The document discusses the flow of fluids. It defines a fluid as a substance that can flow and continuously deforms under applied shear stress or force. It describes three main properties of fluids: viscosity, surface tension, and density. It also discusses fluid statics, which involves fluids at rest, and fluid dynamics, which involves fluids in motion. Some key concepts covered include laminar and turbulent flow, the Reynolds number, and Bernoulli's theorem regarding the conservation of energy in fluid systems. Common fluid flow applications and devices like manometers and orifice meters are also summarized.

1. FLOW OF FLUID
BY
PROF. TAUFIK MULLA
ASSISTANT PROFESSOR
DEPARTMENT OF PHARMACEUTICS
SPBC COLLEGE OF PHARMACY

2. Matter – 3 types
• Solid
• Liquid
• Gas
If we apply pressure on solid material – it move from one place to another
place but do not change its shape.
But if we apply pressure on liquid / gas – it move from one place to another
place and shape of material can be changed.
Pressure means – shear stress

3. WHAT IS FLUID ????
 a substance that has no fixed shape like a gas or a liquid.
 a fluid is a substance that continually deforms (change) under an applied shear stress
(force tending to cause change shape e.g. chewing food between teeth) , or external
force.
 Fluids are a phase of matter and include liquids, gases and plasmas
 Properties of Fluid -
1. Viscosity
2. Surface tension
3. Density

4. 1. VISCOSITY
Viscosity is a measure of a fluid’s resistance to flow.
It describes the internal friction of a moving fluid.
A fluid with large viscosity resists motion because its
molecular makeup gives it a lot of internal friction.
A fluid with low viscosity flows easily because its
molecular makeup results in very little friction when it is in
motion.

5. 2. SURFACE TENSION
• Surface tension is a contractive tendency of the surface of a fluid that
allows it to resist an external force.“
• Surface tension is the tendency of the surface of a liquid to behave like
a stretched elastic membrane.
• Fluid tends to attend the minimum surface area as possible. Why? The
reason behind this is that while a molecule inside the fluid bulk is
pulled in each and every direction by the adjacent molecules But at the
surface of the fluid , the case is different. the adhesive forces causes
downward pull on the molecule due to coherent. So the molecule on
the surface tends to move down.

6. 3. DENSITY
• Density depends on the mass of an individual molecule and the number of such
molecules that occupy a unit of volume.
• For liquids, density depends primarily on the particular liquid and, to a much smaller
extent, on its temperature.
• For gas, density depends on the molecular weight, absolute pressure, and absolute
temperature.
• The density of a fluid is defined as its mass per unit volume and indicates its resistance
to an accelerating force.

7. FLOW OF FLUID
• Fluid flow defined as flow of substance that do not permanently resist distortion (changes of
state of natural).
• Fluid is a substance which continuously flow under applied shear stress. (pressure) E.g. liquid ,
gases
• Flow fluid we can observe by –
Handling of liquid – transportation of solvent, solution , suspension is simple, cheap and
problematic as compared to solid material in industry

8. • Fluid can be study by fluid statics and fluid dynamics.
Fluid statics – study behavior of liquid when it in resting
Fluid dynamics – study behavior of liquid when its in motion
• Flow of fluid involved in different area of pharmaceutical industry like :-
Passing of reactant (liquid / gas) in reactant system
Transferring of broth/ culture media in fermenter
Packaging of liquid dosage form in suitable container
Transferring of sterile water for preparation of parenteral.
Mixing of solid and liquid for suspension.

9. FLUID STATICS
• Fluid static's deals with the fluids at rest in equilibrium and Behavior of
liquid at rest.
• Nature of pressure it exerts and the variation of pressure at different
layers.
Pressure differences between layers of liquids.
• Consider a column of liquid with two openings Which are provided at
the wall of the vessel at different height. The rate of flow through these
openings are different due to the pressure exerted at the different
heights are different.
• Consider a stationary column the pressure P is acting on the surface of
the fluid, column is maintained at constant pressure by applying
pressure.

