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1 DRAG COEFFICIENTS

Objectives of the experiment
a) To investigate free settling flow of spherical particles in Newtonian liquids
...


Equipment
a) Three graduated perspex columns
...
c) Hydrometers, stop watch, rulers, thermometers, balance
...
Some of the physical properties will be
supplied
...
1 Introduction

The modeling of fluid flows past a body is a general problem in science and
engineering
...
The study of the behavior of spherical particles in fluid flow has become a
great interest in research fields such as chemical engineering, mechanical
engineering and environmental engineering
...
In relation to laminar flow, is
possible to derive theoretical relationships for predicting important parameters in
the future
...

𝜌𝑢𝐷
𝑅𝑒 =

𝜇

When the terminal settling velocity of a particle increases, the Reynolds number
increases and the drag coefficient decreases
...
Applying a force balance and taking the
downward direction as positive :-

𝜌!
𝑑𝑢
𝑚
= 𝑚𝑔 −
𝑚𝑔 − 𝐹!
𝑑𝑡
𝜌!






The particle will accelerate until the resistance force exactly balances the

gravitational force
...
Drag force, FD is expressed as :-








!
𝜌! 𝑢
𝐹! = 𝐶! 𝐴

2

In laminar flow or so-called Stokes flow for spherical particles with lower Reynolds
number (Re < 0
...
This is given by :-










24
𝐶! =
𝑅𝑒

The purpose of this experiment is to investigate the free settling flow of spherical
particles in Newtonian fluids, to measure the terminal settling velocities and develop
the drag-factor diagram for spherical particles
...


From this experiment, we could see that the results are relatively close to the
published data, except for some deviation which is due to the lack of data and
human errors
...
2 Experimental Method

The experiment will be conducted by allowing glass spheres to fall freely in liquids
contained in graduated cylindrical columns
...
The Perspex columns are calibrated at ‘0cm’, ‘50cm’ and
‘100cm’
...
A hydrometer is placed into each cylindrical column for the measurement
of density of the respective liquids
...
The
temperatures of each liquid were measure using a thermometer
...
The 10mm diameter glass spheres are made of soda-glass and have
a density of 2
...
The densities of the remaining 3mm, 4mm and 6mm glass
spheres from lead-glass were determined using density bottle and scale balance
...
The
diameters of each glass spheres were measured using a vernier caliper and averaged
to obtain their respective average diameters
...
The drop
test were repeated for four times for each glass sphere diameter (3mm, 4mm, 5mm
and 10mm) and the time taken were recorded
...
3 Discussion

For our experiment, Cd values can be calculated using the 𝐶! =

!!"(!! !!! )
!!! !!



derived from force Balance equation and Drag force expression
...
As Re increases, Cd decreases
...


Region 1
At very low Re, the experimental curve yields almost a straight line, which is very
similar to the published curve
...
3
...
Referring to Figure 4, we could see
that the fluid flow pattern is almost symmetric, smooth and adheres to the body
...
In this region, Stokes Law CD=24/RE for
RE<0
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Region 2
In this region of 0
...
Refering to Figure
5, small eddies start to form at the rear
...
There is a change of slope of

the curve accompanied by unsteady nature of the wake and flow separation of the
body
...
3 ...
Now, the separation point is at the front half of the sphere
...
See
Figure 6
...
44 for 103 ...
At re>2x105, the
separation point is at the rear with a much smaller wake compared to the Newton’s
Law Region
...
3
...

Comparing the experimental and theoretical values, there is a significant %
difference shown, which suggests that there are errors and assumptions involved
...
4 Error Analysis

For error analysis, the errors in this experiment include random error such as
parallax error, where the eye level of the observer is not in line with the marked
calibration
...
The short falling time of spheres may introduce a
high % error
...
For the water column, the sphere
was travelling in a zig zag motion, causing inaccuracy in the time taken and distance
travelled
...
Besides, it is assumed that there is no contamination of fluid where
the fluid properties remain constant
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1
...
The columns used should be of longer
height, essentially for the water column, to ensure that the sphere reaches its
terminal velocity at the 0cm mark
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The % error uncertainty can be improved by using more sensitive apparatus
...
Using larger

parameter value can also reduce the % error
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v = u +at is used to calculate time taken for sphere to reach 99% terminal
settling velocity
...
In our experiment, we assume that the particle reaches terminal
velocity, instead we can only say that the sphere velocity is very close to terminal
velocity
...






































