'tau') equal to F/A between any two layers of a fluid may be
expressed as
τ = F/A = µ.u/y ------------4
The above equation in a differential form becomes
τ = µ ⋅ du / dy ------------5
(The ratio u/y can be replaced by the velocity gradient du/dy.) In the SI system, the shear stress τ is
expressed in N/m2 and the velocity gradient/shear rate or rate of shear deformation is expressed in
1/s or s–1

 Equation (5) is called Newton's law of viscosity. In the rearranged form, it serves to define the
proportionality constant as
6
which is called as the coefficient of viscosity, or the dynamic viscosity (since it involves force), or
simply the viscosity of a fluid.
Hence, the dynamic viscosity µ, may be defined as the shear stress required to produce unit rate of
shear deformation (or shear rate).
Viscosity is the property of a fluid and in the SI system it has the units of (N.s)/m2
or Pa.s or
kg/(m.s).
As the unit (N.s)/m2 is very large for most of the fluids, it is customary to express viscosity as
(mN.s)/m2
or mPa.s, where mN is millinewtons, i.e., 10–3
N and mPa is millipascal, i.e., 10–3
Pa.

 In the C.G.S. system, viscosity may be expressed in poise (P) (the unit poise is named after the French
scientist Poiseuille) or centipoise (cP).
1 poise = 1 P = 1 gm/(cm.s)
= 0.10 kg/(m.s)
= 0.10 (N.s)/m2
or Pa.s
= 100 cP
In many problems involving viscosity, there appears a term kinematic viscosity.
 The kinematic viscosity of a fluid is defined as the ratio of the viscosity of the fluid to its density and is
denoted by the symbol υ (Greek 'nu').
υ = µ/ρ --------------7
 In the SI system, υ has the units of m2
/s. The C.G.S. unit of kinematic viscosity is termed as stoke and is
equal to 1 cm2
/s.

NEWTONIAN AND NON-NEWTONIAN FLUIDS
 For most commonly known fluids, a plot of t v/s du/dy results in a straight line
passing through the origin and such fluids are called as Newtonian fluids.
Fluids that obey Newton's law of viscosity, i.e., the fluids for which the ratio of the shear
stress to the rate of shear or shear rate is constant, are called as Newtonian fluids.
This is true for all gases and for most pure liquids

 Examples of Newtonian Fluids : All gases, air, liquids, such as kerosene, alcohol,
glycerine, benzene, hexane ether etc., solutions of inorganic salts and of sugar in
water.
 Fluids for which the ratio of the shear stress to the shear rate is not constant but is considered
as a function of rate of shear, i.e., fluids which do not follow Newton's law of viscosity are
called as non-Newtonian fluids.
 Generally, liquids particularly those containing a second phase in suspension (solutions of
finely divided solids and liquid solutions of large molecular weight materials) are non-
Newtonian in behaviour.
Examples of Non-Newtonian Fluids : Tooth pastes, paints, gels, jellies, slurries and
polymer solutions.

 A Newtonian fluid is one that follows Newton's law of viscosity.
 If viscosity is independent of rate of shear or shear rate, the fluid is said to be
 Newtonian and if viscosity varies with shear rate, the fluid is said to be non-Newtonian.
There are three common types of non-Newtonian fluids.
(a) Bingham Fluids or Bingham Plastics : These fluids resist a small shear stress indefinitely
but flow linearly under the action of larger shear stress, i.e., these fluids do not deform, i.e.,
flow unless a threshold shear stress value (0) is not exceeded.
These fluids can be represented by
 = 0, du/dy = 0,  > 0,  = 0 + h * du/dy
where 0 is the yield stress / threshold shear stress and h is commonly called as the coefficient
of rigidity.
Examples : Tooth paste, jellies, paints, sewage sludge and some slurries.

(b) Pseudoplastic Fluids : The viscosity of these fluids decreases with increase in
velocity gradient, i.e., shear rate.
 Examples : Blood, solution of high molecular weight polymers, paper pulp, muds,
most slurries and rubber latex.
(c) Dilatent Fluids : The viscosity of these fluids increases with an increase in
velocity gradient.
 Examples : Suspensions of starch in water, pulp in water, and sand filled
emulsions.

 The experimental curves for pseudoplastic as well as dilatent fluids can be
represented by a power law, which is also called the Ostwald-de-Waele
equation.
t = k (du/dy)n ------------(1)
where k and n are arbitrary constants.
Newtonian fluids : n = 1, k = 
Pseudoplastic fluids : n < 1
Dilatent fluids : n > 1
Pseudoplastics are said to be shear-rate-thinning and dilatent fluids are said
to be shearrate-thickening.

 Steady and Unsteady Flow
The flow is said to be steady if it does not vary with time, i.e., the mass flow rate is
constant and the quantities, such as temperature, pressure, etc. are independent of
time, i.e., do not vary with time.
If the mass flow rate and/or other quantities such as temperature, pressure, etc.
vary with time, the flow is said to be unsteady.
Stream Line and Stream Tube
 A stream tube is a tube of small or large cross-section which is entirely bounded by
stream lines. It may be of any convenient cross-sectional shape and no net flow occurs
through the walls of the stream tube.

