Solve a range of numbers

Question

I have an equation and have defined all variables except one. One of the variables is a Range of numbers. I now want to solve for a specific value and was expecting result to also be a range of numbers - unfortunately this was not the case!

Here is a small piece of my code showing my problem:

ClearAll["Global`*"];
(*define known variables*)
rnc = 0
WRes = 10/1000
DRes  = 1/1000
VPE = 0
rho = 1000
r2  = Range[20/1000, 45/1000, 1/1000]
r1  = r2 - 10/1000
V2min = 3/1000/1000/1000
(*define target freq*)
ftarg = 25
omegtarg = ftarg*2*Pi
(*equation for frequency*)
o1targ = Sqrt[
2*(((V1min + V2min)/V1min) - 1)*
P/(rho*((r2 + rnc)^2 - (r1 + rnc + V2min (WRes*DRes) + 
       VPE/(WRes*DRes))^2))]
(*Solutions for V1min*)
V1range = V1min /. Solve[omegtarg == o1targ , V1min]

From this code all I'm getting is V1range = V1min?? The solve was working for me previously (though not for a range of values). I also tried to make omegtarg a range to match o1targ but this also gave me no luck.

any help is much appreciated! Thank you and regards, D

Answer 1

ClearAll["Global`*"];
(*define known variables*)
rnc = 0;
WRes = 10/1000;
DRes = 1/1000;
VPE = 0;
rho = 1000;

Leave r2 undefined until later

(* r2=Range[20/1000,45/1000,1/1000] *)

r1 = r2 - 10/1000;
V2min = 3/1000/1000/1000;
(*define target freq*)
ftarg = 25;
omegtarg = ftarg*2*Pi;
(*equation for frequency*)

o1targ = Sqrt[
    2*(((V1min + V2min)/V1min) - 1)*
     P/(rho*((r2 + rnc)^2 - (r1 + rnc + V2min (WRes*DRes) + 
             VPE/(WRes*DRes))^2))] // Simplify;

Define r2 as a Range

(*Solutions for V1min as a function of P*)

V1range = V1min /. Solve[omegtarg == o1targ, V1min][[1]] /. 
   r2 -> Range[20/1000, 45/1000, 1/1000];

V1range // N

(* {8.10569*10^-13 P, 7.59909*10^-13 P, 7.15208*10^-13 P, 6.75475*10^-13 P, 
 6.39923*10^-13 P, 6.07927*10^-13 P, 5.78978*10^-13 P, 5.52661*10^-13 P, 
 5.28632*10^-13 P, 5.06606*10^-13 P, 4.86342*10^-13 P, 4.67636*10^-13 P, 
 4.50316*10^-13 P, 4.34234*10^-13 P, 4.1926*10^-13 P, 4.05285*10^-13 P, 
 3.92211*10^-13 P, 3.79954*10^-13 P, 3.68441*10^-13 P, 3.57604*10^-13 P, 
 3.47387*10^-13 P, 3.37737*10^-13 P, 3.28609*10^-13 P, 3.19962*10^-13 P, 
 3.11757*10^-13 P, 3.03964*10^-13 P} *)

Or define r2 as an Interval

V1interval = 
  V1min /. Solve[omegtarg == o1targ, V1min][[1]] /. 
   r2 -> Interval[{20/1000, 45/1000}];

V1interval // N

(* P Interval[{3.03964*10^-13, 8.10569*10^-13}] *)