MaplePrimes - Questions and Posts tagged with model
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en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 16 Sep 2014 23:29:57 GMTTue, 16 Sep 2014 23:29:57 GMTThe most recent questions and posts on MaplePrimes tagged with modelhttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with model
http://www.mapleprimes.com/tags/model
Plotting a parameter function another parameter
http://www.mapleprimes.com/questions/200172-Plotting-A-Parameter-Function-Another-Parameter?ref=Feed:MaplePrimes:Tagged With model
<p>Hello,</p>
<p>I study the model of crankshaft in MapleSim.</p>
<p>For the moment, i manage to plot different parameters function of the time. For exemple, the angle of the crank function of the time or the displacement of the slider function of the time.</p>
<p>But, i like to plot the displacement of the slider funtion of the angle of the crank.</p>
<p>Is it possible and how can i do this?</p>
<p>Thank you for your help.</p><p>Hello,</p>
<p>I study the model of crankshaft in MapleSim.</p>
<p>For the moment, i manage to plot different parameters function of the time. For exemple, the angle of the crank function of the time or the displacement of the slider function of the time.</p>
<p>But, i like to plot the displacement of the slider funtion of the angle of the crank.</p>
<p>Is it possible and how can i do this?</p>
<p>Thank you for your help.</p>200172Sun, 10 Nov 2013 11:36:24 ZBendesartsBendesartsChange the unit in a plot made with a probe
http://www.mapleprimes.com/questions/153073-Change-The-Unit-In-A-Plot-Made-With-A-Probe?ref=Feed:MaplePrimes:Tagged With model
<p>Hello,</p>
<p>It's a very easy question but i don't find for the moment.</p>
<p>I want to measure an angle in a revolute joint. For that purpose, i use a probe to measure the angle. The angle is measured in rad. How can i do to change in deg ?</p>
<p>Thank you for your help.</p><p>Hello,</p>
<p>It's a very easy question but i don't find for the moment.</p>
<p>I want to measure an angle in a revolute joint. For that purpose, i use a probe to measure the angle. The angle is measured in rad. How can i do to change in deg ?</p>
<p>Thank you for your help.</p>153073Thu, 17 Oct 2013 11:34:39 ZBendesartsBendesartsChange the unit in a plot made with a probe
http://www.mapleprimes.com/questions/153053-Change-The-Unit-In-A-Plot-Made-With-A-Probe?ref=Feed:MaplePrimes:Tagged With model
<p>Hello,</p>
<p>It's a very easy question but i don't find for the moment.</p>
<p>I want to measure an angle in a revolute joint. For that purpose, i use a probe to measure the angle. The angle is measured in rad. How can i do to change in deg ?</p>
<p>Thank you for your help.</p><p>Hello,</p>
<p>It's a very easy question but i don't find for the moment.</p>
<p>I want to measure an angle in a revolute joint. For that purpose, i use a probe to measure the angle. The angle is measured in rad. How can i do to change in deg ?</p>
<p>Thank you for your help.</p>153053Thu, 17 Oct 2013 00:31:10 ZBendesartsBendesartsGHR car following model
http://www.mapleprimes.com/questions/148823-GHR-Car-Following-Model?ref=Feed:MaplePrimes:Tagged With model
<p>The general formula of GHR (Gazis-Herman-Rothery), the most well known car following model, is given by</p>
<p><img src="http://demonstrations.wolfram.com/GazisHermanRotheryGHRCarFollowingModel/HTMLImages/index.en/1.gif" alt="" align="absmiddle"></p>
<p>an - acceleration of vehicle n implemented at time t<br>v - speed of follower vehicle<br>deltax and deltav - relative spacing and speeds respectively between follower and leader vehicle at a <br>  ...<p>The general formula of GHR (Gazis-Herman-Rothery), the most well known car following model, is given by</p>
<p><img src="http://demonstrations.wolfram.com/GazisHermanRotheryGHRCarFollowingModel/HTMLImages/index.en/1.gif" alt="" align="absmiddle"></p>
<p>an - acceleration of vehicle n implemented at time t<br>v - speed of follower vehicle<br>deltax and deltav - relative spacing and speeds respectively between follower and leader vehicle at a <br> previous time (t-tau), and tau is driver reaction time<br>m, l and c - constants to be determined.</p>
