池水含鹽問題

1、歡迎閱讀西北農(nóng)林科技大學(xué)實(shí)驗(yàn)報(bào)告學(xué)院名稱：理學(xué)院專業(yè)年級：2011級信計(jì)1班姓名：學(xué)號：課程：數(shù)學(xué)模型與數(shù)學(xué)建模報(bào)告日期：2013年11月23日1實(shí)驗(yàn)題目：池水含鹽問題/ I I異字2實(shí)驗(yàn)問題陳述：池中有鹽水2000m 3，含鹽2kg，以6珞分的速率向池中注入濃度 0.5kg/m3的鹽水，又以40/分的速率從池中流出混合后的鹽水。 如果池中鹽水濃度達(dá) 到0.2kg/m3時(shí)，將注入池中的鹽水改變?yōu)榍逅?，問何時(shí)池中鹽水的濃度能夠被稀釋* j |到這個(gè)濃度的50%即達(dá)到0.1kg/m3？3實(shí)驗(yàn)?zāi)康模悍抡娉刂宣}水濃度的變化，給出池中鹽水達(dá)到設(shè)定濃度的時(shí)間。4實(shí)驗(yàn)內(nèi)容：使用步長法仿真系統(tǒng)，令t為仿真時(shí)鐘

2、，需要將整個(gè)仿真的時(shí)間過程用 一系列離散的時(shí)間點(diǎn)t0=0V<< tnV分成許多相等的時(shí)間間隔titi+1,其中 t= ti+1 -t i就是時(shí)間步長。根據(jù)問題要求，在時(shí)間間隔t i, t i+1 作如下轉(zhuǎn)換：/' I,'V(t+ )“(+(j-r0)AtS(t+ t)=S(t)+ripi-r °p(t) tp(t+ H)=S( t+ )"( t+ t)考慮到系統(tǒng)運(yùn)行過程中輸入?yún)?shù)的變化，設(shè)置指標(biāo)ind來標(biāo)志輸入條件的轉(zhuǎn)換，令ind=1表示輸入池中鹽水的濃度為 Pi (工0) , ind=0表示流入池中的水為清水(p-0),在仿真的過程，可以每運(yùn)行

3、 m個(gè)時(shí)間步長打印輸出一次計(jì)算的結(jié)果。輸入條件改變的系統(tǒng)流程圖運(yùn)行程序一，那么可以得到結(jié)果：歡迎閱讀P=0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.1964P=0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.19640.1928P=I *1 IF I* !|0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.19640.19280.1

4、835P=0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.1964i I0.19280.18350.1748P=廠I,0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.19640.19280.18350.17480.1666L / '| I 4P =I I=0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.1964I I0.192

5、80.18350.17480.16660.1589P=0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.19640.19280.18350.17480.16660.15890.1516P=0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.19640.19280.18350.17480.16660.15890.15160.1449P=歡迎閱讀0.00100.02980.05640.08110.10400.12520.14490

6、.16330.18040.19640.20030.19640.19280.18350.17480.16660.15890.15160.14490.1385P=0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.19640.19280.18350.17480.16660.15890.15160.14490.13850.1324P=、,/ Ir I* I I0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.1964'l I

7、 .1 II I0.19280.18350.17480.16660.15890.15160.14490.13850.13240.1268運(yùn)行程序二可以得到結(jié)果：P=i IColu mn s1through220.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.19640.19280.18350.17480.16660.15890.15160.14490.13850.13240.1268Colum n23L / '| I 40.12143 ti I jf ZP=I Ii IColu mn s1throug

8、h220.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.19640.19280.18350.17480.16660.15890.15160.14490.13850.13240.1268Colum ns23through240.12140.1163P=Colu mn s1through220.19280.18350.17480.16660.15890.15160.14490.13850.13240.1268Colum ns23through250.12140.11630.1116P=Colu mn s1thro

9、ugh22i z It i y* /i i0.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20030.1964'l I .1 II I0.19280.18350.17480.16660.15890.15160.14490.13850.13240.1268Colum ns23through260.12140.11630.11160.1070i IP=Colu mn s1through220.00100.02980.05640.08110.10400.12520.14490.16330.18040.19640.20

10、030.19640.19280.18350.17480.16660.15890.15160.14490.13850.13240.1268L / 'I I 心Colum ns23through270.12140.11630.11160.10700.1027I II ja=02.00002.00000.100020.00002.040060.81012.980940.00002.0800117.39955.644260.00002.1200171.93468.110180.00002.1600224.566310.3966100.00002.2000275.431912.5196 120.

11、00002.2400324.656614.4936歡迎閱讀140.00002.2800372.354716.3313160.00002.3200418.630718.0444180.00002.3600463.580419.6432185.00002.3700474.621020.0262180.00002.3600463.580419.6432200.00002.4000462.815019.2840、*/ III I220.00002.4400447.746718.3503Vil T240.00002.4800433.402517.47591/ f 1-.,260.00002.520041

12、9.736816.6562280.00002.5600406.707315.8870300.00002.6000394.275315.1644320.00002.6400382.404714.4850340.00002.6800371.062213.8456360.00002.7200360.217013.2433L / 'I I 心380.00002.7600349.840412.6754, I400.00002.8000339.905712.1395I I420.00002.8400330.388411.6334440.00002.8800321.265211.1550460.00

13、002.9200312.514810.7026480.00002.9600304.117110.2742494.00002.9880298.43849.9879可以得到鹽水濃度變化曲線：由此可以得到結(jié)論：需要t1=186分將水池中鹽水濃度從0.00提高到0.2。又需要t2-11=312分水將池中鹽水濃度從 0.2恢復(fù)到0.1。歡迎閱讀6實(shí)驗(yàn)程序(Matlab或者其它軟件語言陳述)程序一：t=1;v二2000;s二2;p二1/1000;%初始狀態(tài)ri=6;ro=4;po=0.5;p1=0.2;p2=0.1;% 參數(shù)V=v(e nd);S=s(e nd);P=p(e nd);x=0;%打印記錄wh

14、ilep(end)vp1%調(diào)整輸入前動(dòng)態(tài)t=t+1;%時(shí)鐘步進(jìn)v=v,1;s=s,1;p=p,0;%變量步進(jìn)v(t)=v(t-1)+ri-ro;s(t)=s(t-1)+ri*po-ro*p(t-1);p(e nd)二s(e nd)/v(e nd);%仿真計(jì)算end;i It仁t-1;%調(diào)整輸入時(shí)間fork=1:floor(t1/20);% 打印結(jié)果x=x,20*k;V=V,v(20*k+1);S=S,s(20*k+1);P=P,p(20*k+1); _!end廠 y 'O I |4程序二：iffloor(t1/20)<t1/20I Ix=x,t1;V=V,v(e nd);S=S,s(e nd);P=P,p(e nd);endpo=0;%調(diào)整輸入whilep(end)>=p2% 調(diào)整后動(dòng)態(tài)t=t+1;%時(shí)鐘步進(jìn)v=v,1;s=s,1;p=p,0;% 變量步進(jìn)v(t)=v(t-1)+ri-ro;s(t)=s(t-1)+ri*po-ro*p(t-1);p(e nd)二s(e nd)/v(e nd);% 仿真計(jì)算歡迎閱讀end;t