2 FLUID FRICTION

Objectives of the experiment
a) To calibrate and investigate the operating characteristics of an orifice plate
...


Equipment
The following equipment is available for this experiment:
a) Pipes (7
...
8 mm smooth bore; 17
...

b) Orifice plate (20 mm diameter) and venturi meter (14 mm diameter)
...

c) Valves (globe, gate and ball)
...

e) Stop watch
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2
...
Fluid flows are very closely related to our
everyday life such as water flowing in household pipes and the transport of oil from
seabed to chemical plants for processing in chemical engineering aproach
...
Fluid only flows when it has sufficient energy to
overcome the resistances in the pipe
...
In addition to friction losses in
straight pipes, other losses also occur due to the fittings, bends or valves
...

Thus, some energy ends up being dissipated as heat when turbulence form in the
pipe
...
In a long pipe run, these losses can be neglected, but can
be a major loss that has to be considered for short run
...
In order to achieve this, the flow rate of fluid in pipes has to
be known, and flow meters are very useful in determining the desired optimum flow
rate
...
Orifice
plate meter is characterised by having fixed geometries and head measurement
varies with flow
...


𝑝 1 !
+ 𝑢 + 𝑧𝑔 = 𝑐𝑜𝑛𝑠𝑡𝑎 𝑡 𝑎𝑙𝑜𝑛𝑔 𝑠𝑡𝑟𝑒𝑎𝑚𝑙𝑖𝑛𝑒
𝜌 2

Rearranging this equation, we will get

!/!

2𝜌(−∆𝜌)
𝐺 = 𝐴1
𝐴
1 − ! 𝐴2




However, this equation actually over predicts the flow rate, so a factor known as
discharge coefficient, Cd is introduced into EQ2, which takes into account that no
fluids are frictionless
...
The value of Cd is 0
...
7, which
takes into account the frictional losses and the presence of vena contracta
...


In this experiment, there will be 3 equations used for determination of Fanning
Frictional Factor which is the Blausius Equation, Moody Equation and Nikuradse
Equation
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2
...
Q=V/t
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8mm smooth bore, 17
...
5mm smooth bore)
...
It has to be ensured that
air bubbles are removed in the pipe and flow meter by opening the air-releasing
valves on both sides of the apparatus
...
The air-releasing valve is then closed to
isolate the system from the environment
...
To calibrate the manometer, the outlet valve
is closed and the pressure reading at the manometer is made sure to be at 0kPa
...
For the 1st
run, the inlet valve is turned to its maximum for a maximum flow rate
...
The
measurement of time taken, t is repeated 2 more times to reduce human error
...


For the measurement of pressure, starting with the orifice plate meter, the 4 other
valves are closed
...
The 2 small valves are opened
to remove air bubbles and closed after air bubbles are removed
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For 17
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8mm smooth bore pipe is opened
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The
procedure for pressure measurements is repeated for 17
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5mm smooth bore (1m & 2m apart)
...
Similar
procedure as 1st run is applied to determine the water flow rate
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8mm
smooth bore, 17
...
5mm smooth bore)
...
3 Discussion
For orifice plate meter, the equation 𝐺 = 𝐶𝑑𝐴1

!!(!∆!)
!
!! ! !!

!/!



applies
...


The advantage of Orifice Plate meter is it is inexpensive
...
The main disadvantage of Orifice Plate meter is
there will be high permanent pressure loss, thus it is inefficient
...
Orifice plate Meter
also has to be placed at least 50 pipe diameters from any pipe fittings
...
Therefore saving the pump energy cost
...
However, venturi meter is highly expensive, bulky
and heavier to handle
...


Alternative type of meter that could have been used include nozzle meter
...
For better performance, a Dall meter can be used
since the pressure recovery is relatively high, ranging from 92%-98%
...


The discharge coefficient, Cd is calculated by using the gradient of the curve
...
The Cd value depends on the flowrate, pressure drop
and the area at which the pressure drop is measured
...
07 and does not agree with the
literature value of 0
...
7
...
The large deviation may be due to human error when taking
measurement, wrong calibration of equipment (water manometer) or defective
orifice plate meter
...