<p>If we use Chandlers (1958) values for the constants, m=l=0 and the sensitivity constant c proposed at 0.37 sec<sup>-1</sup> and also for the time lag (tau) they recommended 1.5 sec.</p>
<p>How can we graph the velocity vs time for 10 cars?</p>148823Tue, 25 Jun 2013 17:43:45 ZChristopher2222Christopher2222DirectSearch optimization package
http://www.mapleprimes.com/questions/145155-DirectSearch-Optimization-Package?ref=Feed:MaplePrimes:Tagged With model
<p>Hi,</p>
<p>I'm using the DirectSearch package in a 10 periods model and in the first period i get this values:</p>
<pre>"</pre>
<pre>> DirectSearch[SolveEquations](sys, assume = positive);<br>Warning, complex or non-numeric value encountered; trying to find a feasible point<br> [HFloat(1.1842542076623546e-32), <br><br> Vector[column](%id = 18446744078126621390), [<br><br> x1a = HFloat(4204.651582462925), <br><br> x1c = HFloat(4204.651582462925), </pre><p>Hi,</p>
<p>I'm using the DirectSearch package in a 10 periods model and in the first period i get this values:</p>
<pre>"</pre>
<pre>> DirectSearch[SolveEquations](sys, assume = positive);<br>Warning, complex or non-numeric value encountered; trying to find a feasible point<br> [HFloat(1.1842542076623546e-32), <br><br> Vector[column](%id = 18446744078126621390), [<br><br> x1a = HFloat(4204.651582462925), <br><br> x1c = HFloat(4204.651582462925), <br><br> x2a = HFloat(1787.760621851102), <br><br> x2c = HFloat(1787.7606218511032)], 392]</pre>
<pre>"</pre>
<p>How can i define (in which command...) the values of the first period of x1a. x2a,x1c,x2c as the starting point (inventory in my case) of the second period. in other words. i would to define x1a2=4204.651+x1a1 (. noticed that x1a=4204.651 according to results of the package) without using Ctrl c - Ctrlv command...</p>
<p>Thanks</p>
<p> </p>
<p>Gil</p>
<p> </p>
<p>where the values the i get from the </p>145155Wed, 27 Mar 2013 13:24:38 ZgilpgilpModel the Human hand constraining the fingers to a cerain range of angles
http://www.mapleprimes.com/questions/142671-Model-The-Human-Hand-Constraining-The?ref=Feed:MaplePrimes:Tagged With model
<p>I am new to maplesim. I want to model the human hand and constrain the fingers to a certain range of angle. Then apply a controller to analyse its controllability and also see the dynamic equation formulation</p><p>I am new to maplesim. I want to model the human hand and constrain the fingers to a certain range of angle. Then apply a controller to analyse its controllability and also see the dynamic equation formulation</p>142671Sun, 27 Jan 2013 03:58:00 ZKennaKennaHow to plot multiple data points
http://www.mapleprimes.com/questions/141436-How-To-Plot-Multiple-Data-Points?ref=Feed:MaplePrimes:Tagged With model
<p>Hi</p>
<p>I am trying to model the change in lifetime versus mass and have the formula;</p>
<pre>> T := 6.58*10^38*10^(-25)/x^3;<br> <br>> plot(T, x = 10^10, 10^9, 10^8, 10^7, 10^6, 10^5, 10^4, 10^3, 10^2, 10, 10^0);<br>Error, (in plot) unexpected options: [x = 10000000000, 1000000000, 100000000, 10000000, 1000000, 100000, 10000, 1000, 100, 10, 1]</pre>
<pre>I want to plot for values between x=10^-11 and 0, i have this error and i am not sure why.</pre><p>Hi</p>
<p>I am trying to model the change in lifetime versus mass and have the formula;</p>
<pre>> T := 6.58*10^38*10^(-25)/x^3;<br> <br>> plot(T, x = 10^10, 10^9, 10^8, 10^7, 10^6, 10^5, 10^4, 10^3, 10^2, 10, 10^0);<br>Error, (in plot) unexpected options: [x = 10000000000, 1000000000, 100000000, 10000000, 1000000, 100000, 10000, 1000, 100, 10, 1]</pre>
<pre>I want to plot for values between x=10^-11 and 0, i have this error and i am not sure why.</pre>141436Thu, 13 Dec 2012 22:44:47 ZgdoggdogCorrelation coefficient for system of nonlinear differential equations and data
http://www.mapleprimes.com/questions/141392-Correlation-Coefficient-For-System-Of?ref=Feed:MaplePrimes:Tagged With model
<p> </p>
<p>Hey guys..</p>
<p>I need some help on determining the correlation coefficient between my data points for an Influenza epidemic and the SIR model, with my estimated parameters Beta and Alpha. The initial conditions for the equations are defined at the beginning of my worksheet:</p>
<p><a href="/ViewTemp.ashx?f=165695_1355340339/SIR_model.mw">SIR_model.mw</a></p>
<p>Hope someone can help me ;)</p>