10. • Force acting on the liquid At point 1 = Force on the surface + Force excreted by the liquid
Above point 1.
• Application of fluid static –
• Used in manometer
• Pressure difference is measured in term of difference in height of column

11. MANOMETER
• Device used for measurement of
pressure difference.
• 3 types of manometer
• Simple
• Differential
• Inclined
manometer also classified as :
1. Simple manometer
• Piezometer
• U-tube manometer
• single column manometer
 Vertical single column
 Inclined single column
2. Differential manometer
• U – tube differential manometer
• Inverted U – tube differential manometer

12. SIMPLE MANOMETER • Most commonly used manometer in various industry
• It’s a U shape glass tube filled with liquid (A) of density ρA
kilogram / meter cube.
• Above liquid A, arms are filled with liquid B of density ρB kilogram
/ meter cube.
• Liquid A and B are immiscible.
• If we apply two different pressure P1 and P2 on two arms.
• Meniscus of liquid A will be higher in one arm than other.
• Pressure at point 1 is P1 pascal and pressure at point 5 is P2 pascal.
• By the principle of fluid statics, pressure at point 2 will be as follow:
• Pressure at point 2 = P1 +(m+R) ρBg ------ 1
(m+R) = distance from point 3 to 4 and 4 to 5.
Arms

13. • Point 2 and 3 are at same level so, the pressure at point 3 will be as follows :
• Pressure at point 3 = P 1 + (m+R) ρBg - ---------- 2
• Pressure at point 4 (from right side) = P 2 + gm ρB ---------- 3
• Pressure at point 4 (from left side) = P 1 + ρB (m+R) – ρARg ------------ 4
Equation 3 to 4 represent the pressure at point 4 only.
P 1 + ρB (m+R) – ρARg = P 2 + gm ρB
P 1 – P 2 = gm ρB - ρB (m+R) + ρARg ‘
∆P = mρBg – mρBg – RρBg + RpAg
∆P = R(pA – pB)g

14. Conclusion from equation –
• Easy to measure R value (meter)
• The value of ∆P pascal is independent of value of m and also the dimension of the U
tube.
Application –
• Measuring the consumption of gases in chemical reaction.
• Used in conjunction with flow meter for the measurement of flow of fluid.
• Venturi meter and orifice meter used for measurement of pressure head using
manometer.

15. 2. DIFFERENTIAL MANOMETER
• This manometer used to find difference of two pressure
at two different point / pipe.
• Rarely occasionally this manometer is used.
• Very sensitive and mainly used to measure small
pressure difference.
• Also known as two fluid U-tube manometer.
• Contain two immiscible liquid A and B having same
density.
• At both limbs it having a chamber.
• meniscus of liquid in chamber does not change with
change in R value.
LIMBS

16. • By using principle of Simple manometer equation will be like :
∆P = P 1 – P 2 = R (Pc – PA)g
Equation indicate small difference in (Pc – PA), larger reading of R on manometer for given
∆P.
• Micromanometer based on liquid column principle.
• It measure reading with high precision and accurately and its very sensitive.
• Doesn’t require any calibration as it’s a free from error.

17. 3. INCLINED MANOMETER
• Many applications require accurate measurement
of low pressure such as drafts and very low
differentials, primarily in air and gas installations.
• In these applications the manometer is arranged
with the indicating tube inclined.
• This enables the measurement of small pressure
changes with increased accuracy.
P1 –P2 = g R (ρ A - ρ B) sin α

18. FLUID DYNAMICS
• Deals with the study of fluid in motion.
• Study of flow property of fluid is important for those who work in pharmaceutical ,
chemical industry.
• Mfg. of syrup , gel , ointment , cream and paste or liquid preparation.
• This fluid change their behavior when exposed to different stress condition like :
 Mfg. of dosage form – mixing , flowing through pipes and filled in container
 Handling of drug for administration – pouring of liquid , extrusion of ointment
That’s why flow property is a important quality control parameter for mfg. of dosage
form.
The flow of fluid through a pipe can be viscous and it can be determined by Reynolds
number.
Reynolds number have no unit.
mixing
Flow through pipe
Filled in container

19. TYPES OF FLOW
1. LAMINAR FLOW
• Fluid particle move in a straight layer.
• No exchange of fluid particle from one layer to
another.
• Also called as streamline flow.
• It occur when small pipes and low flow rate
involved.
• Shear stress depend upon viscosity of fluid.
• Avg. velocity = 0.5 Vmax

20. TYPES OF FLOW
2. TURBULENT FLOW
• When velocity increase, fluid particles move in
random manner.
• This type of flow called as turbulent flow.
• In this complete mixing of fluid particles are
observed.
• This flow happen generally at high flow rate with
larger pipe.
• Avg. velocity = 0.8 Vmax

21. TYPES OF FLOW
3. TRANSITIONAL FLOW
• It’s a mixture of laminar and turbulent flow.
• Turbulence observe at the center of the pipe.
• Laminar flow observe at near the edge.

