Difference between revisions of "Examples"

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-<div style="font-size:24px">'''Engineering Examples of Java and z3 Programs'''</div><br/>
+<div style="font-size:24px">'''Engineering Examples in z3'''</div><br/>
 ==DESCRIPTION==
 *Basic Engineering examples in z3.<br>
 *z3 codes with z3 notations are shown below.<br>
-*Reflecting different domains like Engineering, Statistics, Medicine, etc.
-*Set of cases that are progressively complex on units are used to show the user how it goes from simple to complex cases.<br>
-*Testing how we can make better solutions to the standard problems compared to other software, due to the presence of units.<br><br>
-==Examples==
+==Engineering Examples==
 '''ExampleS1: Chemical Engineering<br>'''
-*An exhaust pipe is 75mm diameter and it is cooled by surrounding it witha water jacket. The exhaust gas enters at 350C and the water enters at 10C. The surface heat transfer coefficients for the gas and water are 300 and 1500 W/m2K respectively. The wall is thin so the temperature drop due to conduction is negligible. The gasses have a mean specific heat capacity Cp of 1130 J/kgK and they must be cooled to 100C. The specific heat capacity of the water is 4190 J/kgK. The flow rate of the gas and water is 200 and 1400 kg/h respectively. Calculate the required length of pipe for parellel flow and contra flow.
+'''LengthParallelContraFlow'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code1a <span style="color:blue;"> z3 code: Normal Calculation without using Function]</span><br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code1b <span style="color:blue;"> z3 code: Using Function]</span><br>
-'''z3 code: Normal Calculation without using Function'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code1c <span style="color:blue;"> z3 code: Multi-calculation Using Function(variable diameter)]</span><br>
-<source lang="cpp">
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code1d <span style="color:blue;"> z3 code: USING EXAMPLE1 function SOLUTION IN EXAMPLE2 function]</span><br><br>
-/*Overall Heat transfer coefficient
-U = 1/((1/hg)+(1/hw)+(x/k))
-U = 1</>((1</>hg)+(1</>hw))*/
-x = 0  //wall very thin
-hg = 300(W/m2.degK)
-hw = 1500(W/m2.degK)
-cpg = 1130(J/kg.degK)
-cpw = 4190(J/kg.degK)
-mg = 200(kg/hr)
-mw = 1400(kg/hr)
-D = 75mm
-tg1 = 350degC<>degK
-tg2 = 100degC<>degK
-tw1 = 10degC<>degK
-U = 1</>((1</>hg)<+>(1</>hw))
-delt = tg1<->tg2
-φ = mg<*>cpg<*>delt
-tw2 = tw1<+>(φ</>(mw<*>cpw))
-//Parallel flow
-delti = tg1<->tw1
-delt0 = tg2<->tw2
-A = φ<*>(log(delt0</>delti))</>(U<*>(delt0<->delti))
-L = A</>(π<*>D)
-//answer:1.48m
-//Contra Flow
-delti = tg1<->tw2
-delt0 = tg2<->tw1
-A = φ<*>(log(delt0</>delti))</>(U<*>(delt0<->delti))
-L = A</>(π<*>D)
-//answer:1.44m</source>
-'''z3 code: Using Function'''<br>
-<source lang="cpp">
-function Example1(hg,hw,cpg,cpw,mg,mw)
-{
-/*Overall Heat transfer coefficient
-U = 1/((1/hg)+(1/hw)+(x/k))
-U = 1</>((1</>hg)+(1</>hw))*/
-x = 0  //wall very thin
-var D = 75mm
-var tg1 = 350degC<>degK
-var tg2 = 100degC<>degK
-var tw1 = 10degC<>degK