PD=Pmax+Pmin/2
...
From experimental results, it is found that the Re for the 7
...
The Nikarudse eq should be applied since it is
valid for 3000 ...
It is noted that
the Cf calculated for this case might be inaccurate
...
01 the Moody Eq is used to calculate Cf
...
043
...


When experimental values compared on Moody Chart, the experimental Re
values all lies after 2300, we can conclude that all the flow carried out in lab are
turbulent
...
The small
deviation might be due to human error and also inaccurate lab equipment
...
5mm smooth pipe, the % difference of Cf in R1 & R2 is about triple/quadruple of
that in R3 & R4
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For smooth pipe, the Cf decreases as diameter increases
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The
Cf for the 7
...


The Cf is much higher in rough pipe compared to smooth pipe, suggesting pipe
roughness gives huge impact on Cf
...
The Cf values tends remains constant as relative roughness
increases
...


It is also observed that for all pipes, the Cf decreases when flowrate increases
...
4 Error analysis

From results, we could see that the percentage error for Q, u, Cd, Cf are relatively
small
...
The % errors for velocity for all pipes are
the same and similar to Q since Q=uA
...
This means at lower
flowrate, there Is more error
...
8mm smooth
...
There is also human reaction time error where there is a
delay between the moment the observer sees the water level reaching the marked
calibration and starting/stopping of the stopwatch
...
Systematic error such as calibration error is
involved when using water monometer
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Air bubbles that are not thoroughly
removed create resistance to water flow, causing higher pressure loss
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5 Improvements

For improvements, a light sensor-timing device should be used where the water
could be dyed and sensor is started/stopped within 2 points
...
Parallax error can be reduced by making sure that the eye level
of the observer is in line with the calibration
...

b) To design a large scale agitated system (details given in section 6) using design
data obtained experimentally in small scale studies with geometrically similar
systems
...
29 m I
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bench-scale glass tanks containing fluids of different physical
properties
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c) A 1
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d) A 0-6Nm shaft-mounted torque/speed transducer for measuring impeller speed
and the reaction torque on the motor
...

e) Two impellers with diameters 0
...
1m
...


Materials and Data
Glycerol/water mixtures are the main liquids for the experiments
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_____________________________________________________________________

3
...
It simplifies problems greatly as the parameters involved
dramatically decrease
...
In this study, our aim was to create a large mixing vessel
using this technique on experimental model data
...
Geometric
similarity was ensured by maintaining a constant ratio in the length dimensions
between model and prototype
...
For example, as the mixer vessel had
baffles there was no vortex formation and thus the Froude number was neglected
...
It is a function of 5 parameters N, D, ρ, μ and
g where N is the rate of rotation of the impeller, D is impeller diameter, ρ is fluid
density and μ is fluid viscosity
...
This is clearly a time consuming and
costly exercise
...

The objectives of this experiment include inquiring how the process of mixing
affects the power needed for the mixing liquids
...

3
...
From the Figure 9 and Figure 6, the
curves do not give good agreement in the trend of Po number
...
However, from Figure 6, at the high
experimental Re range (~4000with increasing Re
...
Experimental
errors as discussed below might also cause the deviation of results in Figure 9
compared to published results
...
Allowance
is made for motor loading between 50-100%, which will give an approximate motor
efficiency of 80%
...
19W) is done
based on the highest Mixing Power (337
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We consider overdesigning the
motor in the case where largest power is needed for mixing operation to be feasible
(worst case scenario is when Re = 5407
...
However, it is noted that overdesigning
means there is an increase in cost required
...
We firstly used geometric
similarity as our basis
...

!" !"#$%
!"#$%
!"#$%
!"#$%

!"
!"

!"#$% ,
!"#$%

!"
!

!"#$$
!"#$%

=

!"
!"

!"#$%

!"#$% ,
!"#$%

!"

!"#$%

!" !"#$$
!"#$%

=

The geometric and dynamic similarities thus

ensure kinematic similarity, where the geometrically similar systems have all the
velocities of fluid at corresponding positions of a constant ratio
...
Sometimes, it is difficult to keep both dynamic and kinematic
similarity for scale up
...
It is not always
possible to have both systems to be geometrically similar, however we know that it
is the easiest to attain
...


