Conditional Statement with 3 different ranges

I am given the three ranges

h < r

r≤h<H−r

H − r ≤ h ≤ H

I am trying to make the program run v1 when the first range applies, then v2 when the second range applies, and v3 when the third range applies. Simulating a tank with rounded ends filling up. I feel that using the if statements are what's needed.

H is the max height of the tank, h is the current level of the water, and r is the radius of curvature of the ends of the tank.

Then the final values need to be plotted.

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

r = 2; %ft

H = 7; %ft

h = 0:.1:H;

if (h<r)

      v1 = (1/3)*pi*h^2*(3*r-h)

elseif (r<=h<(H-r))

      v2 = (2/3)*pi*r^3+pi*r^2*(h-r)

else ((H-r)<=h<=H)

      v3 = (4/3)*pi*r^3+pi*r^2*(H-2*r)-(1/3)*pi*(H-h).^2*(3*r-H+h)

end

plot(h,v?)

Any help is much appreciated as I don't know where to go next.

Answer 1

[Guillaume]

You cannot use the notation if a<b<c to check that b is between a and c in matlab (in fact, I'm not aware of any programming language where that is valid). a<b<c is interpreted as (a<b)<c. The result of (a<b) is either true (1) or false(0), so your comparison ends up as being 0<c or 1<c. To express what you want you need to use logical operators (& or && if scalar, in this case).

Therefore your tests are:

h < r
r <= h & h < (H-r)
(H-r) <= h & h < H

You can't use these test with if though because h is a vector. The simplest way to obtain what you want is to use logical indexing:

r = 2; %ft
H = 7; %ft
h = 0:.1:H;
v = zeros(size(h));
%temporary variables to help with logical indexing:
v1 = 1/3*pi*h.^2.*(3*r-h); %Important: note the .^2 and .* to work with vectors
v2 = 2/3*pi*r.^3+pi*r.^2.*(h-r); %Again .^3 .^2 and .*
v3 = 4/3*pi*r.^3+pi*r.^2*(H-2*r)-1/3*pi.*(H-h).^2.*(3*r-H+h);
%use logical indexing to assign v1, v2 and v3 to the relevant portion of v
v(h < r) = v1(h < r);
v(r <= h & h < (H-r)) = v2(r <= h & h < (H-r));
v((H-r) <= h & h < H) = v3((H-r) <= h & h < H);
plot(h, v);

[Matthew Garrelts]

Thank you very much!