1. Numerical methods for engineers includes units
(i) The three “3 unit” systems
( lenght, mass, time )
cgs
mks
mks
A mass of stuff accelerating at “standard” sea level gravitational value
1 gram of stuff accelerating at 1 cm/s
1 gram of stuff accelerating at 1 m/s 2 2
mass system
force system
Weighs 981 dynes
Weighs 1 Newton
Weighs 9.8 kg force
The amount stuff that has this weight
has a mass of 1 kg force-s / meter 2
(ii) 2 “national” systems
British Mass System
American Engineering System
1 pound of stuff
Object accelerates
at 1 ft/sec 2
1 slug of stuff
Object weighs 32.2 poundals
Object weighs 32.2 pounds force
(iii) the “4 unit” system
( force, length, mass, time )
Common in USA
1 lb mass
1 lb
force
will make 1 lb
mass
accelerate at 32.2 ft/s 2
< F g 1
= ( )
(mass)
< a 2 s
1 lb
force
32.2 lb ft
mass
Weighs 1 lb
force

2. Example using 4 unit system
water tower is in Tampa = Z
acceleration
( )
mass ft 3
(a)(ft ) 1 P g c
Pressure difference (top to bottom)
10 ft 2
water
density P
= ( ) ft 3 lb
mass 2
( 10 ft) s
( ) Z
= 100 ft 2 s ft lb
mass
Not typical
pressure units but they are still pressure units. 2 P =
(2,020 x )
Since mass is in lb
mass
the force is
force 2 s
1 lb
force
32.2 lb ft
mass
g =
(mass)
< a =
( ) g 1 F
conversion factor between lb and lb
mass
force 2 s
1 lb
force
32.2 lb ft
mass lb
force 2 ft 2 s
1 lb
force
32.2 lb ft
mass 2 s ft lb
mass 2
< F
< a 2 =
62.4 x10 =
(mass) P
(2,020 x )
( )
Note:
The “4 unit” system entertains two density concepts. g
< F
= (mass)
< a 2 s 1
32.2 ft
(force magnitude) ( ) = (mass) ( )
1 lb
force
32.2 lb
mass 2 s
1 lb
force
32.2 lb ft
mass
Both look the same (have units of pounds per foot cubed) but each represents a different concept. 3
1 ft
62.4 lb
force 3
1 ft
62.4 lb
mass
force density
mass density