We will compare the Power curve, Po for stirred tank with the Fanning
Friction Factor, Cf curve for pipe
...
At the laminar region, there is a linear relationship between Cf and Re at larger
range, 100 < Re < 4000, compared to Po and Re curve which is only valid at small
range, 1 < Re < 8
...
At laminar region, the
gradient of the Cf graph is steeper compared to Po curve at low Reynolds number
...
Whereas for Po curve in stirred tank, the Po
number can be read from the graph for all Reynolds values without difficulties
...

At high Re numbers, both the Cf and Po approached constant values, from Curve 2,
at Re > 2000, Po = 4
...

A non-Newtonian fluid is a fluid whose viscosity is dependent on the shear
rate, resulting in a gradient of viscosity in the vessel
...
For shear thinning fluid such as ketchup and paint, the
viscosity decreases as the shear rate increases
...
During mixing, the shear stress increases, the fluid viscosity
decreases, thus allow smoother flows and lower power consumption
...
The opposite happens
...
As mixing
continues, the fluid is harder to flow
...
In particular, the power consumption of
Newtonian fluid will be smaller compared to non-Newtonian fluid
...
Turbines such as the six-bladed disc turbine are
used for gas- liquid dispersion in small vessels, liquid-liquid dispersion and for fast

competitive chemical reactions
...
Anchors and
helical ribbons are used for non-Newtonian fluid
...
Similarly, Z-blade and Banbury mixers are used for high
viscosity fluid such as dough, rubber or paste
...
It provides cost effective solution for small batch
mixing
...
The extrudate is
delivered at high pressure for shaping purposes
...
This mixer is suitable for usage in the laminar or turbulent flow

regime and liquid of wide range of viscosities, with or without solids
...

Besides, a Jet mixer is often used for solid suspensions, sludge mixing and
neutralization, where pressurized liquid energy is used to entrain, mix and pump a
secondary fluid
...
3 Error Analysis
From experimental results, the percentage (%) uncertainty in Po number is
very high (up to 34%) at low speed
...
As the speed increases, there
is a trend where the % uncertainty of Po number decreases
...
There are
errors imposed when the speed and torque reading is taken
...
The speed and torque readings also fluctuate, which made it difficult to
take an exact reading; so several readings are recorded to reduce experimental
errors
...

The percentage (%) uncertainty in Reynolds number is low (< 4%)
...
As the impeller speed increases, the % uncertainty in Reynolds number
decreases
...
Firstly, it is noticed that there are impurities in the solutions
...
For 50% glycerol 50% water mixture, at Re >
4000 there are small uneven waves (vortex) on the interface as compared to the
100% glycerol solution, which has quite an even surface throughout the experiment
...

Furthermore, the impeller is not in a perfect vertical position and it is not
located directly at the center of the tank
...
These conditions are unfavourable and will affect the accuracy of the
results
...
We also
assumed that there is no reaction or no generation of heat in the liquid solution
(temperature remains constant)
...

3
...
This means using a transducer
with higher output pulse count for precise measurements at low rotational speed
...
025m compared to the width of 0
...
Without baffle, large vortex will be formed in low-viscosity fluid, where
the mixing only concentrates at the swirling center and not throughout the entire
tank
...
Using baffles provides
additional disturbance to the flow created by the impeller to improve the rate of
mixing and provide a more effective mixing
...
Alternatively,
baffles are not necessary if the impeller is angled and mounted off-center
...
The impeller should be
attached to a more sturdy and stable motor so that less work is lost as heat due to
vibration
...
So, optimization to this situation has to be
done by considering the best mixing results and lowest power requirement costs
...

Ideally, for viscosity of fluid < 25 000 cP, the impeller clearance from the bottom (HI)

of the tank should be at 1/3 of the height of fluid in tank (HL)
...
0791m instead of 0
...

The diameter of impeller also affects the accuracy of the Re and Po number
...
3-0
...

Therefore, the large impeller, of ratio = 0
...
25 which is not in the reasonable range
...

For tank design, the small-scale tank should be round-bottomed, instead of
flat-bottomed so that the sharp corners, which doesn’t allow any mixing can be
avoided
...

