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

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 = (62.4 ) ft 3 lb mass 2 ( 10 ft) s ( 32.2 ) Z = 100 ft 2 s ft lb mass Not typical pressure units but they are still pressure units. 2 P = (2,020 x 10 ) 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 10 ) ( ) 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