Sizing and Tolerancing
Choosing standard sizes and applying proper tolerances to dimensions are among
the important aspects in the design of mechanical systems. When two parts need to
fit together in order to perform a certain role in a mechanical system, the sizing and
tolerancing of such components becomes of prime importance.
Sizes and Preferred Numbers
The purpose of preferred numbers is to limit the number of choices available for
sizing parts or items. Though preferred numbers limit the number of choices, but at
the same time they cover a wide range of sizes with reasonable increments
between the different sizes.
When manufacturers use the preferred numbers for sizing their products, this
enhances the compatibility and interchangeability of the different types of parts or
items. With this, there are higher possibilities to find different types of parts or
items as readily available off-the-shelf components.
 The Table gives the complete set of Preferred Sizes in millimeters (when a
choice can be made, use one of these sizes; however, not all parts or items are
available in all the sizes shown in the table):
Renard Numbers
Objects are often manufactured in a series of sizes of increasing magnitude. The
manufacturer must decide what those sizes should be. Renard numbers provide a
very limited number of choices that cover a wide range of sizes. The sizes provided
by the Renard numbers are not far apart such that the difference between any two
adjacent sizes is not very significant. Also, Renard numbers may be divided in
different series providing different levels of preference.
Which series provides more evenly distributed sizes?
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 1 of 21
 Renard series of numbers are defined as:
𝑅𝑥 ; 𝑎,
𝑥
( √10)𝑎,
𝑥
2
( √10) 𝑎,
𝑥
3
𝑥
𝑥
( √10) 𝑎, … .. , ( √10) 𝑎
where, 𝑥 = 5, 10, 20, 40
Thus, the different series are as follows:
- R5: 10, 16, 25, 40, 63, 100.
- R10: 10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, 100.
- R20: 10, 11.2, 12.5, 14, 16, 18, 20, 22.4, 25, 28, 31.5, 35.5, 40, 45, 50, 56,
63, 71, 80, 90, 100.
- R40: 10, 10.6, 11.2, 11.8, 12.5, 13.2, 14, 15, 16, 17, 18, 19, 20, 21.2, 22.4,
23.6, 25, 26.5, 28, 30, 31.5, 33.5, 35.5, 37.5, 40, 42.5, 45, 47.5, 50, 53, 56,
60, 63, 67, 71, 75, 80, 85, 90, 95, 100.
 The Table gives the Renard (R-Series) Numbers (ISO 3)divided in different
choice preference levels:
 In addition to the Renard Numbers, there is also the Rounded Renard (R'Series) Numbers (ISO 497):
- R′10: 10, 12.5, 16, 20, 25, 32, 40, 50, 63, 80, 100.
- R′20: 10, 11, 12.5, 14, 16, 18, 20, 22, 25, 28, 32,36, 40, 45, 50, 56, 63, 71,
80, 90, 100.
- R′40:10, 10.5, 11, 12, 12.5, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26,
28, 30, 32, 34, 36, 38, 40, 42, 45, 48, 50, 53, 56, 60, 63, 67, 71, 75, 80, 85,
90, 95, 100.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 2 of 21
Dimensions and Tolerances
Tolerance is the maximum allowable variation in a dimension or in the size of a part.
The tolerance in dimensions can be represented as Direct Limits or
more commonly as plus/minus tolerance values applied directly to
a dimension.
- The difference between the upper and lower limits of a
dimension is called the Tolerance Zone.
 There are two ways for specifying plus/minus tolerance values for dimensions:
 Bilateral tolerance: the variation in both directions from the basic size (the
basic size is the exact desired theoretical size).
Example:
100 ± 0.2
Basic size
Limits
- Usually used for parts that fit besides each other
 Unilateral tolerance: the basic size is taken as one of the limits and the
variation is only in one direction.
Example:
Basic size
40+0
−0.1
𝑜𝑟
40+0.1
−0
Limits
- Usually used for parts that fit inside each other (e.g., shaft & hole, key &
keyway)
Why do we specify tolerance?
Because parts cannot be manufactured to the exact geometry and
dimensions, so we specify the acceptable range of variation.
In general, the variations in dimensions of manufactured parts (the actual size)
occur at random (within the tolerance zone) and, usually, they follow a normal
distribution.
Geometric Dimensioning and Tolerancing (GD&T)
Traditional tolerances can be used for defining the size and location of features.
Geometric dimensioning and tolerancing is a more advanced method for applying
tolerances that can be used for defining the geometric attributes of features (e.g.,
location, orientation, form).
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 3 of 21
The geometric tolerancing method is defined by the standard ASME Y14.5 and it is
used to state the maximum allowable variations in the form of a feature or its
position from the perfect geometry implied on the drawing.
