PCERT LEV COURSES
Page 1
MATHS REVISION For P601/P602
Duct Areas and Diameters
I know that in the field you rarely actually calculate duct diameters—you have little
‘crib’ sheets or an instrument which does it all for you?? In the P601 and P602 exams
however you will need to do these calcs from first principles ….. So here goes.
Now I know that most of you will prefer the second equation (below) as it was quite
probably the one you learned at school …… but if you can—I prefer you to use the
first version (both give the same answers … I promise!)
Area of a circle
A
=
πD2/4
Where π = 3.142
D = dia (m)
Or
A
=
πr2
Where r = radius in metres(!)
Preparation
First thing to note is that you must always …… and I mean always convert your duct
diameters—which you measure (or are given) in millimetres (mm) into metres (m).
This part is quite easy—you simply divide mm by 1000 to get m.
Example
300mm
=
300/1000
= 0.3m
280mm
=
280/1000
= 0.28m
Warning—Do be Careful with where you put your decimal point. It is SO easy to
misread your calculator.
The Life of Pi? Or at least Pi = π
I think we can all accept that for every calculation you will ever do involving Pi (π) it
will always have the same value (you remember it from scholl? Maybe not?)
Pi =
© Oxyl8 2017
π
=
3.142 (always!)
www.oxyl8.com
v1.1
PCERT LEV COURSES
Page 2
So—now back to the main equations. We now know that we have to get mm into m
(metres) and that π = 3.142.
Area of a circle
A
=
πD2/4
Where π = 3.142
D = dia (m)
Or
A
=
πr2
Where r = radius in metres(!)
Examples
Say the duct had a diameter of 100mm
That equals 0.1m
And π = 3.142
So we put those figures into the equations (I’ll show both)
Ah—but before we go on any further—the other little annoyance is that Radius—r is
exactly half Diameter D.
So in our example the radius will be 1/2 of 100mm which is 50mm
Whether Diameter or Radius—it must still be put into Metres (m) before we can work
on it.
Recap: Our example will therefore be:D = 0.1m
or
r=0.05m
do watch your decimal point
placement with radii (fancy new
Word)??
So—using the equations above—the area for a 100mm diameter duct will be:A
=
πD2/4
=
3.142 x 0.1 x 0.1
4
3.142 x 0.05x0.05
=
0.03142
4
0.00786
=
0.00786 m2
0.00786 m2
or
πr2
Do watch those decimal point positions—it is a common area (pun!) for error
© Oxyl8 2017
www.oxyl8.com
v1.1
PCERT LEV COURSES
Page 3
We’ll do another couple of worked examples and then let you loose on some practice
calcs.
Duct diameter = 160mm
A
=
πD2/4
=
3.142 x 0.16 x 0.16
4
3.142 x 0.08x0.08
=
0.08043
4
0.0201
=
0.0201 m2
0.0201 m2
or
πr2
Duct diameter—360mm
A
=
πD2/4
=
3.142 x 0.36 x 0.36
4
3.142 x 0.18x0.18
=
0.4072
4
0.0.1018
=
0.1018 m2
0.1018 m2
or
πr2
Remember—keep watching the position of the decimal point and get the right
number of zeros!!
On the next page—we’ve set out a number of examples for you to work on.
The answers are on the last page—but do try without looking first!
© Oxyl8 2017
www.oxyl8.com
v1.1
PCERT LEV COURSES
Page 4
Trial Examples:Using your preferred equation—work out the Areas in m2 for each of the following
duct diameters:-
Duct diameter
Answer for Duct Area
180mm
240mm
300mm
380mm
420mm
560mm
750mm
800mm
© Oxyl8 2017
www.oxyl8.com
v1.1
PCERT LEV COURSES
Page 5
Trial Examples
Duct diameter
ANSWERS
Answer for Duct Area
180mm
0.0255 m2
240mm
0.0452 m2
300mm
0.0707 m2
380mm
0.1134 m2
420mm
0.1386 m2
560mm
0.2463 m2
750mm
0.4418 m2
800mm
0.5027 m2
© Oxyl8 2017
www.oxyl8.com
v1.1
PCERT LEV COURSES
Page 6
Now—to move on just a touch—many of your hoods are ‘Ovals’ or Ellipses. What to
do with those?
Well we use the same basic equation …… but ……..
In a circle—both diameters and both radii are the same. In an oval one is bigger than
the other (the long diameter and a short diameter). Agreed?
So we simply re-write the equations for a circle to cater for that:A (circle)
=
πD2/4
A (Oval)
=
πDd/4
(ie big D times little
d)
=
πr2
A (Oval)
=
πRr
(ie Big R times little
r)
Or
A (circle)
Example:An oval welding hood has the dimensions—big Diameter = 190mm and little
diameter = 160mm
A (Oval)
=
πDd/4
or
=
3.142 x 0.19 x 0.16
4
3.142 x 0.095 x 0.08
=
0.0239 m2
0.0239 m2
πRr
On the next page there are some examples of Area of an Oval for you to work out on
your own. Answers are in tiny writing at the bottom.
© Oxyl8 2017
www.oxyl8.com
v1.1
PCERT LEV COURSES
Page 7
Calculate the Areas of the following ovals (using your preferred equation)
But—before you start—remember to convert all Radius/Diameters into metres (m)
don’t leave as mm.
Also—to be extra careful (again) on your decimal points and leading zeros.
Examples
Size
Area
Oval 240mm x 160mm
Oval 180mm x 160mm
Oval 195mm x 165mm
Oval 300mm x 190mm
Answers: 0.03016, 0.0226, 0.0253, 0.0448
© Oxyl8 2017
www.oxyl8.com
v1.1