<p> </p>
<p> </p>
<p> </p><p> </p>
<p>Hey guys..</p>
<p>I need some help on determining the correlation coefficient between my data points for an Influenza epidemic and the SIR model, with my estimated parameters Beta and Alpha. The initial conditions for the equations are defined at the beginning of my worksheet:</p>
<p><a href="/view.aspx?sf=141392/449872/SIR_model.mw">SIR_model.mw</a></p>
<p>Hope someone can help me ;)</p>
<p> </p>
<p> </p>
<p> </p>141392Thu, 13 Dec 2012 00:35:44 ZkierstejnkierstejnSimulate Cutting a Rope
http://www.mapleprimes.com/questions/140946-Simulate-Cutting-A-Rope?ref=Feed:MaplePrimes:Tagged With model
<p>I have modeled something like a rope attached to a fixed frame at both ends. Is there a way to detach one end of the rope from the fixed frame during a simulation? Is there a better way to go about this? I want to be able to release one end of the rope during the simulation.</p>
<p>Any advice or thoughts will help.</p>
<p>Thanks </p><p>I have modeled something like a rope attached to a fixed frame at both ends. Is there a way to detach one end of the rope from the fixed frame during a simulation? Is there a better way to go about this? I want to be able to release one end of the rope during the simulation.</p>
<p>Any advice or thoughts will help.</p>
<p>Thanks </p>140946Thu, 29 Nov 2012 07:46:09 Zkarishanson22karishanson22Zemax integration with MapleSim
http://www.mapleprimes.com/questions/139378-Zemax-Integration-With-MapleSim?ref=Feed:MaplePrimes:Tagged With model
<p>Hi,</p>
<p>I was just curious if MapleSim has integration capability with <a href="http://www.radiantzemax.com/">Zemax</a>.</p>
<p>I'm interested in creating a dynamic electro-mechanical model (i.e. optical imaging on a moving system):</p>
<p>Zemax <--> MapleSim</p>
<p>If there isn't a toolbox yet, is there a workaround?</p>
<p> </p>
<p>Thank you again!</p><p>Hi,</p>
<p>I was just curious if MapleSim has integration capability with <a href="http://www.radiantzemax.com/">Zemax</a>.</p>
<p>I'm interested in creating a dynamic electro-mechanical model (i.e. optical imaging on a moving system):</p>
<p>Zemax <--> MapleSim</p>
<p>If there isn't a toolbox yet, is there a workaround?</p>
<p> </p>
<p>Thank you again!</p>139378Fri, 09 Nov 2012 10:28:12 Zrwong1231rwong1231modelling of pile foundations
http://www.mapleprimes.com/questions/138834-Modelling-Of-Pile-Foundations?ref=Feed:MaplePrimes:Tagged With model
<p>I am writing to request some general opinion/support. I’m new to Maple and I’m interested in analysing a pile foundation (long steel pipe driven into the ground). The pile is normally modelled as a series of masses interconnected by straight elements and the soil surrounding the pile is modelled as a series of non-linear springs acting on each of the masses.</p>
<p>I would like to know if this is something that can be done in Maple or if MapleSim is needed.<p>I am writing to request some general opinion/support. I’m new to Maple and I’m interested in analysing a pile foundation (long steel pipe driven into the ground). The pile is normally modelled as a series of masses interconnected by straight elements and the soil surrounding the pile is modelled as a series of non-linear springs acting on each of the masses.</p>
<p>I would like to know if this is something that can be done in Maple or if MapleSim is needed.</p>
<p>Thanks!</p>
<p>Cesar</p>138834Fri, 26 Oct 2012 14:50:42 Zcesar torrescesar torresPhase change
http://www.mapleprimes.com/questions/138417-Phase-Change?ref=Feed:MaplePrimes:Tagged With model
<p>Hi everybody,</p>
<p>Does somebody has an idea about how to model the temperature of water during freezing ?</p>
<p>I mean, if you consider a certain mass of water and you put it, for example on a fridge. I don't consider the convection but only the diffusion, and I would like to model, if possible with an animation the temperature of the water (as a cube for the shape).</p>
<p>Normally, during the freezing I should observe a decrease of the temperature, then a freezing...<p>Hi everybody,</p>
<p>Does somebody has an idea about how to model the temperature of water during freezing ?</p>