Reynolds number
The experimental set up is shown in Fig. It
consists of a horizontal glass tube with a
flared entrance immersed in a glass walled
constant head tank filled with water.
The flow of water through the glass tube
can be adjusted to any desired value by
means of a valve provided at the outlet of
the tube.
A capillary tube connected to a small reservoir containing water soluble dye is
provided at the centre of the flared entrance of the glass tube for injecting a dye
solution in the form of a fine or thin filament into the stream of water.

 By introducing a water soluble dye into the flow of water, the nature of flow could be
observed.
 At low flow rates (i.e., at low water velocities), the filament/thread of coloured water flowed
along with the stream of water in a thin, straight line without any lateral mixing.
 This indicated that the water was flowing in the form of parallel streams which did not
interfere with each other (i.e., the water was flowing in parallel, straight lines).
 This type of flow pattern is called streamline or laminar. The laminar flow is characterised
by the absence of bulk movement at right angles to the main stream direction (lateral
movement).

 As the water flow rate was increased, a definite velocity called the critical velocity was
reached, oscillations appeared in the coloured filament/thread and the thread of coloured water
became wavy, gradually disappeared and the entire mass of water in the tube became
uniformly coloured.
 In other words, the individual particles instead of flowing in an orderly manner parallel to the
axis of the tube, moved erratically in the form of cross-currents and eddies which resulted into
complete mixing. This type of flow pattern is known as turbulent.
 The turbulent flow is characterised by the rapid movement of fluid in the form of eddies in
random directions across the tube.
 In between these two types of flow, there exists a transition region wherein the oscillations in
the flow were unstable and any disturbance would quickly disappear.
 The velocity at which the flow changes from laminar to turbulent is known as the critical
velocity.

 Reynolds further found that the critical velocity for the transition from laminar flow to turbulent
flow depends on the diameter of the pipe, the average velocity of the flowing fluid, the density and
viscosity of the fluid.
 He grouped these four variables into a dimensionless group, Du/μ.
 This dimensionless group is known as the Reynolds number and found that the transition from
laminar to turbulent flow occurred at a definite value of this group.
 The Reynolds number is a basic tool to predict the flow pattern in a conduit and is of a vital
importance in the study of fluid flow.
 When the value of the Reynolds number is less than 2100, the flow is always laminar and when
the value of the Reynolds numbers is above 4000, the flow is always turbulent.
 For Reynolds numbers between 2100 and 4000, a transition region exists and in this region the
flow is changing rapidly from laminar to turbulent. The Reynolds number is denoted by the
symbol NRe.

= (N.s)/m2 = Pa.s
 The Reynolds number is a dimensionless group and its magnitude is independent of the units used,
provided that the consistent units are used.
For flow in a pipe, the inertia force is proportional to u2
and the viscous force is proportional to
μ.u/D.

Variation of pressure with height – hydrostatic equilibrium
 The forces that exist within a fluid at any point may arise from various sources.
 These include gravity, or the ‘‘weight’’ of the fluid, an external driving force such as
a pump or compressor, and the internal resistance to relative motion between fluid
elements or inertial effects resulting from variation in local velocity and the mass of
the fluid (e.g., the transport or rate of change of momentum).

Consider the vertical column of a single static fluid.
In this column of the static fluid, the pressure at any point
is the same in all directions.
The pressure is also constant at any horizontal plane
parallel to the earth's surface, but it varies with the height
of the column (it changes along the height of the column).
Let the cross-sectional area of the column be A m2
and the
density of the fluid be ρ kg/m3
. Let 'P', N/m2
be the
pressure at a height 'h' (meter) from the base of the
column.
At a height h + dh from the base of the common (another
horizontal plane), let the pressure be P + dP
, N/m2
.
The forces acting on a small element of the fluid of a
thickness dh between these two planes are :
HYDROSTATIC EQUILIBRIUM

This is the desired basic equation that can be used for obtaining the pressure at any height.
1
2
3
4

 Incompressible Fluids : For incompressible fluids, density is independent of
pressure. Integrating Equation (1), we get
dP + dh.ρ.g = 0-------------------------1
From the above Equation, it is clear that the pressure is maximum at the base of the column or
container of the fluid and it decreases as we move up the column.
If the pressure at the base of the column is P1 where h = 0 and the pressure at any height h
above the base is P2 such that P1 > P2 , then
3
2
4

 Integrating, we get
(P1 – P2 ) = h . ρ . g 5
where P1 and P2 are expressed in N/m2
, ρ in kg/m3
, h in m, 'g' in m/s2
in SI. With
the help of Equation 5, the pressure difference in a fluid between any two points can
be obtained by measuring the height of the vertical column of the fluid.
Compressible Fluids :
For compressible fluids, density varies with pressure. For an ideal gas, the density is
given by the relation
6
Where, P = absolute pressure M = molecular weight of gas R = universal gas constant T =
absolute temperature.

