Hydraulic geometry relations express the velocity V, width B, and depth H of a river as a function of the discharge (or flow) Q, which is the volume of water that passes a cross section in a unit time. These relations have the form (e.g., Leopold and Mattuck 1953)
V = a1 Q^e1, B = a2 Q^e2, H = a3 Q^e3
where the coefficients have the appropriate dimensions.
Write a function that takes two each of the coefficients and exponents and determines the third such that the relation between flow and velocity (i.e., Q = VBH) is satisfied. The coefficients and exponents will be given as 1x3 vectors in the order velocity, width, and depth, and the unknown values will be given as NaN.
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George Berken David Hill Dyuman Joshi Tomoaki Takagi

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