22. REYNOLD’S NUMBER
Its a dimensionless number.
Turbulent flow and laminar flow is determined
by Reynold’s number.
It’s a ratio of inertial force to viscous force.
Re = inertial force / viscous force
Inertial force = mass X acceleration of liquid
flowing
Viscous force = shear stress X area
Formula for Reynold’s number as follows
:
Re = Dup / n
Where,
D = diameter of pipe (m)
u = velocity of flow (m/s)
p = density of fluid (kg/m3)
n = viscosity of fluid

23. REYNOLDS EXPERIMENT
• Glass tube connect with reservoir of
water.
• Rate of water flow through tube
increase or decrease by valve.
• Reservoir of colored solution connected
at one end of glass tube with nozzle.
• Colored solution entered in glass tube
as fine stream.
• By performing this experiment we can
conclude below details :
GLASS TUBE

24. a. When velocity of water is low, water will move in line parallel to tube. i.e. laminar flow
b. If velocity of water is high, it move in wave form. i.e. transitional flow.
c. If velocity of water is more, it do not move in straight line. i.e. turbulent flow.
The flow is –
• Laminar flow = Re < 2000
• Transitional flow = 2000 < Re < 4000
• Turbulent flow = Re > 4000

25. • Application –
Reynold’s number is used
• To predict nature of flow
• To study flow of incompressible fluid in closed pipe.
• Heat transfer in liquid also depend on flow.
• To study sedimentation rate of suspension.

26. MATHEMATICAL PROBLEM
When liquid is flow through a pipe having diameter 200mm. Tube with mean velocity of oil
2m/sec. if density of liquid is 910 kg/m3. and viscosity is 0.35 N.S/m2. then what will be the
type of the flow.
Re = Dup / n
D = 200 mm = 0.2 . U = 2 . P = 910 / 0.35 = 1040.

27. BERNOULLI’S THEOREM / EQUATION
• Principle of conservation of energy is applied to the flow of fluid , resulting equation
called as Bernoulli’s equation.
• This theorem state that total energy (pressure energy, kinetic energy and potential
energy) per unit mass in steady state are constant.
• It based on conversation of energy when applied to flow of fluid.
• It said that, in steady state – ideal flow of incompressible fluid – total energy per unit
mass – also include pressure energy , kinetic energy and datum energy at any point of
fluid is CONSTANT.

28. • At point A , 1kg of liquid is assumed to enter in pipe.
• At that point liquid experience pressure energy , kinetic
energy and datum energy (potential).
• It represented as –
pressure energy = PA / gpA
PA = pressure in pascal at point A
g = acceleration due to gravity m/s2
pA = density of liquid kg/m3

29. • Potential energy = it possessed by body by behavior of its configuration or position. Point A is placed at
height XA meter above datum plane. potential energy = XA
• Kinetic energy = it possessed by body by behavior of its motion. consider uA as velocity of liquid m/s at
point A. kinetic energy = uA2 / 2g
At point A total energy as follows :
total energy = pressure energy + potential energy + kinetic energy
As per Bernoulli’s theorem , total energy at point A is constant. The equation will be :
= CONSTANT

30. • Once the system reaches to steady state, flow become steady at each point in pipe. And
the 1kg of liquid leaves at point B.
• Energy content of 1 kg liquid at point B written as :
PB = pressure at point B
pB = density at point B kg/m3
XB = height of point B from datum
uB = velocity at point B m/s

31. • If there is no loss or gain of energy then principle of energy conversation applied at
point A & B.
Input = Output
Theoretically all types of energy involved in fluid flow should be accountable. During
transportation of fluid , pump has added some amount of energy is W joule and Some
energy converted to heat due to frictional forces so energy loss is F joule.
The final equation of energy conservation written as

32. • This equation called as Bernoulli’s equation.
• APPLICATION
• Measuring flow rate of fluid using head meter like orifice meter , venture meter.
• Applied in working of centrifugal pump