The system should be well insulated against the surroundings such as using a
closed tank, so that the solution is free from impurities, as impurities will interfere
the fluid flow
...
The temperature
of the liquid after mixing should be taken to account for any temperature changes,
which might also indicate heat losses/gained
...
DIFFUSIVITY OF ORGANIC SOLVENTS

Objectives of the experiment
The objective of this experiment is to determine and compare the diffusion
coefficients of organic vapours in air
...
Vernier microscope
...
1 Procedure

1
...

2
...
* Note : Inverted image is
seen from the vernier microscope
...
The vernier microscope is moved down, with cross hair
aligned with the bottom of meniscus
...
Height measurements are taken and stopwatch are
started simultaneously
...
Vernier microscope is moved left to the red labeled capillary tube
...

6
...

7
...

8
...









































4
...
This trend is true for all the 3 values obtained for each organic solvent
from the experiment, prediction by FSG method and published literature
...
Using the Stefan’s method for experimental value calculations,
the diffusion coefficient of Methanol, Ethanol and Acetone is 2
...
15
x 10-5 m2s-1 and 9
...


The rate of diffusion is afftected by several factors such as pressure,
temperature, composition, molecular shape, molecular size, solvent viscosity and
etc
...
However, it is noted that in practical chemical
engineering processes, these 2 parameters are usually never constant
...


!
From FSG correlation , D α !
...
The diffusivity
reduces, thus the diffusion coefficient, D is low
...
75
...
This results in higher mass transfer from organic solvent to
stagnant air film and eventually larger diffusion coefficient value
...


Methanol and ethanol are both alcohol group molecules having the hydroxyl
(-OH) group, which in turn allow them to form hydrogen bond with other molecules
...
Thus, Hydrogen bond are only
present in methanol and ethanol while Van der Waals and dipole-dipole forces of
attraction are present for all the 3 organic solvents
...
Thus, theoritically, it will be easier for acetone to
overcome its weaker intermolecular forces of attraction compared to methanol and
acetone
...
08 g mol-1 compared to ethanol of 46
...
04 g mol-1
...
The presence of large electron cloud
increases the Van der Waals force of attraction between molecules
...


Therefore, based on the values of diffusion obtained, the effect of molecular
weight outweighs the effect of the presence of hydrogen bond on diffusivity
...
This explains the higher diffusion coefficient value in the lighter
methanol than the heavier ethanol
...
This is
due to the presence of hydrogen bonds in ethanol which contributes to stronger
intermolecular forces of attraction compared to weak intermolecular force within
acetone molecule
...


There are deviations of experimental values from FSG rediction values and
literature values
...
We can never
achieve the ideal gas condition, which requires a system of very low pressure so that
the intermolecular forces of attraction is negligible and the volume of molecules are
negligible compared to the total volume occupied by gas
...
The values obtained would have
been different if ideal gas is not assumed
...
There might be some movement in the gas film (air) since the system
is not completely isolated from the surroundings
...


One of the key assumptions when FSG using the method is temperature and
pressure are constant
...


Literature value assumes ideal gas behaviour, non-polar molecule, binary gas
systems at low pressures
...
Clearly in the experiment, there is no
constant gas stream being passes above the tubes, which means there is an
accumulation of vapor above the tubes which might affect the rate of diffusion and
thus the diffusion coefficient values
...
3 Error Analysis

• Parallax error when taking height gauge readings
• Random error such as human reaction time error when using stopwatch –
delay between the
• moment height gauge reading is taken and stopwatch reading is read
...
4 Improvements

• Repeating and averaging height measurement readings
• Ensure eye level in line with calibration to reduce parallax error

•

•
•






































Experimental apparatus is set up in a sealed box, with constant gas stream
passing through the top of tube
...

Using thermocouple probe instead of thermometer to give a more accurate
temperature reading
Real gas equation such as Peng-Robinson equation of state should be used
instead of ideal gas equation to inprove accuracy of experimental diffusivity
values
...


5 FLUID MECHANICS

Objectives of the experiment
a) To study velocity-pressure drop characteristics of a packed column for:
i) drypacking
ii) wet packing
iii)a countercurrent flow of air and water
...
To use this information in
order to predict the stable operating region for the column
...
D
...
52 m long (height of packing) perspex column packed with 1⁄2 inch
(1
...
Air is supplied, through a rotameter, at the bottom of
the column
...
A manometer connected
across the bed gives the pressure drop
...
Also see the attached
generalised pressure drop correlation
...
1 Discussion

From literature, Ergun equation allows us to determine the pressure drop for
!"

