/* 
**	tanks.eu	: A program to solve the Tank leackage problem
**	Assumptions: inner_tank has a leaking point higher than the outer
**		tank overflow level
**
**	To solve user query
**		?- solve_problem(H,Hi,Sl,Ri,Ro,Ho,G,DVi,Hfi,Hfo).
**	Or just
**		?- solve_problem.
**
**	Needs cleaning up
**
**	Copyright (C) 1995 K J Dryllerakis - ALL RIGHTS RESERVED
**	
**	$Id: tanks.eu,v 1.3 1995/03/24 15:43:29 kd Exp kd $
*/

/*  
**	inner_tank(?[Leakage_Height,Leackage_Surface,LiqHeight,Radius_of_tank],
**		?Liquid_height_function,dV/dt_out)
**			If we are losing
**		liquid from the tank of radius R from a leaking point of
**		height Hl and surface Sl, then Hf is the height function of
**		the liquid in the tank and dV/dt_out is the amount of liquid
**		wasted through the leakage
*/
inner_tank(Hl,Sl,H,R,G,Hf,DVout):-
	formulae([F1,F2]),
	Hl < H,
	EndTime=(sqrt(H-Hl)*pi*R^2)/(2*sqrt(2*G)*Sl),
	F01=sqrt(2*G)*Sl,
	F02=sqrt(H-Hl)/4,
	F03=(Sl*sqrt(G/2))/(pi*R^2),
	F2 = ( F01*( F02 - F03*T2 ))//T2 ,
	F1 = ( F02- F03*T )//T ,
	DVout={[
		cc(0,EndTime):F1,
		oo(EndTime,infinity):0//LL
		]},
	Hf={[
		cc(0,EndTime):F2,
		oo(EndTime,infinity):(Hl)//LL
	 ]}.


/*  
**	outer_tank_type_A(?dV/dt_in,[?Height,?Radius,?InnerRadius],?Hf)
**		if the input of liquid is dV/dt and the geometric 
**		characteristics are as described the height of the
**		liquid in the outer vessel is given by Hf.
**
*/

outer_tank_type_A(DV,H,R,R0,Hf):-
%	reals([H,R,R0]),
%	functions([DV,Hf]),
	Hf@0=0,
	Hf= (1/(pi*(R^2-R0^2))) * integral(DV),
	continuous(Hf). 



/*  
**	outer_tank_type_B(?dV/dt_in,[?Height,?Radius,?InnerRadius],?Hf)
**		if the input of liquid is dV/dt and the geometric 
**		characteristics are as described, the height of the
**		liquid in the outer vessel is given by Hf.
**		Type B has overflow problems if Hf becomes Higher than
**		Height.
**
*/

outer_tank_type_B(DV,H,R,R0,Hf):-
%	reals([H,R,R0]),
%	functions([DV,Hf,DVout]),
	Hf@0=0, 
	Hf@T1=H,
	DVout={[
		cc(0,T1):0//LL,
		oo(T1,infinity):(DV@T)//T
	      ]},
	Hf= (1/(pi*(R^2-R0^2))) * integral(DV-DVout), 
	continuous(Hf). /* the height is a continuous function */


/*  
**	solve_problem
**		solve the problem and print the answer
**		change the type of the outer tank accordingly
**
*/

solve_problem:-
	reals([Hl,Hi,Sl,Ri,Ro,Ho,G]),
	functions([DVi,Hfi,Hfo]),
	inner_tank(Hl,Sl,Hi,Ri,G,Hfi,DVi),
	outer_tank_type_A(DVi,Ho,Ro,Ri,Hfo),
	dump(['Hfi'=Hfi,'Hfo'=Hfo]).

solve_problem(H,Hi,Sl,Ri,Ro,Ho,G,DVi,Hfi,Hfo):-
	reals([Hl,Hi,Sl,Ri,Ro,Ho,G]),
	functions([DVi,Hfi,Hfo]),
	inner_tank(Hl,Sl,Hi,Ri,G,Hfi,DVi),
	outer_tank_type_A(DVi,Ho,Ro,Ri,Hfo).

/* EOF */