All of the info I seem to find on calculating the terminal velocity of a bubble in a fluid relates to bubbles rising in a column of static fluid, or at least there is no mention of flow rate. What I want to calculate is the terminal velocity of a bubble in a horizontal cylinder (pipe), with a given flow rate. Would the cross flow create additional drag, or would standard Stokes Law (Stokes, buoyancy, viscosity, surface tension, etc) be adequate? Considering the vertical column again, if the fluid was not static, and was moving in the same direction as the bubble, the fluids velocity would be added to the terminal velocity of the bubble, at least partially. If the fluid is moving in the opposite direction, it would negate part of the bubbles terminal velocity. What would a perpendicular flow do? How does flow rate calculate into the equation?
Well, irrespective of whether the flow is horizontal or vertical, if the flow velocity is constant and uniform, that is exactly the same thing as a change in inertial frame of reference of the observer. So it must just 100% add to the flow or subtract from it.