;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Units demo session
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(in-package :units)


;;
;; Creating quantities with base units
;; (kilogram meter second ampere mole kelvin candela)
;;

UNITS 1 > (quantity 10 '(m (sec -1)))
10 m sec-1

UNITS 2 > (quantity 34 'kg)
34 kg









;;
;; Creating quantities with derived units 
;; (e.g. hour, kilometer, pascal, newton, joule,
;; watt, atmosphere)
;;

UNITS 3 > (quantity 2 'hour)
7200 sec

UNITS 4 > (quantity 90 '(km (hour -1)))
25 m sec-1

UNITS 5 > (quantity 1.05 'atm)
106364.99999999985 kg m-1 sec-2









;;
;; Defining new derived units
;;

UNITS 6 > (define-unit inch 2.54 cm)
INCH

















;;
;; Now you can use INCH like any other unit
;;

UNITS 7 > (quantity 12 'inch)  
0.30480000000000007 m

UNITS 8 > (quantity 10 '(gram (inch -2)))
15.500031000061995 kg m-2

















;;
;; Multiplying quantities
;;


UNITS 9 >  (* (quantity 10 '(m (sec -1)))
              (quantity 15 'sec))
150 m

UNITS 10 > (* (quantity 10 '(m (sec -1)))
              (quantity 2 'hour))
72000 m







;;
;; You can't compare or add quantities if they don't have the
;; same base units.
;;

UNITS 11 > (+ (quantity 10 '(m (sec -1)))
              (quantity 2 'hour))

Error: Unit mismatch between 10 m sec-1 and 7200 sec.
  1 (abort) Return to level 0.
  2 Return to top loop level 0.












;;
;; But you can add quantities with different derived units
;; that reduce to the same base units.
;;

UNITS 12 > (+ (quantity 2 'hour) (quantity 5 'minute))
7500 sec

UNITS 13 > (let ((radius (quantity 5 'cm)))
             ;; Compute area of a circle with 5 cm radius.
             (* pi (expt radius 2)))
0.007853981633974483 m2











;;
;; You can explicity check for correct units.
;;

UNITS 14 > (check-units (quantity 10 'newton) 'newton)
10 kg m sec-2


UNITS 15 > (check-units (quantity 10 'newton) 'pascal)

Error: The quantity 10 kg m sec-2 should have units PASCAL.
  1 (abort) Return to level 0.
  2 Return to top loop level 0.










;;
;; Defining physics constants and formulas.
;;


UNITS 16 > (defconstant +gas-constant+
             (quantity 8.315 '(joule (mole -1) (kelvin -1))))
+GAS-CONSTANT+


UNITS 17 > (defun gas-pressure (gas-density temperature 
                                            molecular-weight)
             (check-units gas-density '(kg (m -3)))
             (check-units temperature 'kelvin)
             (check-units molecular-weight '(kg (mole -1)))
             (check-units (/ (* gas-density +gas-constant+ 
                                temperature)
                             molecular-weight)
                          'pascal))
GAS-PRESSURE









;;
;; Using the gas-pressure formula.
;;

UNITS 18 > (gas-pressure (quantity 2 '(kg (meter -3)))
                         (quantity 295 'kelvin)
                         (quantity 32 '(gram (mole -1))))
153307.81249999997 kg m-1 sec-2












;;
;; With wrong units, the same function results in a unit
;; mismatch error.
;;

UNITS 19 > (gas-pressure (quantity 2 '(kg (meter -1)))
                         (quantity 295 'kelvin)
                         (quantity 32 '(gram (mole -1))))

Error: The quantity 2 kg m-1 should have units (KG (M -3)).
  1 (abort) Return to level 0.
  2 Return to top loop level 0.