Intersection point

Questions
,
1

Hi,

I was trying to do a program with units.
I want to find the intersection point of two functions

cau=Quantity[Range[.1,1,.2],"Meters"^3/"Seconds"];
h=Quantity[{100,90,78,64,46},"Meters"];
hs=Quantity[{50,60,72,86,108},"Meters"];

fh=Interpolation[Transpose[{cau,h}]];          (*function 1*)
fhs=Interpolation[Transpose[{cau,hs}]];      (*function 2*)

cau1=cau1/.FindRoot[fh[cau1]==fhs[cau1],{cau1,.1}]

Is it possible?

2

Just my guess: Interpolation and InterpolatingPolynomial are not (yet?) compatible with physical units. The documentation for QuantityVariable shows an example of DSolve with units:

DSolve[{Derivative[1][QuantityVariable[x, "Length"]][
    QuantityVariable[t, "Time"]] == 
      Quantity[5, "Meters"/"Seconds"]}, 
 QuantityVariable[x, "Length"][
    QuantityVariable[t, "Time"]], QuantityVariable[t, "Time"]]

but the equivalent for NDSolve does not work, at least with the following syntax:

NDSolve[{Derivative[1][QuantityVariable[x, "Length"]][
    QuantityVariable[t, "Time"]] == 
      Quantity[5, "Meters"/"Seconds"]}, 
 QuantityVariable[x, "Length"][
    QuantityVariable[t, "Time"]], {QuantityVariable[t, "Time"], 
  Quantity[0, "Seconds"], Quantity[10, "Seconds"]}]