 The different types of geometric tolerances are defined using standard
Geometric Characteristic Symbols as shown in the table.
 Geometric tolerances are indicated
on drawings using a feature control
frame as shown in the figure.
 The datum is the reference relative to which the geometric
tolerance is defined (multiple references can be used at the same
time) and it is identified on drawings using the symbol shown in the
figure.
 The modifiers are used to specify the condition to which the tolerances are
applied. There are three modifiers that can be applied to the tolerance value:
- Maximum Material Condition (MMC) and its symbol is:
- Regardless of Feature Size (RFS) and it is the default, thus it has no symbol
- Least Material Condition (LMC) and its symbol is:
 Examples of using geometric tolerances in drawings are shown in the figure.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 4 of 21
Standard Tolerance Values
The values of tolerances to be assigned depend largely on the application.
Commercial products for instance does not require tight tolerances, while on the
contrast, for precision measuring tools, tight tolerances must be used.
 In general, the value of the tolerance depend on
the dimension where smaller tolerances are
used for small dimensions and bigger tolerances
are used for big dimensions.
 The tighter the tolerances, the higher the COST.
Thus, tight tolerances should not be specified
unless such tight tolerances are needed.
The international standard ISO 286 defines 20 different tolerance grades (01, 0, 1, 2,
...., 18) where the bigger the tolerance grade number, the bigger the tolerance is.
 The figure shows the practical use of the International Tolerance Grades
(IT#):
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 5 of 21
 The IT Grade number that can be obtained is related to the manufacturing
process used for making a part. The table shows the range of the IT grades
that can be obtained using the different manufacturing processes.
 The Table gives the Total Tolerance values for IT Grades from IT1 to IT18:
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 6 of 21
 It should be noted the tolerance values given in the table are the full
tolerance zone (full range), therefore the value should be divided by 2 when it
is written as a bilateral tolerance.
Example: Write the following dimensions with bilateral tolerances using
IT12:
6, 50, 150 mm
6 ± 0.06 , 50 ± 0.125 , 150 ± 0.2
Non-Toleranced Dimensions Standard
It is a common practice to apply tolerances even to the non-toleranced dimensions.
The ISO standard (ISO 2768-1) defines general tolerance values divided in four
categories (fine, medium, coarse and very course) to be used for non-toleranced
dimensions on drawings where tolerances are dependent on the nominal sizes.
 The tables below show the general tolerance values to be used for nontoleranced dimensions.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 7 of 21
Tolerance Stack-up Analysis
When tolerances are applied to the dimensions
of individual features of a part (such as in chain
dimensioned parts), tolerances will stack-up
and the overall dimension of the part will be
influenced by all the individual tolerances.
The same tolerance stack-up effect also applies to assemblies where the size of an
assembly will be influenced by the tolerances applied to the dimensions of the
individual parts.
There are two methods used for tolerance stack-up analysis:
 Worst Case Scenario Analysis: The upper and lower limits of the dimensions
are added (or subtracted when needed) algebraically to find the upper and
lower limits for the desired dimension.
𝑑 𝑇𝑜𝑡𝑎𝑙 ± 𝑡𝑇𝑜𝑡𝑎𝑙 = (𝑑1 + 𝑑2 +. . . ) ± (𝑡1 + 𝑡2 +. . . )
For the example above that will be:
x = 7.5 ± 0.15
- This method is not accurate, but it is easy and used more often.
 Statistical Analysis: Each of the dimensions is treated as an independent
random variable and its tolerance limits are taken as the ±3𝜎 limits (𝜎 is the
standard deviation). Then the variances (𝜎 2 ) of each of the dimensions are
added (or subtracted when needed) algebraically.
𝑑 𝑇𝑜𝑡𝑎𝑙 ± 𝑡𝑇𝑜𝑡𝑎𝑙 = (𝑑1 + 𝑑2 +. . . ) ± 3√∑𝑛𝑖=1 𝜎𝑖 2
For the example above that will be:
±3𝜎1 = ±0.04 → 𝜎1 = 0.0133
±3𝜎2 = ±0.06 → 𝜎2 = 0.02
±3𝜎3 = ±0.05 → 𝜎3 = 0.0167
Thus, x = 7.5 ± 3√0.01332 + 0.022 + 0.01672 = 7.5 ± 0.088
- This method is more accurate, however it is not used that often.
 The stack-up of tolerances in the dimensions of parts can be avoided by using
baseline dimensions instead of chain dimensions.
