<html><body><div style="color:#000; background-color:#fff; font-family:lucida console, sans-serif;font-size:14pt"><div><font size="2" face="Arial"><br></font><span><var id="yui-ie-cursor"></var>Hi All,</span></div><div style="font-family: lucida console, sans-serif; font-size: 14pt;"><div style="font-family: times new roman, new york, times, serif; font-size: 12pt;"><div class="y_msg_container"><div id="yiv7093776338"><div><div style="color: rgb(0, 0, 0); font-family: lucida console, sans-serif; font-size: 14pt; background-color: rgb(255, 255, 255);"><div style="color: rgb(0, 0, 0); font-family: lucida console, sans-serif; font-size: 18.66px; font-style: normal; background-color: transparent;"><span><br></span></div><div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal">I humbly seek kind <span> </span>assistance in solving a Simulation Problem (GRAVITY
FLOW TANK) that was initially written <span> </span>with FORTRAN to numerically integrate two ODEs
(to be given below, eqns 1&2).</div>
<div class="yiv7093776338MsoNoSpacing"><b>Gravity-flow tank
data:</b></div>
<div class="yiv7093776338MsoNoSpacing"><i>Pipe:</i></div>
<div class="yiv7093776338MsoNoSpacing">Internal Diameter = 3 ft<span> </span>Area
= 7.06 ft<sup>2<span> </span></sup>Length
= 3000 ft</div>
<div class="yiv7093776338MsoNoSpacing"><i>Tank:</i></div>
<div class="yiv7093776338MsoNoSpacing">Internal Diameter = 12ft<span> </span>Area
= 113 ft<sup>2<span> </span></sup>Height
= 7 ft</div>
<div class="yiv7093776338MsoNoSpacing"><b> </b></div>
<div class="yiv7093776338MsoNoSpacing"><b>Steady State
values:</b></div>
<div class="yiv7093776338MsoNoSpacing">F = 35.1 ft<sup>3</sup>/s (15, 700 gpm)</div>
<div class="yiv7093776338MsoNoSpacing">h = 4.72 ft</div>
<div class="yiv7093776338MsoNoSpacing"><span>υ</span>
= 4.97 ft/s</div>
<div class="yiv7093776338MsoNoSpacing"> </div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal">d<span>υ/dt
= 0.0107h – 0.00205υ<sup>2 </sup>…………………eqn(1)</span></div><div style="text-align: justify; color: rgb(0, 0, 0); font-size: 16.21px; font-style: normal; background-color: transparent;" class="yiv7093776338MsoNormal"><span><br></span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>dh/dt
= 0.311 – 0.0624υ………………………eqn(2)</span></div><div style="text-align: justify; color: rgb(0, 0, 0); font-size: 18.66px; font-style: normal; background-color: transparent;" class="yiv7093776338MsoNormal"><span><br></span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>The
following FORTRAN program numerically integrates the two ODEs describing the
system for two different initial conditions of flow and liquid level in the
tank: (1) when the initial flow rate is 50 percent of the design rate, and (2)
when the initial flow rate is 67 percent of the design flow rate. At time equal
zero, the flow rate into the tank is increased to the maximum design flow rate
of 35.1 ft<sup>3</sup>/s.</span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>Gravity-flow
tank simulation (FORTRAN)</span></div>
<div class="yiv7093776338MsoNoSpacing">C<span> </span><span> </span>(TIME IN SECONDS)</div>
<div class="yiv7093776338MsoNoSpacing">C TWO CASES ARE RUN. AT TIME EQUAL ZERO THE FEED FLOW
RATE IS</div>
<div class="yiv7093776338MsoNoSpacing">C<span> </span><span> </span>INCREASED TO 100% OF THE DESIGN FLOW RATE
(15, 700 GPM)</div>
<div class="yiv7093776338MsoNoSpacing">C<span> </span><span> </span>CASE NO.1 STARTS FROM 67% OF DESIGN FLOW
RATE</div>
<div class="yiv7093776338MsoNoSpacing">C<span> </span><span> </span>CASE NO.2 STARTS FROM 50% OF DESIGN FLOW
RATE</div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>DATA
V1,H1/3.40,2.05/</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>DATA V2,H2/2.50,1.2/</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>DO 200 N=1,2</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>IF(N.=EQ.1)THEN</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>V=V1</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>H=H1</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>ELSE</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>V=V2</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>H=H2</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"></span><span class="yiv7093776338tab"></span><span class="yiv7093776338tab"></span>ENDIF</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>TIME=0.</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>DELTA=1.</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>TPRINT=0.</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>WRITE(6,1)V,H</div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>1