!!

Single-Phase Flow : ! = 𝐶! ! , where Z is height of packing (m), G is superficial gas
-2 -1

!

mass velocity (kgm s ), ρG is density of gas (kgm-3) and CD is a constant depending
on size and type of packing, in this case to be 909 for a 0
...

However, the pressure drop data for Two-Phase Flow shows wide discrepencies
because of the various packing density and manufacture, such as changes in wall
thickness
...
The pressure drop at flooding point shown in
experimental result is 1604
...
32 Pa m-1 for a column of 1
...
The experimental value is slightly below the lower limit of literature range
...


When operating a packed column, it has to be ensured that the packing is
properly ‘wetted’ by the liquid phase, to ensure good efficiency of column
...
However, wetting the column might
be problematic particularly during low liquid flowrate, where a continous liquid film

could not be formed around the column wall, thus some area will be ineffective
...
Since at low liquid flowrate, there will be poor wetting, we tend to think
that using a high liquid flowrate might resolve the problem
...


Thus, for packing to be adequately wetted, wetting rate provided in Eq 8
should be calculated and made sure to be above the ‘minimum wetting rate’, of
range (1
...
5) x 10-5 m2 s-1
...
04 x 10-5 m2 s-1 while for counter-current flow with 3 L min-1 is 1
...
However, for counter-current flow with 7 L
min-1, the wetting rate of 2
...
Hence,
flooding happens for counter-current flow with 7 L min-1, at a much lower gas flow
rate compared to the other 2 cases
...
45 - 6
...
As such an optimum
liquid flow rate of 5 L min-1 is suggested to ensure that any accidental disturbance to
the liquid flow rate will not cause an immediate flooding condition
...
37,
which is more than 8
...
Usually for column with random packings, the packing size should
not exceed one eighth of the column diameter
...
By meeting the
stated conditions, error caused when channeling water down the columns wall can
be minimised
...


It is not practical to operate a tower in a flooded condition
...
It is
ideal to operate at gas flow rate ranging between the loading point and the flooding
point
...
Therefore, using the loading velocity as the
basis for design is reasonable
...


In industrial application of packed columns, it is useful to know the
volumetric hold-up of liquid phase in the column
...
Theoritically, the liquid hold up in the column increases with the
increase of gas flowrate
...
This might be due
to experimental error, such as insufficient time to allow water to drip down from
packed column, and human reaction time error
...
It is important to ensure that the liquid holdup is not
too large, as this will cause flooding to the system, which is undesired when
designing a packed column
...
A balance must be
made between these criterion to give an optimum packed column design
...

However, there will be an increase in the operational cost since pumping energy has
to be increased to account for the higher pressure drop
...
The type of packings used in columns is an
important design consideration
...
When structured packings are used, it is possible
to use columns with smaller diameters
...

For high pressure operation, the column shell which contributes to the capital cost
plays a significant role, since stronger shell material such as stainless steel will incure
a higher capital cost
...
2 Error Analysis

From error calculations, the percentage error decreases as gas flowrate
increases
...
This might be due to the water manometer being not sensitive enough to
measure the small changes in pressure at low gas flow rate
...


The error in this experiment includes random error such as parallax error,
wehere the eye level of the observer is not in line with marked calibration during the

pressure, flowrate and liquid hold up measurement
...
There are
difficulties to judge whether the experiment has reached a steady state, where the
meniscus of water in water manometer is fluctuating when readings are being made,
causing inaccurate pressure measurements
...
This is due to the vigorous
bubble formation on the surface of the liquid, with continous fluctuation of water
level due to water flowing down from the above packed column
...
It is also hard to judge when should the reading of L2 to be taken
since there will still be droplets of water driping from the packed column continously
after the apparatus is shut off
...


5
...
A stop watch
should be used to measure the time gap after the shut off the apparatus, until the L2
reading is taken to ensure a more accurate liquid hold up measurement
...


























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Title: Example Experiments Report
Description: Module : Engineering Experimentation Couse : 2nd Year Chemical Engineering

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