<p>I mean, if you consider a certain mass of water and you put it, for example on a fridge. I don't consider the convection but only the diffusion, and I would like to model, if possible with an animation the temperature of the water (as a cube for the shape).</p>
<p>Normally, during the freezing I should observe a decrease of the temperature, then a freezing at constant temperature, and finally again a ccoling of the ice. During the freezing, the temperature of the water stay constant but it also release heat (latent enthalpie), so the air just around the cube is for a moment higer.</p>
<p>My idea was to work with one cube (let say a square initially) into a other cube (air of the fridge) and model the temperature change in the smallest cube. The temperature of the air is constant initially (and the animation shows the decrease of temperature in the water square) until the release of energy during freezing (Then the fridge evacuate this energy) and at the end everything is at the same temperature and stable.</p>
<p>Any ideas or advices to solve this ?</p>
<p> </p>
<p>Thanks in advance,</p>
<p> </p>
<p>Lisa</p>138417Wed, 17 Oct 2012 18:37:43 Zlisa1301lisa1301Model Spiderweb in MapleSim
http://www.mapleprimes.com/questions/137976-Model-Spiderweb-In-MapleSim?ref=Feed:MaplePrimes:Tagged With model
<p>I have been messing around with MapleSim for a while now, and I cannot find a good way to model something such as a spiderweb. I want to be able to model a spiderweb (using something like cables), and then measure the tension in the cables, and also vibrations as they travel through the cables. Is this something that I can accomplish using MapleSim? If so, what is the best way to approach this problem? Any suggestions or comments would be helpful. Thanks. </p><p>I have been messing around with MapleSim for a while now, and I cannot find a good way to model something such as a spiderweb. I want to be able to model a spiderweb (using something like cables), and then measure the tension in the cables, and also vibrations as they travel through the cables. Is this something that I can accomplish using MapleSim? If so, what is the best way to approach this problem? Any suggestions or comments would be helpful. Thanks. </p>137976Fri, 05 Oct 2012 00:47:42 Zkarishanson22karishanson22Linear Population Models
http://www.mapleprimes.com/questions/137681-Linear-Population-Models?ref=Feed:MaplePrimes:Tagged With model
<p>I am trying to plot a Linear Population Model using Maple, could anybody tell me what I am doing wrong. My plot is just registering as a straight line at 1.0 and I know this is incorrect.</p>
<p>> <p>I am trying to plot a Linear Population Model using Maple, could anybody tell me what I am doing wrong. My plot is just registering as a straight line at 1.0 and I know this is incorrect.</p>
<p>> <img src="data:image/png;base64,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" alt=""><br> <br>> N0 := 1;<br> <br>> r := 10;<br> <br>> plot(N(t), t = 0 .. 100);</p>
<p> </p>
<p>Thanks :)<br><br></p>137681Tue, 25 Sep 2012 14:16:47 ZChrissieh18Chrissieh18Modelling Flow Inertia in Three Coupled Liquid Tanks
http://www.mapleprimes.com/maplesoftblog/136969-Modelling-Flow-Inertia-In-Three-Coupled?ref=Feed:MaplePrimes:Tagged With model
<p><strong>1 Introduction</strong></p>
<p>Three tanks are connected with two pipes. Each tank is initially filled to a different level. A valve in each pipe opens, and the liquid levels gradually reach equilibrium. Here, we model the system in MapleSim (including the influence of flow inertia), and also derive and solve the analytical equations in Maple.</p>
<p><a href="/view.aspx?sf=136969/442080/tank1.png"></a><p><strong>1 Introduction</strong></p>
<p>Three tanks are connected with two pipes. Each tank is initially filled to a different level. A valve in each pipe opens, and the liquid levels gradually reach equilibrium. Here, we model the system in MapleSim (including the influence of flow inertia), and also derive and solve the analytical equations in Maple.</p>
<p><a href="/view.aspx?sf=136969/442080/tank1.png"><img style="display: block; margin-left: auto; margin-right: auto;" src="/view.aspx?sf=136969/442080/tank1.png" alt="" width="543" height="211"></a></p>
