Here is a something I want to figure out. I really appreciate if anybody could help. It is a constant force F (kinda pressure gradient) forced channel flow and there is a cylinder in the channel. In other words, there is a cylinder in the planar poiseuille flow. The wall effect is neglected. There are three values that I am concerning, the force F, the viscosity of the fluid v and the total drag force D. I know that the reynolds number is coupled with the F and v. But I can say that it is a really low Re problem and we can assume it is a creeping flow. If I set the viscosity v a constant, is there any relationship between the force F and the total drag force? If so, could you please give me some detail information about that?

Thanks you all.

If the wall effect can be neglected, and it's a creeping flow, does it mean that cylincer is small enough compared to channel size? Then you can neglect the influence of the cylinder on channel hydraulic resistance, calculate fluid velocity basing on force F and viscosity (it's simple hydraulics with analytical formulas), then calculate Reynolds number for cylinder and get the drag force (there are plenty of D vs Re charts and formulas around). Then you can even make a second iteration, adding the drag to total channel resistance and correcting the velocity.

In any flow regime (with or without wall effects).

Total drag force (Fd) = Pressure drag force (Fdp)+Viscous drag force (Fdv)

Total drag coefficient (Cd) = Cdp+Cdv = A+B/Re^C

where Fdp (or Cdp) and Fdv (or Cdv) are related to pressure gradients and shearing forces, respectively.

A,B and C are the fitting constants.

In the literature, you can find a bulk of information on the flow parameters, their numerical values and their dependence on the governing parameters (Reynolds number, wall effects, etc).

You might like to look up some of the following references:

Books:

Zdravkovich, M.M. (1997). Flow around circular cylinder. Volume 1: Fundamentals.Oxford University Press, New York, USA.

Zdravkovich, M.M. (2003). Flow around circular cylinder. Volume 2: Applications. Oxford University Press, New York, USA.

Few jrnl papers:

Kaplun, S. (1957). Low Reynolds number flow past a circular cylinder. Journal of Mathematical Mechanics 6, 595-603

Ben Richou, A., Ambari, A. and Naciri, J.K. (2004). Drag force on a circular cylinder midway between two parallel plates at very low Reynolds numbers. Part 1: Poiseuille flow (numerical).Chemical Engineering Science 59, 3215-3222.

Ben Richou, A., Ambari, A., Lebey, M. and Naciri, J.K. (2005). Drag force on a circular cylinder midway between two parallel plates at Re<<1. Part 2: moving uniformly (numerical and experimental).Chemical Engineering Science 60, 2535-2543.

Curtis, A. R. and Marr, G. R. (1978). The viscous drag on cylinders falling symmetrically between parallel walls.Journal of Physics D 11, 1173-1178.

Dennis, S.C.R. and Chang, G.-Z. (1970). Numerical solutions for steady flow past a circular cylinder at Reynolds number up to 100. Journal of Fluid Mechanics 42, 471-489.

Faxen, O.H. (1946). Forces exerted on a rigid cylinder in a viscous fluid between two parallel fixed planes. Proceedings of the Royal Swedish Academy of Engineering Sciences 187, 1--13.

Proudman, I. and Pearson, J. (1957). Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder.Journal of Fluid Mechanics 2, 237--262.

Stalnaker, J.F. and Hussey, R.G. (1979). Wall effects on cylinder drag at low Reynolds number.Physics of Fluids 22, 603--613.

White, C.M. (1946).The drag of cylinders in fluids at slow speeds. Proceedings of the Royal Society A 186, 472--480.

Handerson, R.D. (1995). Details of the drag curve near the onset of vortex shedding. Physics of Fluids 7, 2102-2104.

Best regards....Ramp

http://scienceworld.wolfram.com/phys...inderDrag.html