# Trouble calculating the Reynolds number

1. Apr 30, 2015

### spearo

Hi,

I am having trouble calculating the reynolds number for 2 spear shafts underwater. The two shafts vary in diameter and velocity. The tips are identical, stream lined to a fine point so the flow should be laminar. Both spears are 1.9304 m long. The diameters are 11/32" (8.73125mm) and 3/8" (9.525mm) and their respective velocities are 48.33 m/s and 43.062 m/s.

I assume they will have little or no form drag (please feel free to correct me) and therefore I am focusing on skin friction. The fluid is seawater at 20 degrees.

I tried the calculation and got a ridiculous value over ninety million ((48.33*1.9304)/ 1.004 * 10^-6). I used Re=V.L/mu. I can't move on to F=Cf(pV^2/2)S wetted with this value. Where have I gone wrong? Is the reynolds equation different for such an object?

Any information is appreciated.

Thanks

2. Apr 30, 2015

### spearo

I realise that that kinematic viscosity is for water not seawater but that is not the problem as I still got ~88 mllion...

Last edited: Apr 30, 2015
3. Apr 30, 2015

### spearo

This is not a coursework question to be clear, it is the science behind a homemade speargun DIY project. The velocities were estimated based on the mass of the components and the force of the rubbers.

4. Apr 30, 2015

### Staff: Mentor

You should be using the local diameter at each location along the shaft, not the length.

Chet

5. Apr 30, 2015

### spearo

Could you please explain a little further, surely the length has some significance as it determines the "skin". which of these is appropriate to this shape as they do not all have reference to Re. I am finding so much mixed information.

1/7 power law:

1/7 power law with experimental calibration (equation 21.12 in [3]):

Schlichting (equation 21.16 footnote in [3])

Schultz-Grunov (equation 21.19a in [3]):

(equation 38 in [1]):

The following skin friction formulas are extracted from [2],p.19. Proper reference needed:

Prandtl (1927):

Telfer (1927):

Prandtl-Schlichting (1932):

Schoenherr (1932):

Schultz-Grunov (1940):

Kempf-Karman (1951):

Lap-Troost (1952):

Landweber (1953):

Hughes (1954):

Wieghard (1955):

ITTC (1957):

Granville (1977):

Date Turnock (1999):

6. Apr 30, 2015

### Staff: Mentor

These equations that you have written are all for axial flow along a cylinder, correct? Or are they for flow over a flat plate?

Let's just consider the case of a cylinder, and neglect the drag in the vicinity of the leading edge. So, you are going to get a boundary layer building up along the cylinder, starting at the leading edge, and growing toward the trailing edge. At some point, if the flow is laminar, the thickness of the boundary layer is going to be larger than the radial dimension of the shaft, and the flow will no longer be like flow over a flat plate (i.e., negligible curvature normal to the flow). So the cylindrical (curved geometry) would dominate.

But, no matter how streamlined you make the tip, the boundary layer is rapidly going to become turbulent. Some of these correlations are definitely for turbulent flow. If the correlations you are using are for turbulent axial flow along a cylinder, then you should be OK. The 90 million for the Rex is not a concern (to me).

Chet

7. Apr 30, 2015

And before you ask, there is no magical Reynolds number at which laminar-turbulent transition occurs. You have to determine that experimentally or else just make assumptions (such as entirely turbulent flow, which would over-estimate drag).

8. Apr 30, 2015

### spearo

To be honest I am not sure if they are the appropriate equations as the source only made reference to laminar and turbulent flow. Based on what you said then I take it there will be turbulent flow, not laminar? Sorry for all the questions I have not studied maths or physics for years. Regarding what you said about the local diameter, which in this case will not change, what should I sub in to the reynolds equation in place of the length?

9. Apr 30, 2015

### spearo

Is it a range than similar to the transonic region for airfoils?

10. Apr 30, 2015

### SteamKing

Staff Emeritus
You also have to be careful applying some of these Cf equations, since they are not all derived for the same physical phenomenon.

In particular, the ITTC equation is used when correlating the friction drag from a model test to a full-sized vessel. In a model test, for example, the total resistance of the model is measured, but Froude showed that the total resistance of a vessel is composed of the frictional resistance, which is a function of the Reynold's number, plus the residuary, or wave-making resistance, which depends on the shape of the hull and the speed, among other factors. In a model test, trying to obtain the same Reynold's number for the model as the full-sized vessel would mean that the model would have to be towed at a very high speed, giving unrealistic values for the residuary resistance. To overcome this problem with Reynolds scaling, an empirical equation like the ITTC line was developed to allow for the model test friction to be separated out of the total resistance of the model, and then the frictional resistance could be scaled up using the Reynold's number for the full-sized vessel.

The danger in grabbing up a bagful of different formulas is that you may not realize that each has a different purpose, although similar symbology may be used.

11. Apr 30, 2015

### spearo

So which one should I use? I posted them all to illustrate why this is confusing. I want to be able to compare the drag on the 2 different spears at the stated velocities to determine which is has more kinetic energy and momentum at a given range. I understand that it will only be an approximation but one will be better than the other and that is the point. It will be expensive and time consuming to determine this outcome experimentally.

12. Apr 30, 2015

### SteamKing

Staff Emeritus
I can't tell you which formula to use without researching them all. Some equations may be for model testing ships (which travel along the water-air interface), some may be for airfoils, etc.

The best advice I can give is to find someone who has determined the drag of a spear fired underwater and written a paper on the method of analysis. If you can't find a paper about spears, then you'll have to settle for a situation which most closely resembles a long, narrow cylinder moving in a completely submerged manner.

13. May 1, 2015

Well yes, the transition region is nonzero in length. The distance it takes to transition from laminar to turbulent flow is variable depending on the situation though. You will most likely have a mix of laminar and turbulent flow and there really isn't a great way to determine where the transition occurs without experiments.

14. May 2, 2015

### spearo

I found a study on sonar arrays being dragged through the ocean, I will post it when I find it again. The diameter was only 1mm however and the length was 100m in a 900m test tank. Before I read this comprehensive report would this be appropriate? If it cannot be estimated and I make a test model out of pine, what instrumentation do I need to test drag?

15. May 2, 2015