<p>Liquid inertia is significant for high liquid densities, high flowrates, and large pipe diameters. This will affect the flow dynamics in the coupled tank system, and can result in oscillating flow as liquid sloshes back and forth between the tanks.</p>
<p>Section 2 demonstrates the modelling approach in MapleSim, while Section 3 derives the analytical system equations. Section 4 offers download links for a Maple worksheet (which solves the analytical equations) and a MapleSim model of the system.</p>
<p><strong>2 Modeling the Coupled Tank System in MapleSim</strong></p>
<p>MapleSim’s Circular Pipe simulates frictional pressure drop with Darcy’s equation, but only applies to equilibrium flow. Flow inertia results in an additional pressure drop.</p>
<p>Consider one of the connecting pipes. The net force ΔF acting on the liquid in the pipe is given by Newton’s Second Law. </p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic2a.jpg"><img src="/view.aspx?sf=136969/442061/pic2a.jpg" alt=""></a></p>
<p>These additional relationships also apply.</p>
<p style="text-align: right;"><strong><a href="/view.aspx?sf=136969/442061/pic3a.jpg"><img src="/view.aspx?sf=136969/442061/pic3a.jpg" alt=""></a></strong></p>
<p>ΔP is the pressure drop across the pipe, A and L are the cross-sectional area and length of the pipe, ρ is the liquid density, and Q is the volumetric flowrate.</p>
<p>Substituting equations 2.2, 2.3 and 2.4 into 2.1 gives the following equation for the pressure drop across the pipe due to fluid inertia.</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic4.JPG"><img src="/view.aspx?sf=136969/442061/pic4.JPG" alt=""></a></p>
<p>This is the equation used in MapleSim’s Fluid Inertia block. This block will be used to model the inertial effects of flow in the coupled tank system.</p>
<p><a href="/view.aspx?sf=136969/442083/figure_2.png"><img style="display: block; margin-left: auto; margin-right: auto;" src="/view.aspx?sf=136969/442083/figure_2.png" alt=""></a></p>
<p>A pipeline with resistive and inertial properties can be modelled by connecting the Circular Pipe and Fluid Inertia components together, as demonstrated in Figure 3.</p>
<p><a href="/view.aspx?sf=136969/442085/figure_3.png"><img style="display: block; margin-left: auto; margin-right: auto;" src="/view.aspx?sf=136969/442085/figure_3.png" alt=""></a></p>
<p>The total pressure drop is hence the sum of the frictional pressure drop and inertial pressure drop.</p>
<p>MapleSim does not have a tank component, but a simple model can be developed. The pressure at the bottom of the tank and the height of liquid in the tank are given by these equations</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic7.JPG"><img src="/view.aspx?sf=136969/442061/pic7.JPG" alt=""></a></p>
<p>where g is the gravitational constant. Figure 4 demonstrates how equations 2.6 and 2.7 are implemented in a Custom Component.</p>
<p><a href="/view.aspx?sf=136969/442085/figure_4.png"><img style="display: block; margin-left: auto; margin-right: auto;" src="/view.aspx?sf=136969/442085/figure_4.png" alt=""></a> </p>
<p>The simple tank equations allow the liquid height to fall below 0 or rise indefinitely. A more complex model would limit the minimum and maximum liquid heights.</p>
<p>This is the completed tank component in MapleSim.</p>
<p><a href="/view.aspx?sf=136969/442085/Figure_5.png"><img style="display: block; margin-left: auto; margin-right: auto;" src="/view.aspx?sf=136969/442085/Figure_5.png" alt=""></a></p>
<p>The top connector outputs the liquid height as a signal. The connector on the bottom right is a hydraulic connector, and has pressure and flowrate mapped to it.</p>
<p>The entire model can now be assembled in MapleSim like so.</p>
<p><a href="/view.aspx?sf=136969/442085/Figure_6.png"><img style="display: block; margin-left: auto; margin-right: auto;" src="/view.aspx?sf=136969/442085/Figure_6.png" alt=""></a></p>
<p><strong>3 Theoretical Analysis of Coupled Tank System</strong></p>
<p>Consider the pipe connecting tanks 1 and 2. The pressure drop across the pipe is</p>
<p><a href="/view.aspx?sf=136969/442061/pic11.JPG"><img style="float: right;" src="/view.aspx?sf=136969/442061/pic11.JPG" alt=""></a></p>
<p> </p>
<p> </p>
