Tu.114 - sort of double doppler for each path, the sound pulses have to travel further forward than rearward
Sailplane variometers are well described (including math) in the book by Lorne Welch, alas I do not have current access to a copy. You need to express the quantites in algebra and differentiate.
A rearward facing variometer 'pitot' as used in sailplanes is carefully designed and mounted. It looks like a tube with crosswise slots embracing 120 degrees of the rear facing surface and is mounted with its axis vertical above the tailfin. Alternatively electronic computation from pitot and static is possible.
Airspeed sensing pitots are generally pointed forward and clear of the boundary layer. In protoype aircraft they are mounted way out ahead of the aircraft to get the cleanest possible air. Static vents are always a problem because they can only see already disturbed air. It is usual to calibrate them during a series of low-level test flights.
Your arithmetic would be correct if you could find a way of supplying your rear-facing orifice with undisturbed air.