-var U = 1</>((1</>hg)<+>(1</>hw))
-var delt = tg1<->tg2
-var φ = mg<*>cpg<*>delt
-var tw2 = tw1<+>(φ</>(mw<*>cpw))
-//Parallel flow
-var delti = tg1<->tw1
-var delt0 = tg2<->tw2
-var A1 = φ<*>(log(delt0</>delti))</>(U<*>(delt0<->delti))
-var LParallel = A1</>(π<*>D)
-//answer:1.48m
-//Contra Flow
-delti = tg1<->tw2
-delt0 = tg2<->tw1
-var A2 = φ<*>(log(delt0</>delti))</>(U<*>(delt0<->delti))
-var LContra = A2</>(π<*>D)
-//answer:1.44m
-return [LParallel,LContra]
-}
-hg = 300(W/m2.degK)
-hw = 1500(W/m2.degK)
-cpg = 1130(J/kg.degK)
-cpw = 4190(J/kg.degK)
-mg = 200(kg/hr)
-mw = 1400(kg/hr)
-Example1(hg,hw,cpg,cpw,mg,mw)</source>
-'''z3 code: USING EXAMPLE1 function SOLUTION IN EXAMPLE2 function'''<br>
-<source lang="cpp">
-function Example1(hg,hw)
-{
-/*Overall Heat transfer coefficient
-U = 1/((1/hg)+(1/hw)+(x/k))
-U = 1</>((1</>hg)+(1</>hw))*/
-x = 0  //wall very thin
-var U = 1</>((1</>hg)<+>(1</>hw))
-return [U]
-}
-hg = 300(W/m2.degK)
-hw = 1500(W/m2.degK)
-Example1(hg,hw)</source>
-<source lang="cpp">
-function Example2(tw1,mg,mw,cpg,cpw)
-{
-var tg1 = 350degC<>degK
-var tg2 = 100degC<>degK
-var delt = tg1<->tg2
-var φ = mg<*>cpg<*>delt
-var tw2 = tw1<+>(φ</>(mw<*>cpw))
-//Parallel flow
-var delti = tg1<->tw1
-var delt0 = tg2<->tw2
-var A1 = φ<*>(log(delt0</>delti))</>(Example1(hg,hw)<*>(delt0<->delti))
-var LParallel = A1</>(π<*>D)
-//answer:1.48m
-//Contra Flow
-delti = tg1<->tw2
-delt0 = tg2<->tw1
-var A2 = φ<*>(log(delt0</>delti))</>(Example1(hg,hw)<*>(delt0<->delti))
-var LContra = A2</>(π<*>D)
-//answer:1.44m
-return [LParallel,LContra]
-}
-cpg = 1130(J/kg.degK)
-cpw = 4190(J/kg.degK)
-mg = 200(kg/hr)
-mw = 1400(kg/hr)
-tw1 = 10degC<>degK
-Example2(tw1,mg,mw,cpg,cpw)</source>
 '''ExampleS2: Civil Engineering<br>'''
-A steel pipe 5 ft (1.5 m) in diameter and 3/5 in. (9.53 mm) thick sustains a fluid pressure of
+'''HoopStress'''<br>
-lb/sq.in. (1241.1 kPa). Determine the hoop stress, the longitudinal stress, and the increase
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code2a <span style="color:blue;"> z3 code: Using Function]</span><br>
-in diameter of this pipe. Use 0.25 for Poisson’s ratio.
-'''z3 code: Using Function'''<br>
-<source lang="cpp">
-function civil1(p,D,t){
-var E = 30e+6(lb/sqin)//for steel
-var v = 0.25
-/*hoop stress
-s = pD/2t
-longitudinal stress
-s'= pD/4t
-increase in cyl diameter
-delD = D(s-vs')/E */
-var s = p<*>D</>(2<*>t)
-var sdash = p<*>D</>(4<*>t)
-var delD = D<*>(s<->v<*>sdash)</>E
-return [s,sdash,delD<>inch]
-}
-p = 180(lb/sqin)
-D = 5(ft)
-t = (3/8)<>(inch)
-civil1(p,D,t)</source>
 '''ExampleS3: Civil Engineering<br>'''
-A 1/2-in. (12.7-mm) diameter Copperweld bar consists of a steel core 3/8 in. (9.53 mm) indiameter and a copper skin 1/16 in. (1.6 mm) thick. What is the elongation of a 1-ft (0.3-m) length of this bar, and what is the internal force between the steel and copper arising from a temperature rise of 80°F (44.4°C)? Use the following values for thermal expansion coefficients: cs = 6.5*106 and cc = 9.0*106 , where the subscripts s and c refer to steel and copper, respectively. Also, Ec = 15*106 lb/sq.in. (1.03*108 kPa).
