# Friction factor on very very low reynolds number

1. Apr 7, 2006

### han168

hai all,
I'm now doing a research about castor oil. i've a got a few a confusing problems..

1. to flow castor oil in a 12 mm acrylic pipe i use a reservoir 1 metres from the outlet. Because castor oil is very thick (dyn visc. = 0.5 Pa-m), the velocity of the flow is very low just about 0.02 m/s, therefore the reynolds number i got is very small just about 0.35. do u guys think it's normal? coz' i've never found any case that has a reynolds number below 1 in an internal flow.

2. related to the first question, i got the friction factor for laminar flow using the eg f=64/Re, so i got about 140-150. do u guys think it's normal to have a friction factor > 1.

that's my confusing problem, btw i dont want to use pump, because pump will break the oil's molecule.

Thanks.

2. Apr 8, 2006

### Staff: Mentor

Very low Reynolds numbers are encountered with motor oils. I have an example of oil leakage past a cylinder head/bore in which Re = 0.0375.

The formula I have for volumetric flow rate is

Q = $$\frac{\pi\,\Delta{p}D^4}{128\,\mu\,L}$$, where D is pipe/tube diameter and L is pipe/tube length, p is pressure, and $\mu$ is dynamic or absolute viscosity.

Q = V A where V is mean fluid velocity.

The f is probably correct for the Re, but I am not familiar with the application at such low Re.

What is the temperature of application?

Last edited: Apr 8, 2006
3. Apr 9, 2006

### han168

so u think it's normal to have a friction factor > 1 with such Reynolds number?
the temperatur is ambient about 30 deg Celcius
Thanks btw

4. Apr 9, 2006

### Clausius2

The friction factor for laminar flows can be derived analytically and has a value of 64/Re. There's no further problem if it is larger than one.

5. Apr 9, 2006

### Staff: Mentor

It would appear to be normal for oils, e.g. motor oil in a warm engine. At some point, the oil temperature increases to around 100°C or slightly higher, so viscosity will vary considerably. The dimensions used in lubrication are generally very small (parallel surfaces).

As Clausius2 mentioned it should not be a problem. I believe that f = 64/Re is derived from the formula I posted by virtue of the definition of the Darcy friction factor - http://en.wikipedia.org/wiki/Darcy_Friction_factor

http://en.wikipedia.org/wiki/Hagen-Poiseuille_law

6. Apr 9, 2006

### han168

thank you very much for the answers..i really really appreciates it. =)

7. Apr 20, 2006

### han168

continuing my research about oil for lubricants, could you guys tell me where can i find the rheology overview of oil (viscosity change under shear) chart?
i want to compare it with castor oil..
thanks