41 Cistern Program

[Gerson W. Barbosa]

(08-19-2016 05:03 AM)Gerson W. Barbosa Wrote:  

(08-17-2016 04:51 PM)aurelio Wrote:  Here they take in account also the different shape of the heads, unfortunately not a case of sloped vessels..
This can help of course, but is not actually what we are looking for, cause it is a "on-line" calculation.

The Oil & Gas article has the formulas. For instance, my unoptimized program for the elliptical head case (237 bytes) gives 0.916297857295 m^3 for D=1m, L=2m, a=0.25m and H=0.5m.
No stack-only code this time :-)

(08-19-2016 05:03 AM)Gerson W. Barbosa Wrote:  

(08-17-2016 04:51 PM)aurelio Wrote:  Here they take in account also the different shape of the heads, unfortunately not a case of sloped vessels..
This can help of course, but is not actually what we are looking for, cause it is a "on-line" calculation.

The Oil & Gas article has the formulas. For instance, my unoptimized program for the elliptical head case (237 bytes) gives 0.916297857295 m^3 for D=1m, L=2m, a=0.25m and H=0.5m.
No stack-only code this time :-)

Code:


%%HP: T(3)A(D)F(.);
\<< \-> L D a h
  \<< 'SQ(D)/4.*(L*(IM(ACOSH(1.-2.*h/D))-2./D*(1.-2.*h/D)*\v/(h*(D-h)))+2.*a*\pi/D*(h+4./(3.*SQ(D))*(D/2.-h)^3.-D/6.))' EVAL
  \>>
\>>

Fill the stack with L, D, a, h. For a spherical tank, just make L=0 and a = D/2 (for instance, L=0, D=4, a=2 and h=4 --> a full spherical tank).

This can be simplified as

Code:



%%HP: T(3)A(D)F(.);
\<< \-> L D a h
  \<< 'SQ(D)/4.*L*IM(ACOSH(1.-2.*h/D))+\pi*a*SQ(h)*(1.-2.*h/(3.*D))+L*\v/(h*(D-h))*(h-D/2.)' EVAL
  \>>
\>>

The angle mode is irrelevant on the HP 50g if IM(ACOSH) is used instead of ACOS. Size has now been reduced to 191 bytes.

2 1 0.25 0.5 --> 0.916297857295

0 4 2 4 --> 33.5103216383 (32*π/3)

0 4 2 2 -->16.7551608191 (16*π/3)

Is the latter half full or half empty? :-)

----------------------------------------------------------------------------------------




\(V= L\left [ \frac{D^{2}}{4}\cos^{-1}\left ( 1-\frac{2h}{D} \right )+ \sqrt{h\left ( D-h \right )}\left ( h-\frac{D}{2} \right ) \right ] +\pi a h^{2}\left ( 1-\frac{2h}{3D} \right )\)

Edited to include diagram and equation