數(shù)學(xué)建模實(shí)習(xí)報(bào)告3

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西北農(nóng)林科技大學(xué)試驗(yàn)報(bào)告

學(xué)院名稱：理學(xué)院姓名：xxx

1試驗(yàn)題目：池水含鹽問題2試驗(yàn)問題陳述：

池中有水2000m3，含鹽2kg，以6m3/min的速率向池中注入濃度為0.5kg/m3的鹽水，又以4m3/min的速率從池中流出混合后的鹽水。假使池中鹽水濃度達(dá)到0.2kg/m時(shí)將注入池中的鹽水改變?yōu)榍逅瑔柡螘r(shí)池中鹽水濃度能夠被稀釋到這個(gè)濃度的50%，即達(dá)到0.1kg/m3？

3試驗(yàn)?zāi)康?

仿真池中鹽水濃度的變化，給出達(dá)到給定濃度的時(shí)間。4試驗(yàn)內(nèi)容:問題分析：池中有鹽水，勻速注入濃鹽水，

勻速流出混合后的鹽水，池中鹽水的濃度變化。變量、參量

時(shí)間t，體積V(t),鹽量S(t),濃度p(t);流入流速rI=6,流入濃度pI=0.5,流出流速rO=4,

改變時(shí)候的鹽水濃度p*=0.2，改變的時(shí)刻t*，終止時(shí)候的鹽水濃度p*=0.1，終止的時(shí)刻t**。時(shí)間步長(zhǎng)Δt,打印步長(zhǎng)T.

在時(shí)間間隔[t,t+Δt]內(nèi)將有如下的轉(zhuǎn)換關(guān)系

3

專業(yè)年級(jí)：2023級(jí)信計(jì)1班

學(xué)號(hào)：xxx

報(bào)告日期：2023年11月23日

課程：數(shù)學(xué)模型與數(shù)學(xué)建模

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（≠0）ind=0表示流入池中的水為清水（pI=0）

在仿真的過程，可以每運(yùn)行m個(gè)時(shí)間步長(zhǎng)打印輸出一次計(jì)算的結(jié)果。

5試驗(yàn)結(jié)果分析與探討:P=

Columns1through9

0.00100.02980.05640.08110.10400.12520.14490.16330.1804

Columns10through11

0.19640.2023P=

Columns1through9

0.00100.02980.05640.08110.10400.16330.1804

Columns10through12

0.19640.20230.1964P=

Columns1through9

0.00100.02980.05640.08110.10400.16330.1804

Columns10through13

0.19640.20230.19640.1928P=

Columns1through9

0.00100.02980.05640.08110.10400.16330.1804

Columns10through14

0.19640.20230.19640.19280.1835P=

Columns1through9

0.12520.14490.12520.14490.12520.1449

0.00100.02980.05640.08110.10400.12520.14490.16330.1804

Columns10through15

0.19640.20230.19640.19280.18350.1748P=

Columns1through9

0.00100.02980.05640.08110.10400.12520.16330.1804

Columns10through16

0.19640.20230.19640.19280.18350.17480.1666P=

Columns1through9

0.00100.02980.05640.08110.10400.12520.16330.1804

Columns10through17

0.19640.20230.19640.19280.18350.17480.1589P=

Columns1through9

0.00100.02980.05640.08110.10400.12520.16330.1804

Columns10through18

0.19640.20230.19640.19280.18350.17480.15890.1516P=

0.14490.14490.16660.14490.1666

Columns1through9

0.00100.02980.05640.08110.10400.12520.14490.16330.1804

Columns10through18

0.19640.20230.19640.19280.18350.17480.16660.15890.1516

Column19

0.1449P=

Columns1through9

0.00100.02980.16330.1804

Columns10through18

0.19640.20230.15890.1516

Columns19through20

0.14490.1385P=

Columns1through9

0.00100.02980.16330.1804

Columns10through18

0.19640.20230.15890.1516

Columns19through21

0.05640.08110.19640.19280.05640.08110.19640.19280.10400.12520.18350.17480.10400.12520.18350.17480.14490.16660.14490.1666

0.14490.13850.1324P=

Columns1through9

0.00100.02980.05640.08110.10400.12520.14490.16330.1804

Columns10through18

0.19640.20230.19640.19280.18350.15890.1516

Columns19through22

0.14490.13850.13240.1268P=

Columns1through9

0.00100.02980.05640.08110.10400.16330.1804

Columns10through18

0.19640.20230.19640.19280.18350.15890.1516

Columns19through23

0.14490.13850.13240.12680.1214P=

Columns1through9

0.00100.02980.05640.08110.10400.16330.1804

Columns10through18

0.17480.16660.12520.14490.17480.16660.12520.1449

0.19640.20230.19640.19280.18350.17480.16660.15890.1516

Columns19through24

0.14490.13850.13240.12680.12140.1163P=

Columns1through9

0.00100.02980.05640.08110.10400.12520.16330.1804

Columns10through18

0.19640.20230.19640.19280.18350.17480.15890.1516

Columns19through25

0.14490.13850.13240.12680.12140.11630.1116P=

Columns1through9

0.00100.02980.05640.08110.10400.12520.16330.1804

Columns10through18

0.19640.20230.19640.19280.18350.17480.15890.1516

Columns19through26

0.14490.13850.13240.12680.12140.11630.1070P=

Columns1through9

0.14490.16660.14490.16660.1116

0.00100.02980.05640.08110.10400.12520.14490.16330.1804

Columns10through18

0.19640.20230.19640.19280.18350.17480.16660.15890.1516

Columns19through27

0.14490.13850.13240.12680.10700.1027a=

02.00002.00000.100020.00002.040060.81012.980940.00002.0800117.39955.644260.00002.1200171.93468.110180.00002.1600224.566310.3966100.00002.2000275.431912.5196120.00002.2400324.656614.4936140.00002.2800372.354716.3313160.00002.3200418.630718.0444180.00002.3600463.580419.6432185.00002.3700474.621020.0262180.00002.3600463.580419.6432200.00002.4000462.815019.2840220.00002.4400447.746718.3503240.00002.4800433.402517.4759260.00002.5200419.736816.6562280.00002.5600406.707315.8870300.00002.6000394.275315.1644320.00002.6400382.404714.4850340.00002.6800371.062213.8456360.00002.7200360.217013.2433380.00002.7600349.840412.6754400.00002.8000339.905712.1395420.00002.8400330.388411.6334440.00002.8800321.265211.1550460.00002.9200312.514810.7026480.00002.9600304.117110.2742494.00002.9880298.43849.9879

0.12140.11630.1116

鹽水濃度變化曲線：

結(jié)論：

需要t1=186分將水池中鹽水濃度從0.001提高到0.2。又需要t2-t1=312分水將池中鹽水濃度從0.2恢復(fù)到0.1。

6試驗(yàn)程序（Matlab或者其它軟件語(yǔ)言陳述）：t=1;v=[2000];s=[2];p=[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(end)];S=[s(end)];P=[p(end)];x=[0];%打印記錄whilep(end)p1;%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(