+'''InternalForce'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code3a <span style="color:blue;"> z3 code: Normal Calculation without using Function]</span><br>
-'''z3 code: Normal Calculation without using Function'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code3b <span style="color:blue;"> z3 code: Using Function]</span><br>
-<source lang="cpp">
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code3c <span style="color:blue;"> z3 code: USING EXAMPLE1 function SOLUTION IN EXAMPLE2 function]</span><br>
-dc = 12.7(mm)
-ds = (3/8)<>(inch)
-dcs = (1/16)<>(inch)
-Es = 30e+6(lbf/in2)
-Ec = 1.03e+11(Pa)
-cs = 6.5e-6(diffF-1)
-cc = 9e-6(diffF-1)
-L = 1(ft)
-delT = 44.4(diffC)
-//cross-sectional area
-A = π<*>(dc)^2</>4
-As = π<*>(ds)^2</>4
-Ac = A<->As
-//coeff of expansion
-//c = ((As<*>Es<*>cs)<+>(Ac<*>Ec<*>cc))</>(As<*>Es<+>Ac<*>Ec)
-a = (As<*>Es<*>cs)
-b = (Ac<*>Ec<*>cc)<>(lbf.diffF-1)
-d = (As<*>Es<+>Ac<*>Ec)
-c = (a<+>b)</>d
-//thermal expansion
-delL = c<*>L<*>delT
-//expansion w.o restraint
-delLc = cc<*>L<*>delT
-delLcs = delLc<->delL
-delLs= cs<*>L<*>delT
-delLsc = delL<->delLs
-//restraining force
-P1 = Ac<*>Ec<*>delLcs</>L
-P2 = As<*>Es<*>delLsc</>L</source>
-'''z3 code: Using Function'''<br>
-<source lang="cpp">
-function civil2(dc,ds,dcs,L){
-var Es = 30e+6(lbf/in2)
-var Ec = 1.03e+11(Pa)
-var cs = 6.5e-6(diffF-1)
-var cc = 9e-6(diffF-1)
-var delT = 44.4(diffC)
-//cross-sectional area
-var A = π<*>(dc)^2</>4
-var As = π<*>(ds)^2</>4
-var Ac = A<->As
-//coeff of expansion
-//c = ((As<*>Es<*>cs)<+>(Ac<*>Ec<*>cc))</>(As<*>Es<+>Ac<*>Ec)
-var a = (As<*>Es<*>cs)
-var b = (Ac<*>Ec<*>cc)<>(lbf.diffF-1)
-var d = (As<*>Es<+>Ac<*>Ec)
-var c = (a<+>b)</>d
-//thermal expansion
-var delL = c<*>L<*>delT
-//expansion w.o restraint
-var delLc = cc<*>L<*>delT
-var delLcs = delLc<->delL
-var delLs= cs<*>L<*>delT
-var delLsc = delL<->delLs
-//restraining force
-var P1 = Ac<*>Ec<*>delLcs</>L
-var P2 = As<*>Es<*>delLsc</>L
-return[P1,P2]
-}
-dc = 12.7(mm)
-ds = (3/8)<>(inch)
-dcs = (1/16)<>(inch)
-L = 1(ft)
-civil2(dc,ds,dcs,L)</source>
-'''z3 code: USING EXAMPLE1 function SOLUTION IN EXAMPLE2 function'''<br>
-<source lang="cpp">
-function civil2(dc,ds,dcs){
-var Es = 30e+6(lbf/in2)
-var Ec = 1.03e+11(Pa)
-var cs = 6.5e-6(diffF-1)
-var cc = 9e-6(diffF-1)
-//cross-sectional area
-var A = π<*>(dc)^2</>4
-var As = π<*>(ds)^2</>4
-var Ac = A<->As
-//coeff of expansion
-//c = ((As<*>Es<*>cs)<+>(Ac<*>Ec<*>cc))</>(As<*>Es<+>Ac<*>Ec)
-var a = (As<*>Es<*>cs)
-var b = (Ac<*>Ec<*>cc)<>(lbf.diffF-1)
-var d = (As<*>Es<+>Ac<*>Ec)
-var c = (a<+>b)</>d
-return[As,Ac,c]
-}
-dc = 12.7(mm)
-ds = (3/8)<>(inch)
-dcs = (1/16)<>(inch)
-civil2(dc,ds,dcs)</source>
-<source lang="cpp">
-function civil3(L,delT){
-var Es = 30e+6(lbf/in2)
-var Ec = 1.03e+11(Pa)
-var cs = 6.5e-6(diffF-1)
-var cc = 9e-6(diffF-1)
-//thermal expansion
-var delL = civil2(dc,ds,dcs)[2]<*>L<*>delT
-//expansion w.o restraint
-var delLc = cc<*>L<*>delT
-var delLcs = delLc<->delL
-var delLs= cs<*>L<*>delT
-var delLsc = delL<->delLs
-//restraining force
-var P1 = civil2(dc,ds,dcs)[1]<*>Ec<*>delLcs</>L
-var P2 = civil2(dc,ds,dcs)[0]<*>Es<*>delLsc</>L
-return [P1,P2]
-}
-L = 1(ft)
-delT = 44.4(diffC)
-civil3(L,delT)</source>
+'''ExampleS4: Civil Engineering<br>'''
+'''NotchDesign'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code4a <span style="color:blue;"> z3 code: Using Function]</span><br>
-'''ExampleS4: Civil Engineering<br>'''
