Dropping Marbles in Different viscous liquids

[bbq2014]

Hi Forum.

So I'm doing a physics experiment where I drop marbles in different viscous liquids and I am suppose to discuss the relationship of the marble's velocity. But I am changing the marble's diameter and mass at the same time since I don't have any marbles which have the same mass but different radius and vis versa. So now i can't come up with a reasonable researchable question. Will this work? The relationship of the velocity when the density of the marble is changed. Or, since i am just scaling the marbles up, i can assume that the mass is negligible or something?

Now the second bit of my problem. Since both variable contribute to the change in velocity, I don't understand entirely why my results are this. My experiment - I am keeping the volume of the liquid constant but changing the viscosity of the liquids. The marbles mass and volume are increasing successively, i.e. those ordinary small sized marble and then a bigger mass and bigger volume. It is dropped in the liquid and timed how long it takes to reach the bottom. My data shows that the bigger marbles takes longer to fall through the liquid. It seems reasonable since there is less room to flow past the marble and that the velocity of the liquid near the sides are slower which would in turn slow down the velocity of the flowing liquid? (dunno whether i am right 'bout the second reason) But the increasing weight more drag is required to slow down the marble. So how can I explain why its all happening the way its happening when I'm changing two variables at the same time. As I can't model one variable and its result. Also I tried to keep the mass constant and changing the volume using blue tack. But they have different drag coefficient and it would also be a different variable.

Also using stokes law μ=(2r^2 g(ρ_(sphere)-ρ_fluid ))/9v, how do i calculate the velocity as it fall since it always decelerate? I think your suppose to use the terminal velocity?


Thank you for reading!

 

[Chestermiller]

Suppose you do a force balance on the marble, including drag and mdv/dt. Can you solve the resulting differential equation? Have you learned about dimensional analysis and dimensionless groups yet?

Chet

 

[bbq2014]

Nop. I don't think i can, I am in yr yr 12 physics.

 

[Chestermiller]

Nop. I don't think i can, I am in yr yr 12 physics.

That makes it difficult to make sense out of the experiments that use a range of values for several different parameters. Things would be much more straightforward if you knew how to apply dimensional analysis. This would substantially reduce the number of variables you have to consider. Sorry. I'm at a loss for suggesting how to proceed.

Chet

 

[Chestermiller]

I think I may be able to help you, but I have a couple of questions. Is the marble released at the liquid surface, or is it dropped from above, so that it hits the surface with a velocity? Do you measure the velocity vs time? Do you measure the distance vs time? Do you measure the time required for the marble to fall to the bottom, and is this a key parameter? If so, do you vary the depth of the liquid in the tank?

Chet

 

[bbq2014]

It is released at the liquid's surface. Yeah for the experiment I am measuring the distance vs time. So, I am keeping everything constant but with different density of the marbles. And will be comparing the velocity of the marbles when dropped in different liquids. It is a cylindric tube with a 40 by ~5 cm volume of liquid. I am recording the ball as it falls and will figure out the velocity as it falls with a program.

Thank you so much!

 

[Chestermiller]

It is released at the liquid's surface. Yeah for the experiment I am measuring the distance vs time. So, I am keeping everything constant but with different density of the marbles. And will be comparing the velocity of the marbles when dropped in different liquids. It is a cylindric tube with a 40 by ~5 cm volume of liquid. I am recording the ball as it falls and will figure out the velocity as it falls with a program.

Thank you so much!

Initially, the marble's velocity will be zero. As time progresses, it will speed up, and eventually approach a final "terminal" velocity. This should be equal to the Stokes velocity. So, in each case, if you make a graph of x vs t, the graph will be curved at short times, but at long times it will approach a straight line. The slope of this straight line portion will be the terminal velocity. You can measure this slope (terminal velocity) in all the runs, and plot it against the calculated Stokes velocity for that run (all the runs for this are done on a single graph). The result should be a straight line through the origin, with a slope of 1. This will be a test of how closely the Stokes equation predicts the terminal velocity.

Chet

 

[bbq2014]

Initially, the marble's velocity will be zero. As time progresses, it will speed up, and eventually approach a final "terminal" velocity. This should be equal to the Stokes velocity. So, in each case, if you make a graph of x vs t, the graph will be curved at short times, but at long times it will approach a straight line. The slope of this straight line portion will be the terminal velocity. You can measure this slope (terminal velocity) in all the runs, and plot it against the calculated Stokes velocity for that run (all the runs for this are done on a single graph). The result should be a straight line through the origin, with a slope of 1. This will be a test of how closely the Stokes equation predicts the terminal velocity.

Chet

Thanks for the suggestion!

I have a question about the theory of the experiment. Does Bernoulli's principle apply for this scenario?

 

[Chestermiller]

Thanks for the suggestion!

I have a question about the theory of the experiment. Does Bernoulli's principle apply for this scenario?

No. Bernoulli's equation applies to situations primarily without viscous drag, and this situation is dominated by viscous drag.

Chet