 Putting the value of 'ρ' from Equation (6) into Equation (1),
dP + g (PM/RT) dh = 0 7
Rearranging Equation (7)
8
Integrating
9
Integrating the above equation between two heights h1 and h2 where the pressures acting
are P1 and P2 , we get
10
11
Equation (11) is known as the barometric equation and it gives us the idea of pressure distribution within
an ideal gas for isothermal conditions.

Devices of measurement of pressure

 U-tube manometer is the simplest form of manometer. It consists
of a small diameter U-shaped tube of glass.
 The tube is clamped on a wooden board. Between the two arms or
legs of the manometer, a scale is fixed on the same board.
 The Utube is partially filled with a manometric fluid which is
heavier than the process fluid.
 The two limbs of the manometer are connected by a tubing to the
taps between which the pressure drop is to be measured.
 Air vent valves are provided at the end of each arm for the
removal of trapped air in the arm.
 The manometric fluid is immiscible with the process fluid. The
common manometric fluid is mercury.

 U-tube manometer is filled with a given manometric fluid (fluid M) upto a certain height.
 The remaining portion of the U-tube is filled with the process fluid/flowing fluid of density
ρ including the tubings.
 One limb of the manometer is connected to the upstream tap in a pipeline and the other limb
is connected to the downstream tap in the pipeline between which the pressure difference P1
– P2 is required to be measured.
 Air, if any, is there in the line connecting taps and manometer is removed.
 At steady state, for a given flow rate, the reading of the manometer, i.e., the difference in
the level of the manometric fluid in the two arms is measured and it gives the value of
pressure difference in terms of manometric fluid across the taps (stations). It may then be
converted in terms of m of flowing fluid.

 Consider a U-tube manometer as shown in Fig. connected in a pipeline.
 Let pressure P1 be exerted in one limb of the manometer and pressure P2 be exerted in the
another limb of the manometer.
 If P1 is greater than P2 , the interface between the two liquids in the limb 1 will be depressed
by a distance 'h' (say) below that in the limb 2.
 To arrive at a relationship between the pressure difference (P1 – P2 ) and the difference in the
level in the two limbs of the manometer in terms of manometric fluid (h), pressures at points
1, 2, 3, 4 and 5 are considered.

 where ∆P is the pressure difference and 'h' is the difference in levels in the two arms
of the manometer in terms of manometric fluid.
 If the flowing fluid is a gas, density ρ of the gas will normally be small compared
with the density of the manometric fluid, ρM and thus Equation (2) reduces to
3

Inclined Manometer
 Inclined manometers are used for measuring small pressure differences. This
type of manometer is shown in Fig.
 One arm of the manometer is inclined at an angle of 5 to 10o with the
horizontal so as to obtain a larger reading. (e.g., movement of 7 to 10 mm is
obtained for a pressure change corresponding to 1 mm head of liquid.)

 In the vertical leg of this manometer an enlargement is provided so that the movement of the
meniscus in this enlargement is negligible within the operating range of the manometer.
 If the reading R(in m) is taken as shown, i.e., distance travelled by the meniscus of the
manometric fluid along the tube, then
h = R sin α (1)
where α = angle of inclination
(P1 – P2 ) = R sin α (ρM – ρ) g (2)

Differential Manometer / Two Liquid Manometer /
Multiplying Gauge
Differential manometer is used for the measurement of very small
pressure differences or for the measurement of pressure differences
with a very high precision.
It may often be used for gases. It consists of a U-tube made of
glass. The ends of the tube are connected to two enlarged
transparent chambers / reservoirs.
The reservoirs at the ends of each arm are of a large cross-section
than that of the tube.
The manometer contains two manometric liquids of different
densities and these are immiscible with each other and with the fluid
for which the pressure difference is to be measured. This type of
manometer is shown in Fig.

 The densities of the manometric fluids are nearly equal to have a high sensitivity of the manometer.
Liquids which give sharp interfaces are commonly used, e.g., paraffin oil and industrial alcohol, etc.
Let the flowing fluid be 'A' of density ρA and manometric fluids be
B and C of densities ρB and ρC (ρC > ρB), respectively [ρA < ρB
and ρC].
The pressure difference between two points (1 and 7) can be
obtained by writing down pressures at points 1, 2, 3, 4, 5, 6, and
7 and is given by
If the level of liquid in two reservoirs is approximately same, then h' ≈
0 and above Equation reduces to
where h is the difference in level in the two arms/limbs of the manometer. When the densities ρB
and ρC are nearly equal [(ρC – ρB) small], then very large values of h can be obtained for small
pressure differences.

 Alternately, the pressure at the level a – a in Fig. must be the same in each of
the limbs and therefore,

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