+'''ExampleS5: Engineering Economics<br>'''
-M1 is a 4x4, F = 5500 lb (24,464 N), and Phi = 30°. The allowable compressive
+'''RateOfEarnings'''<br>
-stresses are P = 1200 lb/sq.in. (8274 kPa) and Q = 390 lb/sq.in. (2689.1 kPa). The
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code5a <span style="color:blue;"> z3 code: Using Function]</span><br>
-projection of M1 into M2 is restricted to a vertical distance of 2.5 in. (63.5 mm).
-'''z3 code: Using Function'''<br>
-<source lang="cpp">
-function civil4(){
-var b = 3.625(inch)
-var φ = 30(deg)
-var P = 1200(lbf/sqin)
-var Q = 2689.1e+3(Pa)
-var F = 24464(N)
-var A = 13.1(sqin)
-//lengths
+'''ExampleS6: Fluid Mechanics<br>'''
-var AB = b</>DSIN(φ)
+'''BernoullisPressure'''<br>
-var AC = (b<*>DSIN(φ/2))</>DSIN(φ)
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code6a <span style="color:blue;"> z3 code: Using Function]</span><br>
-var BC = (b<*>DCOS(φ/2))</>DSIN(φ)
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3code6b <span style="color:blue;"> z3 code: Multi-calculation Using Function(variable diameter)]</span><br>
-//stresses f1 and f2
-var f1 = (F<*>DSIN(φ))</>(A<*>DTAN(φ/2))
-var f2 = (F<*>DSIN(φ)<*>DTAN(φ/2))</>(A)
-//allowable stresses
+==Examples of Java and z3 Programs==
-var N1 = P<*>Q</>((P<*>(DSIN(φ/2))^2)<+>Q<*>(DCOS(φ/2))^2)
+'''ExampleR1: Check if number is Odd/Even'''<br>
-var N2 = P<*>Q</>((P<*>(DCOS(φ/2))^2)<+>Q<*>(DSIN(φ/2))^2)
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes1a <span style="color:blue;"> Java code]</span><br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes1b <span style="color:blue;"> z3 code]</span>
-return[AC;BC;f1<>(lbf/sqin);f2<>(lbf/sqin);N1<>Pa;N2<>Pa]
+'''ExampleR2: Sum of a given Array'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes2a <span style="color:blue;"> Java code]</span><br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes2b <span style="color:blue;"> z3 code]</span>
-}
+'''ExampleR3: Linear Search'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes3a <span style="color:blue;"> Java code]</span><br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes3b <span style="color:blue;"> z3 code]</span><br>
+'''ExampleR4: Floyd's Triangle'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes4a <span style="color:blue;"> Java code]</span><br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes4b <span style="color:blue;"> z3 code]</span><br>
-civil4() </source>
+'''ExampleR5: Reverse Number'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes5a <span style="color:blue;"> Java code]</span><br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes5b <span style="color:blue;"> z3 code]</span><br>
+'''ExampleR6: Calculate the Factorial of a number'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes6a <span style="color:blue;"> Java code]</span><br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes6b <span style="color:blue;"> z3 code]</span><br>
+'''ExampleR7: Area of Rectangle'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes7a <span style="color:blue;"> Java code]</span><br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes7b <span style="color:blue;"> z3 code]</span><br>
+'''ExampleR8: Display Prime Numbers'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes8a <span style="color:blue;"> Java code]</span><br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes8b <span style="color:blue;"> z3 code]</span><br>
