Drag force on cylinder in parallel flow

In summary, the conversation is discussing the search for a correlation of drag force on a cylinder in parallel creeping flow. The speaker has found useful equations from Batchelor and Keller that use slender body theory, but they are looking for an exact solution. They mention Stokes' paradox, which is present for both perpendicular and parallel flow, and the possibility of using Lamb's solution for an infinite cylinder. However, the speaker prefers the results from slender body theory as they apply to finite cylinders and Lamb's solution also involves approximations.
  • #1
MichielM
23
0
Hi,
I'm looking for a correlation of the drag force on a cylinder in parallel creeping (stokes') flow (i.e. the flow is alongside the axis of the cylinder). My length-to-width ratio is such that assuming an infinitely long cylinder is perfectly okay.

Does anyone know where I can find such a correlation?

I've tried deriving it myself but I ran into something called the Stokes' paradox. I know this can be solved by an approximation method (taking a linear inertia term into account), but I do not want to dive in that deep, I just need the equation for a calculation.
 
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  • #2
I've found useful equations from Batchelor (1970) and Keller (1976) who use 'slender-body theory' in which the rod is approximated as a line of stokeslets (singular force terms)
 
  • #3
Are you asking if the flow is parallel to or or perpendicular to the axis of the cylinder?

Stokes' paradox is, IIRC, for flow perpendicular to the axis of the cylinder. There's an exact solution in Lamb's 'hydrodynamics', which is at work. It involves the Euler constant (0.577...).
 
  • #4
Stokes' paradox was first found for a cylinder perpendicular to the flow, but the same effect (and for the same reason) is present for flow parallel to the cylinder. The basic problem is not the direction of flow but rather the fact the effect of inertial as compared to viscous forces are no longer negligible at large distances from the body.

As for the flow solution: slender body theory provides results for both parallel and perpendicular flow for finite cylinders. Lamb's solution is for an infinite cylinder. Although I said that would be perfectly fine given my length to width ratio, the results for slender body theory apply to finite cylinders which is more useful to me. Moreover, lamb's solution is not exact either, it also involves assuming a linear inertia term in the navier stokes equation
 
  • #5


Sure, I can help you with finding a correlation for the drag force on a cylinder in parallel flow. This is a common problem in fluid mechanics and there are several equations that can be used to calculate the drag force.

One of the most well-known equations for this is the drag force equation for a circular cylinder in parallel flow, which is given by:

Fd = 0.5 * ρ * U^2 * Cd * A

Where Fd is the drag force, ρ is the density of the fluid, U is the velocity of the flow, Cd is the drag coefficient, and A is the cross-sectional area of the cylinder.

The drag coefficient, Cd, is a dimensionless quantity that depends on the shape of the cylinder and the Reynolds number (Re) of the flow. The Reynolds number is a dimensionless parameter that relates the inertial forces to the viscous forces in the flow and is given by:

Re = ρ * U * D / μ

Where D is the diameter of the cylinder and μ is the dynamic viscosity of the fluid.

For a circular cylinder in parallel flow, the drag coefficient can be approximated as:

Cd = 24 / Re

Using this equation, you can calculate the drag force on the cylinder for a given flow velocity and cylinder diameter.

Other equations for the drag force on a cylinder in parallel flow exist, such as the Dallavalle equation or the Blasius equation, which take into account the effects of the boundary layer and the Reynolds number. These equations may provide more accurate results, but they are more complex and may require additional parameters.

I hope this helps you in finding the correlation you need. Remember to always consider the assumptions and limitations of the equations you use and to validate your results with experimental data if possible. Good luck with your calculations!
 

1. What is drag force?

Drag force is a force that opposes the motion of an object as it moves through a fluid, such as air or water. It is caused by the friction between the object's surface and the fluid it is moving through.

2. How does drag force affect a cylinder in parallel flow?

When a cylinder is placed in a fluid flow that is parallel to its axis, the fluid exerts a drag force on the cylinder. This force is perpendicular to the direction of the fluid flow and is dependent on the fluid's density, the cylinder's size and shape, and the velocity of the fluid.

3. What factors affect the drag force on a cylinder in parallel flow?

The main factors that affect the drag force on a cylinder in parallel flow are the fluid's density, the cylinder's size and shape, and the velocity of the fluid. Other factors that can have an impact include the surface roughness of the cylinder and the fluid's viscosity.

4. How is the drag force on a cylinder in parallel flow calculated?

The drag force on a cylinder in parallel flow is typically calculated using the drag coefficient, which is a dimensionless parameter that takes into account the cylinder's size and shape, as well as the fluid's density and velocity. This coefficient is then multiplied by the fluid's density, the velocity squared, and the cylinder's projected area to determine the drag force.

5. Can the drag force on a cylinder in parallel flow be reduced?

Yes, the drag force on a cylinder in parallel flow can be reduced by altering the cylinder's shape, increasing the fluid's viscosity, or changing the fluid's velocity. Other methods, such as adding a streamlined fairing or using a different material for the cylinder, can also help to reduce drag force.

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