<p>where P<sub>1</sub>(t) and P<sub>2</sub> (t) are the pressures at the bottom of tanks 1 and 2, V<sub>12</sub>(t) is the liquid velocity, f is the friction factor, ρ is the liquid density, L<sub>p</sub> is the length of the pipe, and D<sub>p</sub> is the pipe diameter. The term associated with f is the pressure loss due to friction.</p>
<p>At the pipe inlet at the bottom of tank 1, the pressure is</p>
<p style="text-align: right;"><strong><a href="/view.aspx?sf=136969/442061/pic12.JPG"><img src="/view.aspx?sf=136969/442061/pic12.JPG" alt=""></a></strong></p>
<p> At the pipe inlet at the bottom of tank 2, the pressure is</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic13.JPG"><img src="/view.aspx?sf=136969/442061/pic13.JPG" alt=""></a></p>
<p>Substituting equations 3.2 and 3.3 into equation 3.1 gives</p>
<p><a href="/view.aspx?sf=136969/442061/pic14.JPG"><img style="float: right;" src="/view.aspx?sf=136969/442061/pic14.JPG" alt=""></a></p>
<p> </p>
<p> </p>
<p>If the mass of liquid in the pipe is m, the net force on the liquid in the pipe is</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic15.JPG"><img src="/view.aspx?sf=136969/442061/pic15.JPG" alt=""></a></p>
<p>The force and the mass are also given by</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic16.JPG"><img src="/view.aspx?sf=136969/442061/pic16.JPG" alt=""></a></p>
<p> Substituting equations 3.6 and 3.7 into equation 3.5 gives</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic17.JPG"><img src="/view.aspx?sf=136969/442061/pic17.JPG" alt=""></a></p>
<p>Substituting equation 3.8 into equation 3.4 gives</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic18.JPG"><img src="/view.aspx?sf=136969/442061/pic18.JPG" alt=""></a></p>
<p>Recasting equation 3.9 in terms of the volumetric flowrate gives</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic19.JPG"><img src="/view.aspx?sf=136969/442061/pic19.JPG" alt=""></a></p>
<p>The cross-sectional area of the pipe is </p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic20.JPG"><img src="/view.aspx?sf=136969/442061/pic20.JPG" alt=""></a></p>
<p>Substituting 3.11 into 3.10 gives</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic21.JPG"><img src="/view.aspx?sf=136969/442061/pic21.JPG" alt=""></a></p>
<p>Note the <a href="/view.aspx?sf=136969/442061/q.JPG"><img src="/view.aspx?sf=136969/442061/q.JPG" alt=""></a> term associated with the frictional pressure loss. This should act in the opposing direction to flow. To model this, the equation is rewritten</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic22.JPG"><img src="/view.aspx?sf=136969/442061/pic22.JPG" alt=""></a></p>
<p> A similar analysis gives the following equation for the flow between tanks 2 and 3.</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic23.JPG"><img src="/view.aspx?sf=136969/442061/pic23.JPG" alt=""></a></p>
<p>The rates of change of liquid height in each tank are given by</p>
<p style="text-align: right;"><a href="/view.aspx?sf=136969/442061/pic24.JPG"><img src="/view.aspx?sf=136969/442061/pic24.JPG" alt=""></a></p>
<p>where the cross-sectional area of each tank is A<sub>1­</sub>, A<sub>2</sub> and A<sub>3</sub>, and the liquid height in each tank is h<sub>1</sub>(t), h<sub>2</sub>(t) and h<sub>3</sub>(t).</p>
<p>Given a suitable set of initial conditions and parameter values, equations 3.13, 3.14, 3.15, 3.16 and 3.17 can be solved with Maple.</p>
<p>A correlation for f is needed; MapleSim uses the Haaland correlation.</p>
<p><strong>4 MapleSim Model and Maple Worksheet of Coupled Tank System</strong></p>
<p>Here are download links for a Maple worksheet and MapleSim model of the coupled tank system, each with the same parameters values. Both approaches give the same results.</p>
<p><a href="/view.aspx?sf=136969/442085/Figure_7.png"><img style="display: block; margin-left: auto; margin-right: auto;" src="/view.aspx?sf=136969/442085/Figure_7.png" alt=""></a></p>
<p><strong>Download Maple worksheet for the coupled tank system</strong></p>
<p><strong></strong><a href="/view.aspx?sf=136969/442088/Coupled_Tank_Syste.mw">Coupled_Tank_System.mw</a></p>
<p><strong>Download MapleSim modelfor the coupled tank system</strong></p>
<p><strong></strong><a href="/view.aspx?sf=136969/442061/FlowDynamics.msim">Coupled Tank System.msim</a></p>136969Fri, 31 Aug 2012 03:42:55 ZSamir KhanSamir Khan