Script Name: prob2 Script Variables: amount (double) - Contains the amount of ic

Question

Script Name: prob2 Script Variables: amount (double) - Contains the amount of ice cream necessary to fill an ice cream cone of the given dimensions time_to_fill (double) - The amount of time it takes to the fill an ice cream cone, if each cone is filled at a rate of 1.0 in^3/s. Answer should be in seconds. Problem Statement: Write a script named "prob2" that will calculate the volume of ice cream needed to fill an ice cream cone. The ice cream cone is 4 inches tall and its rim has a diameter of 0.8 inches. Assume that the ice cream completely fills the cone, and that the ice cream above the cone is in the shape of a perfect hemisphere. Store the volume needed in a variable called "amount". Also, assume that the cone is filled at a rate of 1.0 in^3/s. Find the amount of time it takes to fill one ice cream cone, and store that value in a variable called "time_to.fill". Note: Your answer should be in units of in^3. Don't convert to any other unit of measurement such as ft^3, or yd^3. Also, don't forget to include the hemispherical dome of ice cream above the cone.

Explanation / Answer

function sol = prob2 % This problem considers a cardiovascular model, which can be found in % 'Modelling of the Baroflex-Feedback Mechanism With Time-Delay' by J.T. % Ottesen in J. Math. Biol., 36 (1997), 41-63. (This is reference % 14 of the tutorial). % Copyright 2004, The MathWorks, Inc. % Problem parameters, visible in nested functions. p.ca = 1.55; p.cv = 519; p.R = 1.05; p.r = 0.068; p.Vstr = 67.9; p.alpha0 = 93; p.alphas = 93; p.alphap = 93; p.alphaH = 0.84; p.beta0 = 7; p.betas = 7; p.betap = 7; p.betaH = 1.17; p.gammaH = 0; P0 = 93; Paval = P0; Pvval = (1 / (1 + p.R/p.r)) * P0; Hval = (1 / (p.R * p.Vstr)) * (1 / (1 + p.r/p.R)) * P0; history = [Paval; Pvval; Hval]; for tau = [1 7.5] sol = dde23(@prob2f,tau,history,[0, 350]); figure plot(sol.x,sol.y(1,:)) title(['Problem 2. Baroflex Feedback Mechanism with' ... ' au = ',num2str(tau),'.']) xlabel('time t') ylabel('P_a(t)') axis([0 350 82 96]) end %----------------------------------------------------------------------- % Nested function % function yp = prob2f(t,y,Z) %PROB2F The derivative function for Problem 2 of the DDE Tutorial. % Local variables are used to express the equations in terms % of the physical quantities of the model. ylag = Z(:,1); Patau = ylag(1); Paoft = y(1); Pvoft = y(2); Hoft = y(3); dPadt = - (1 / (p.ca * p.R)) * Paoft + (1/(p.ca * p.R)) * Pvoft ... + (1/p.ca) * p.Vstr * Hoft; dPvdt = (1 / (p.cv * p.R)) * Paoft ... - ( 1 / (p.cv * p.R) + 1 / (p.cv * p.r) ) * Pvoft; Ts = 1 / ( 1 + (Patau / p.alphas)^p.betas ); Tp = 1 / ( 1 + (p.alphap / Paoft)^p.betap ); dHdt = (p.alphaH * Ts) / (1 + p.gammaH * Tp) - p.betaH * Tp; yp = [ dPadt; dPvdt; dHdt ]; end % prob2f %----------------------------------------------------------------------- end % prob2

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