+'''ExampleR9: Ascending Order'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes9a <span style="color:blue;"> Java code]</span><br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes9b <span style="color:blue;"> z3 code]</span><br>
-'''ExampleS4: Engineering Economics<br>'''
+'''ExampleR10: Inputting Matrix and Calculating it's Inverse'''<br>
-The QRS Corp. purchased capital equipment for use in a 5-year venture. The equipment
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes10a <span style="color:blue;"> Java code]</span><br>
-cost $240,000 and had zero salvage value. If the income tax rate was 52 percent and the
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes10b <span style="color:blue;"> z3 code]</span><br>
-annual income from the investment was $83,000 before taxes and depreciation, what was
-the average rate of earnings if the profits after taxes were invested in tax-free bonds yielding 3 percent? Compare the results obtained when depreciation is computed by the straight-line method.
-'''z3 code: Using Function'''<br>
+'''ExampleR11: Inputting 2 Matrices and Calculating Sum,Difference and Product'''<br>
-<source lang="cpp">
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes11a <span style="color:blue;"> Java code]</span><br>
-function economics(){
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples#z3codes11b <span style="color:blue;"> z3 code]</span><br><br>
-var EC = 240000
-var n = 5
-var GI = 83000
-var r = 0.52
-var i = 0.03
-//taxable income
+==Unit Conversion Examples==
-var DC = EC</>n
+'''ExampleP1: FrictionFactor'''<br>
-var TI = GI<->DC
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3codep1 <span style="color:blue;"> z3 code: Solution with SI units<br> Solution with SI and Imperial units<br> Solution with imperial units<br>]</span><br>
-//annual tax payment
+'''ExampleP2: ReynoldsNumber'''<br>
-var TP = r<*>TI
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3codep2 <span style="color:blue;"> z3 code: Solution with SI units<br> Solution with SI and Imperial units<br> Solution with imperial units<br>]</span><br>
-//net income
+'''ExampleP3: FouriersLaw'''<br>
-var NI = GI<->TP
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3codep3 <span style="color:blue;"> z3 code: Solution with SI units<br> Solution with SI and Imperial units<br> Solution with imperial units<br>]</span><br>
-//S = R(USCA)
-//SPCA = (1<+>i)^n
-var s = NI<*>(5.309)
-var sp = s</>EC
-var i = [(sp^0.2)<->1]<*>100
-return i
+'''ExampleP4: MaximumHeight'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3codep4 <span style="color:blue;"> z3 code: Solution with SI units<br> Solution with SI and Imperial units<br> Solution with imperial units<br>]</span><br>
-}
+'''ExampleP5: DopplerEffect'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3codep5 <span style="color:blue;"> z3 code: Solution with SI units<br> Solution with SI and Imperial units<br> Solution with imperial units<br>]</span><br>
+'''ExampleP6: CircularSegmentArea'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3codep6 <span style="color:blue;"> z3 code: Solution with SI units<br> Solution with SI and Imperial units<br> Solution with imperial units<br>]</span><br>
-economics()</source>
+'''ExampleP7: CoulombsLaw'''<br>
+<span class="plainlinks">[http://wiki.zcubes.com/Manuals/calci/Examples1#z3codep7 <span style="color:blue;">  z3 code: Solution with SI units<br> Solution with SI and Imperial units<br> Solution with imperial units<br>]</span><br><br>