 Tolerance stack-up can have a significant
effect on the gap or interference in
assemblies since the gap or interference
values are usually small by nature.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 8 of 21
When several parts are assembled, the gap (or interference) depends on both
the dimensions and tolerances of the individual parts.
Consider the shown assembly:
𝐺𝑎𝑝 = 𝑎 − 𝑏 + 𝑐 − 𝑑 + 𝑒 − 𝑓
Using 𝑥 for ( → ) and 𝑦 for ( ← ) we can write;
𝑤 = (𝑥1 + 𝑥2 + ⋯ ) − (𝑦1 + 𝑦2 + ⋯ )
 𝑤 = ∑ 𝑥𝑖 − ∑ 𝑦𝑗
Using worst case scenario analysis we find:
- The largest gap 𝑤𝑚𝑎𝑥 occurs when the 𝑥 values are the largest possible &
the 𝑦 values are the smallest possible.
If we call the bilateral tolerance as “ 𝑡 ” we get,
 𝑤𝑚𝑎𝑥 = ∑(𝑥𝑖 + 𝑡𝑖 ) − ∑(𝑦𝑗 − 𝑡𝑗 ) = ∑ 𝑥𝑖 − ∑ 𝑦𝑗 + ∑𝑎𝑙𝑙 𝑡
- The smallest gap 𝑤𝑚𝑖𝑛 occurs when the 𝑥 values are the smallest possible &
the 𝑦 values are the largest possible.
 𝑤𝑚𝑖𝑛 = ∑(𝑥𝑖 − 𝑡𝑖 ) − ∑(𝑦𝑗 + 𝑡𝑗 ) = ∑ 𝑥𝑖 − ∑ 𝑦𝑗 − ∑𝑎𝑙𝑙 𝑡
Example: Find the maximum and minimum gap using
worst case scenario analysis, then give the size of the
gap using bilateral tolerance.
𝑎 = 500 ± 1 𝑚𝑚
𝑏 = 350 ± 0.7 𝑚𝑚
𝑐 = 120 ± 0.1 𝑚𝑚
Solution:
𝑤𝑚𝑎𝑥 = 500 − 350 − 120 + (1 + 0.7 + 0.1) = 31.8 𝑚𝑚
𝑤𝑚𝑖𝑛 = 500 − 350 − 120 − (1 + 0.7 + 0.1) = 28.2 𝑚𝑚

𝑤 = 30 ± 1.8 𝑚𝑚
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 9 of 21
Limits & Fits
The fit is the degree of tightness or looseness between two mating parts to perform
a definite function, while the limits are the two extreme permissible sizes of a
dimension between which actual size of dimension is contained.
When a shaft or pin needs to be inserted into a hole, the type of fit is decided based
on the intended application.
- For example if the shaft and the hole are to form a pin-joint or a journal
bearing , then the hole needs to be slightly bigger than the shaft to allow the
shaft to rotate inside the hole (clearance is needed).
- Another example when the shaft is inserted into a rolling-contact bearing, the
shaft needs to be slightly bigger than the hole of the inner-ring in order to
prevent any slipping between the shaft and the inner-ring of the bearing
(interference is needed).
Since tolerances are always present, fits are divided in three types:
 Clearance fit: It occurs when two toleranced mating parts will always leave a
space or clearance when assembled.
 Interference fit: It occurs when two toleranced mating parts will always
interfere when assembled.
 Transition fit: It occurs when two toleranced mating parts will sometimes be
an interference fit and sometimes be a clearance fit when assembled.
Important Terms
- Nominal size: a dimension used to describe the general size (the size we
use in speaking of an element).
- Basic size: the theoretical size used as a starting point for the application
of tolerances (the exact desired theoretical size).
- Actual size: the measured size of the finished part after machining.
Limits and fits are standardized according to the international standard (ISO 286)
where there are two different systems that can be used for obtaining any desired
type of fit:
 Hole Basis System: The hole size is kept constant and the size of the shaft is
varied.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 10 of 21
 Shaft Basis System: The shaft size is kept constant and the size of the hole is
varied.
 Because of considerations related to manufacturing, the hole basis system
is more commonly used.
 The figure shows the shaft and hole configurations for hole basis system under
a clearance type of fit where the terms used for defining the fit are illustrated
graphically.
- Capital letters refer to the hole and lower case letters refer to the shaft.
- The Basic size (or nominal size) is the size to which limits are assigned and it
is the same for both members of the fit.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 11 of 21
 The table lists the specific types of Preferred Fits for both hole and shaft basis
systems.
 Once the type of fit is decided according to the intended use, the fit is
described by the basic size and the ISO fit symbol.
