Numerical methods for engineers includes units

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 (ii) 2 “national” systems British Mass System American Engineering System 2 has a mass of 1 kg force-s / meter 1 pound of stuff 1 slug of stuff Object accelerates 2 s 2 at 1 ft/sec Object weighs 32.2 poundals Object weighs 32.2 pounds force a F (iii) the “4 unit” system ( force, length, mass, time ) Common in USA 1 lb mass (mass) = ( ) 1 lb 1 force g Weighs 1 lb force 1 lb 2 force accelerate at 32.2 ft/s 32.2 lb ft will make 1 lb mass mass

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