This is a critical question when it comes to flow meter performance. Ideally the meter would be mounted so that flow is along the horizontal position. In addition, if it is a paddlewheel type meter it is best if the paddlewheel is oriented vertically and not lying flat. Finally, if you have a low flow less than 2.5 GPM like as 6000 Series Flow Meter, it is also helpful to have the flow ports at the top side of the meter. This will help in removing any trapped air in the meter. Air in the meter will cause the readings to read higher than actual.
If it is not possible to mount it in the horizontal position and it must be vertical it is in most cases important to have the flow going from bottom to top (upwards). This ensures that there is a full pipe to allow for accurate measurements. If not then you may have readings of no flow, lower than expected flow or erratic readings.