Example: A joint with basic size of 40 mm having a Hole Basis Sliding fit
 The fit can be identified as: 40 H7/g6
where,
The hole  40 H 7
International tolerance
The shaft  40 g 6
grade number (IT#)
Fundamental deviation letter
 It should be clear that for the Hole Basis system, the fundamental deviation
is applied to the shaft dimension only.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 12 of 21
 The table gives the Fundamental Deviations for Shafts (to be used for the
hole basis system):

For the Hole Basis system, the maximum and minimum diameters for the hole
and shaft are found as follows:
𝐷𝑚𝑎𝑥 = 𝐷 + ∆𝐷
Hole:
&
𝐷𝑚𝑖𝑛 = 𝐷
&
𝑑𝑚𝑖𝑛 = 𝑑 + 𝛿𝐹 − ∆𝑑
Shaft:
- For clearance fits: c, d, f, g, & h
𝑑𝑚𝑎𝑥 = 𝑑 + 𝛿𝐹
- For interference fits: k, n, p, s, & u
𝑑𝑚𝑎𝑥 = 𝑑 + 𝛿𝐹 + ∆𝑑
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
&
𝑑𝑚𝑖𝑛 = 𝑑 + 𝛿𝐹
Lecture Notes by: Dr. Ala Hijazi
Page 13 of 21
where,
𝐷 : basic size of the hole
same value
𝑑 : basic size of the shaft
𝛿𝐹 : fundamental deviation
∆𝐷: tolerance grade for the hole
∆𝑑: tolerance grade for the shaft
found from the table according to
the fundamental deviation letter
found from the table
according to the IT#
Example: Find the shaft and hole dimensions for a sliding fit (Hole Basis system)
with 25mm basic size then specify the dimensions of both members using unilateral
tolerance.
Solution:
ISO symbol: 25 H7/g6
Hole: 25 H 7
𝐷 = 25
IT 7  ∆𝐷 = 0.021
𝐷𝑚𝑎𝑥 = 𝐷 + ∆𝐷 = 25.021 𝑚𝑚
𝐷𝑚𝑖𝑛 = 𝐷 = 25 𝑚𝑚
Shaft: 25 g 6
𝑑 = 25
IT 6  ∆𝑑 = 0.013
g  𝛿𝐹 = −0.007
Sliding fit: g 
𝑑𝑚𝑎𝑥 = 𝑑 + 𝛿𝐹 = 25 + (−0.007) = 24.993 𝑚𝑚
𝑑𝑚𝑖𝑛 = 𝑑 + 𝛿𝐹 − ∆𝑑 = 25 + (−0.007) − 0.013 = 24.98 𝑚𝑚
Hole: 25+0.021
𝑚𝑚
−0
Shaft: 24.993+0
−0.013 𝑚𝑚
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 14 of 21
 Alternatively, instead of using the equations, the limit values of the shaft and
hole dimensions for different types of fits and different basic sizes can be
obtained directly from tables.
 An example of such tables is given below where it gives the hole and shaft
sizes for the Preferred Hole Basis Clearance Fits (for basic sizes from 7 to 19
mm divided in three preference levels: F, S & T):
Example: Find the shaft and hole dimensions for a close running fit (Hole Basis
system) with 10 mm basic size and specify the dimensions using unilateral tolerance.
Find the answer using the equations given earlier then compare the results with
that given in the table above.
Solution: Hole: 10+0.022
𝑚𝑚
Shaft: 9.987+0
−0
−0.015 𝑚𝑚
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 15 of 21
Surface Finish
The development of high speed machines has resulted in increasing the loads and
speeds of moving parts. Such highly loaded surfaces running at high speeds require
accurate control of surface quality in order to minimize friction and wear. Designers
are responsible for specifying a surface that will give the maximum performance
and surface life at the lowest cost. The required surface finish can be specified
based on past experience with similar parts, on field service data, or on engineering
tests. Generally speaking, the ideal finish is the roughest one that will do the job
satisfactorily.
The two main reasons for surface finish control are:
 Friction Reduction: When a film of lubricant must be maintained between
two moving parts (such as in bearings, gears, etc.), the surface irregularities
must be small enough so they will not penetrate the oil film under the most
severe operating conditions.
 Wear Control: Surface finish is also important to the wear service of certain
parts that are subject to dry friction, such as dies, clutches, brakes, etc.
Also, surface finish must be controlled for the purpose of increasing the fatigue
strength of highly stressed members which are subjected to load reversals (i.e.,
fatigue loading). A smooth surface eliminates the sharp irregularities which are the
greatest potential source of fatigue cracks.
