To get the low velocity in water, you willl need a much smaller ball, and/or a ball with lower density (plastic, or even a hollow ball) so the buoyancy force is greater compared with its weight. The terminal velocity should be low, say about 1 cm / second or less. The tube should be much wider that the ball, say at least 5 times as wide.Ģ. Stokes law doesn't even apply to separated flows, let alone turbulent ones.įor the OP, I would suggest that to get reasonable results you need two things.ġ. You disagreed with my comments about turbulence earlier and said the flow would separate but not be turbulent. The number is ludicrous because Stoke's law only applies for VERY low Reynolds numbers. Something is definitely up, though, because if you do the calculation with the correct viscosity of 0.001 Pas and your parameters, it says that the terminal velocity has to be 1308 m/s, which is just ludicrous. The only remaining 2-D, viscous instability is the Tollmein-Schlicting instability, and those grow very slowly. It won't be a Görtler instability, and in fact, the convex surface would actually stabilize the system. It won't be an inviscid instability because there is (as far as I can see) no inflection point in the boundary layer. In order for the flow to transition, there needs to be such an instability. I have a very hard time believing that, in this situation, the necessary instabilities would develop and grow fast enough to be turbulent before the sphere has passed. My claim is that an external flow is a fundamentally different phenomenon in many respects, including with respect to transition to turbulence. I realize airfoils are not spherical, and I don't claim that transition Reynolds number would be the same for a sphere. Look up a graph of the drag coefficient of a sphere against Re, if you don't believe me. A small plastic sphere might work even better.Īirfoils are not usually spherical either, so the transition Re for a typical airfoil doesn't apply. The way to do that is use a much smaller ball, preferably with a lower density as well. So using a bigger tube won't fix the problem, because you need to reduce the speed by a lot. Unfortunately Stokes Law only applies for completely laminar flow, when Re < 1. Re > 3000 means the fluid flow will be fully turbulent. Using the correct value of mu for water (about 0.01 in CGS units) and your measured values, Its physical meaning is the the ratio of the inertia forces (mass x acceleration) to the viscous forces on an object. In fluid dyamics there is an important non-dimensional number called Reynolds number. The other problem is your velocity is much too high, at least for water. The answer of 0.08 is probably nonsense, except that it shows assumptions behind the formulas do not apply.Ģ. In your case d/D = 2/2.5 = 0.8 and the some of the 'correction terms' are bigger than the measured value.

Mu_c = muīut that is only accurate when d/D is fairly small. In my PDF link there is an approximate correction formula for this effect Stokes assumes that upwards water velocity is zero. if you just about the relative areas (64% ball and 36% water), the water must be flowing upwards past the ball 64/36 = 1.8 times faster than the ball is moving downwards.

The ball is blocking up 64% of the area of the tube, so the flow pattern will be very different from the assumptions. Stokes Law gives the force on a sphere in an infinite volume of fluid, at low velocities. I think you have two big problems with the experiment. Is there a simple formula that my measurements can easily 'slot' into that someone can recommend, which will give me results which are not necessarily 100% spot on, but just a simple measure of viscosity that is near the value. they all put the viscosity in a different units, some do not give the required unit of density for the calculation (kg/g per cm/m/mm), some have weird units I have never heard of, some use a terminal velocity, some use variable velocity, some involve Brenner’s Law due to the influence of the boundaries of the tube on the sphere, and some from a few university lecture notes go into further complexities! I honestly have no idea which is the best/right one (my physics teacher is ill till after the christmas holidays so I can't ask him). I could really do with someone's help one the formula I would use, has anybody done this before for their coursework? I know some people will say 'just google it,' but I have spent far too long doing so, and right now have dozens of tabs and each formula is a slight variation on the other.

I have completed all the practical, now just the write up (using density of fluid, sphere, sphere diameter etc). Hi, I am doing physics coursework on finding viscosity of fluids by dropping a marble into fluids, finding terminal velocity, then using stoke's law to find viscosity.

Water dynamic viscosity pa s