33. ENERGY LOSS
• According to the law of conversation of energy ,energy balance have to be properly calculated
• fluids experiences energy losses in several ways while flowing through pipes, they are
Frictional losses
Losses in the fitting
Enlargement losses
Contraction losses

34. FRICTIONAL LOSS
• During flow of fluids frictional forces causes a loss in pressure . Type of fluid flow also influences
the losses.
• In general pressure drop will be
• Directly proportional to VELOCITY of fluid (u)
• Directly proportional to Density of fluid(ρ)
• Directly proportional to Length of the pipe (L)
• inversely proportional to diameter of the pipe (D)
• These relationships are proposed in Fanning equation for calculating friction losses
• Fanning equation Δp = 2fu2Lρ / D
F = frictional factor
• For viscous flow pressure drop Hagen –Poiseullie equation = 32 Luη / D2 (n = viscosity of liquid)

35. LOSSES IN FITTING
• Fanning equation is applicable for the losses in straight pipe When fitting are introduced into a
straight pipe, They cause disturbance in the flow, Which result in the additional loss of energy
• losses in fitting may be due to
• Change in direction
• Change in the type of fittings
Tee fitting
Equivalent length = 90 Globe valve equivalent length = 300
Equivalent length of fitting = Equivalent length x internal
diameter
For globe valve = 300 x 50
= 15 meter
That means globe valve is equal to 15 meters straight line,
so this
length is substituted in fanning equation

36. ENLARGMENT LOSS
• If the cross section of the pipe enlarges gradually, the fluid adapts itself to the changed section
with out any disturbance So no loss of energy.
• If the cross section of the pipe changes suddenly then loss in energy is observed due to eddies
These are greater at this point than straight line pipe
Than u2< u1
For sudden enlargement = Δ H = (u1 – u2 )2 / 2g
Δ H = loss of head due to sudden enlargement

37. CONTRACTION LOSS
• If the cross section of the pipe is reduced suddenly the fluid flow is disturbed, the diameter of the
fluid stream is less than the initial value of diameter this point of minimum cross section is known
as vena contracta.
• the velocity of fluid at smaller cross section will be greater than at larger cross section, u2> u1

38. ORIFICE METER
Principle:
• Orifice meter is a thin plate containing a narrow and sharp aperture
• When a fluid stream is allowed to pass through a narrow constriction the velocity of the fluid increase
compared to up stream
• This results in decrease in pressure drop and the difference in the pressure may be read from a
manometer
• The velocity of the fluid at thin constriction may be written as U0 =C0 √ 2g ΔH
• ΔH = difference in height, can be measured by manometer
• C0 = constant
• U0 = velocity of fluid at the point of orifice meter

39. Construction;
• It is consider to be a thin plate containing a sharp aperture
through which fluid flows
• Normally it is placed between long straight pipes
• For present discussion plate is introduced into pipe and
manometer is connected at points A and B
Working:
• Orifice meter is referred as the variable head meter, ie it
measure the variation in the pressure across a fixed
construction placed in the path of flow

40. • When fluid is allowed to pass through the orifice the velocity of the fluid at point B increase, as a result at point
A pressure will be increased
 Difference in the pressure is measured by manometer
 Bernoulli's equation is applied to point A and point B for experimental conditions
√μ02 –μA2 =C0 √2g ΔH
• μ0 = velocity of fluid at orifice
• μA = velocity of fluid at point A
• C0 = constant
• If the diameter of the orifice is 1/5 or less of the pipe diameter then μA is neglected so,
μ0 = C0 √2g ΔH
Applications
• Velocity at either of the point A and B can be measured
• Volume of liquid flowing per hour can be determined

41. VENTURI METER
Principle:
• Venturi meter consist of two tapered sections in the pipe line with a gradual constriction at its
centre.
• when fluid stream is allowed to pass through the narrow throat the velocity of the fluid increases at
the venturi compared to velocity of the upstream.
• This results in decrease in the pressure head.
• This resulting decrease in the pressure head is measured directly from the manometer.

44. Disadvantages
• Expensive
• Need technical expert
• Not flexible
• Occupies more space
Advantages
• Power loss is less
• Head loss is negligible
Applications:
• It is commonly used for liquids, specially for water.
• It can also be used for the measurement of gases.