FORMAT(‘INITIAL CONDITIONS: V= ‘,F6.3,’ H=’,F8.3)</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>WRITE(6,2)</div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>2 FORMAT(‘<span> </span>TIME<span> </span>V<span> </span>H’)</div>
<div class="yiv7093776338MsoNoSpacing">C</div>
<div class="yiv7093776338MsoNoSpacing">C EVALUATE DERIVATIVES</div>
<div class="yiv7093776338MsoNoSpacing">C</div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>100
VDOT=0.0107*H-0.00205*V**2</div>
<div class="yiv7093776338MsoNoSpacing"><span>
</span>HDOT=0.311-0.0624*V</div>
<div class="yiv7093776338MsoNoSpacing"><span>
</span>IF(<a href="http://time.lt.tp/" target="_blank">TIME.LT</a>.TPRINT)GO TO 10</div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>WRITE(6,3)TIME,V,H</div>
<div class="yiv7093776338MsoNoSpacing"><span class="yiv7093776338tab"> </span><span class="yiv7093776338tab"> </span>3 FORMAT(3X,3F8.2)</div>
<div class="yiv7093776338MsoNoSpacing"><span>
</span>TPRINT=TPRINT+20.</div>
<div class="yiv7093776338MsoNoSpacing">C</div>
<div class="yiv7093776338MsoNoSpacing">C INTEGRATE USING EULER</div>
<div class="yiv7093776338MsoNoSpacing">C</div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>10 V = V+
VDOT+VDELTA</div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>H=
H+HDOT+DELTA</div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>TIME=TIME+DELTA</div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>IF(TIME.LE.200.)GO
TO 100</div>
<div class="yiv7093776338MsoNoSpacing">200 CONTINUE</div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>STOP </div>
<div class="yiv7093776338MsoNoSpacing"><span> </span>END</div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span> </span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>The
explicit first-order Euler algorithm is used. The variables that we are solving
for as functions of time are V and H. the right-hand sides of eqns (1) and (3)
are the derivative functions. These are called VDOT and HDOT in the program. At
the nth step in time</span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>(VDOT)<sub>n
</sub>= 0.0107(H)<sub>n </sub>– 0.00205[(V)<sub>n</sub>]<sup>2 </sup>…………………………….eqn(3)</span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>(HDOT)<sub>n
</sub>= 0.311 – 0.0624(V)<sub>n</sub>…………………………………….eqn(4)</span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>The
new values of H and V at the (n+1)st step are calculated from the Euler
algorithm with a step size of DELTA.</span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>(H)<sub>n+1
</sub>= (H)<sub>n </sub>+ DELTA(HDOT)<sub>n</sub>……………………………eqn(5)</span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>(V)<sub>n+1
</sub>= (V)<sub>n</sub> +DELTA(VDOT)<sub>n</sub>……………………………eqn(6)</span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>A
plot was equally generated to illustrate the relationship between h, ft and
process time, s.</span></div><div style="text-align: justify; color: rgb(0, 0, 0); font-size: 18.66px; font-style: normal; background-color: transparent;" class="yiv7093776338MsoNormal"><span><br></span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"><span>Thanks
as I anticipate various professional inputs.</span></div>
<div style="text-align: justify;" class="yiv7093776338MsoNormal"> </div>
</div><div>ABDULJELEEL A. OSUNKUNLE<br>SCIENTIFIC OFFICER<br>PROJECTS DEVELOPMENT INSTITUTE, P.M.B. 01609, EMENE INDUSTRIAL LAYOUT, ENUGU, NIGERIA.<br>+2347058408440.</div></div></div></div><br>_______________________________________________<br>users mailing list<br><a href="mailto:users@lists.scilab.org" ymailto="mailto:users@lists.scilab.org">users@lists.scilab.org</a><br><a href="http://lists.scilab.org/mailman/listinfo/users" target="_blank">http://lists.scilab.org/mailman/listinfo/users</a><br><br><br></div> </div> </div> </div></body></html>