# How does flow rate affect the terminal velocity of a bubble rising?

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?

• What are your thoughts on this? – Chet Miller Nov 20 '18 at 12:29
• I would assume if the flow of the liquid was in the direction of the bubble, most if not all of the flow velocity would be applied to the bubbles velocity. If the flow was counter to the bubble, the flow velocity would be deducted from the bubbles to a degree, not 100%. Using just Stokes Law, viscosity, buoyancy, etc., you would have to add a modifier for the counter flow to properly calculate the velocity of the bubble. For a perpendicular flow, the modifier would be 1/2(?) of the counter flow? I am just unsure of how to start the calculation to factor in the flow rate. – Bubba Hotep Nov 20 '18 at 15:05
• An example, pouring honey from a jar. A bubble in honey would have a very slow velocity. If the jar were tipped and a stream poured out, the bubble would then be pulled down with the honey, because its velocity would be far less than the honeys. Once it settled it would then begin to accelerate to the surface again. I am fairly certain my line of thinking is correct (though I have been wrong before), I am just at a loss as to how to factor flow rate in, and have exhausted all of my usual avenues for finding the proper calculations for something like this. – Bubba Hotep Nov 20 '18 at 15:19

## 1 Answer

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.