In some cases, a slightly rough surface finish is required. When boundary lubrication
condition exist, or when two extremely hard surfaces running together, a slightly
roughened surface will usually assist in lubrication. Also, most new moving parts do
not attain a condition of complete lubrication as a result of imperfect geometry,
running clearances, and thermal distortions. Therefore, the surfaces must wear in
by a process of actual removal of metal.
Surface finish, also known as surface texture, has three components: lay, surface
roughness, and waviness, as shown in the figure.
 Lay: It is the direction of the predominant surface pattern and it is usually
determined by the production method used.
 Surface Roughness: (commonly shortened to roughness) It is a measure of the
finely spaced surface irregularities.
 Waviness: It is the measure of surface irregularities with a spacing greater
than that of surface roughness. These usually occur due to warping,
vibrations, or deflection during machining.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 16 of 21
Surface roughness can be quantitatively measured using a device called
Profilometer. A roughness parameter is used to give a numerical representation of
the surface roughness. There are many different roughness parameters in use, but
𝑅𝑎 is by far the most commonly used. Other common parameters include 𝑅𝑞 , 𝑅𝑧
and 𝑅𝑠𝑘 .
The 𝑅𝑎 roughness parameter is the arithmetic average of the absolute values of the
deviations of surface height readings from the surface roughness mean line. The 𝑅𝑎
is given in micrometers and it is mathematically defined as:
𝑖=1
1
𝑅𝑎 = ∑|𝑦𝑖 |
𝑛
𝑛
According
to
older
standards,
Roughness Grade Numbers (N1, ... N12)
were alternatively used instead of the
roughness 𝑅𝑎 values. However, these
roughness grade numbers are no
longer used in the recent ISO
standards.
 The table shows the 𝑅𝑎 values
corresponding to the roughness
grade numbers (for reference
purposes) and the corresponding
old Finish Marks symbols (also not
being used anymore).
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 17 of 21
Surface Finish Symbols
Requirements for surface texture are indicated in technical drawings by several
variants of standard graphical symbols (ISO 1302), each having its own significant
meaning.
 The simplest form of the surface finish symbols used in technical drawings is
shown in the figure (the symbol may be omitted on views of parts when the finish
quality of a surface is not important).
 The symbol is always placed in upright
position or it can be rotated 90⁰ CCW if
needed (never at an angle or upside down)
such that it can be read from the bottom
side or the right side. The symbol is
generally placed directly on the surface.
An extension line or a leader can be used
for placing the symbol when needed, as
seen in the figure.
 If additional surface characteristics need to be specified, the Complete Graphical
Symbol (it has an additional horizontal line similar to the square root symbol) can
be used. When the complete graphical symbol is used, additional
complementary surface requirements may be indicated on the symbol and they
are positioned as shown in the figure.
The complementary requirements that are shown at each position are as follows:
- Position a - Single surface texture requirement
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 18 of 21
Indicate the surface texture parameter designation, the numerical limit value
and the transmission band or sampling length.
Example 1: 0.0025-0.8/Ra 3.2 (transmission band and sampling length are
indicated)
Example 2: 0.8/Ra 3.2 (only sampling length is indicated)
- Position a and b - Two or more surface texture requirements
Indicate the first surface texture requirement at position “a” and indicate the
second surface texture requirement at position “b”.
- Position c - Manufacturing method
Indicate the manufacturing method, treatment, coatings or other
requirements for the manufacturing process etc. to produce the surface (for
example, turned, ground, plated).
- Position d - Surface lay and orientation
Indicate the symbol of the required surface lay and the orientation, if any, of
the surface lay, as shown in the figure:
- Position e - Machining allowance
Indicate the required machining allowance, if any, as a numerical value given
in millimeters.
 When the same surface texture is required on all surfaces around a part outline,
a circle shall be added to the complete graphical symbol as shown in the figure.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 19 of 21
 An example of a surface finish symbol showing a complete set of complementary
requirements is shown in the figure.
 The surface finish is highly dependent on the manufacturing process being used
to produce the surface of a part as shown by the chart.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 20 of 21
 The surface finish 𝑅𝑎 value to be specified depends on the intended application.
For instance, when stresses applied to a part are not that high and the
appearance of the surface is not important, 𝑅𝑎 value of 6.3 micrometers will be
acceptable. However, when the surface of a component is subjected to stress
concentration, a smoother surface finish (𝑅𝑎 value of 0.8 micrometers) will be
necessary.
 The table provides some guidance on specifying the appropriate 𝑅𝑎 values for
surfaces according to the intended application.
MENG 204 - Mechanical Drawing
Sizing and Tolerancing
Lecture Notes by: Dr. Ala Hijazi
Page 21 of 21