Understanding Fluid Flow in Physics Lab: Poiseuille Equation

[svoboda32]

Hi everyone,

I have to answer some question about a physics lab..here are the questions
A tank is empty by a pipe and we measure the height (y-y0) of fluid in the tank as a function of time. We obtain this graph ( I join the graph)
We can find the relaxation time

with the relation :

with (yin -y0) is the initial height of the fluid in the tank and (y-y0) is the height of the fluid at a time t.
I can easily isolate

but the teacher say that it's a part of the graph which is the best to evaluate

.
He ask what is this part and why ??
It's a physics lab about the fluid flow and poiseuil equation for viscosity...
If someone can give me some track ..
Sorry for my English I'm French..

 

[haruspex]

Assume your time measurements are accurate, but there may be some small error up to Δy in each height measurement.
If you pick two points (times) on the graph, how large might your error be in τ?

 

[Chestermiller]

The data in your graph does not satisfy your equation. If it did, the data would fall on a straight line.

 

[svoboda32]

@haruspex if I have an error Δy on y I can eventually calculate the error on τ by the method of partial differentiation..

@Chestermiller I know because we obtain this curve experimentally and there is certainly another factors that interfer. That's why the teacher as what's the best part of the curve to evaluate τ

 

[haruspex]

we obtain this curve experimentally and there is certainly another factors that interfer. That's why the teacher as what's the best part of the curve to evaluate τ

That will depend on the cause of the error; which part of the curve does it least affect?

 

[svoboda32]

That's what I'm looking for ! Maybe the first part from t = 0s to t= 30s because we have a straight line like Chestermiller said ...

 

[Chestermiller]

That's what I'm looking for ! Maybe the first part from t = 0s to t= 30s because we have a straight line like Chestermiller said ...

There is also a straight line section between 80 and 110. Do you think inertial effects will be more important at short times or at long times?

 

[haruspex]

There is also a straight line section between 80 and 110. Do you think inertial effects will be more important at short times or at long times?

Any chance there could be turbulence in some stage? I'm guessing not.

 

[Chestermiller]

Any chance there could be turbulence in some stage? I'm guessing not.

Turbulence could definitely be a factor. At short times, when velocities are highest, the laminar-turbulent transition could be exceeded in the tube. Also, the hydrodynamic entrance length in the tube could be a significant factor at short times.

 

[svoboda32]

I think at the beginning of the experience the velocity of water through the pipe is greater and we don't have a laminar flow...so the best measure will occur at long times when (y-y0) is small .. what do you think about that ??

 

[haruspex]

I think at the beginning of the experience the velocity of water through the pipe is greater and we don't have a laminar flow...so the best measure will occur at long times when (y-y0) is small .. what do you think about that ??

Up to a point. The difficulty at small y-y0 is the accuracy in measuring it. The pipe has some width. How exactly is y0 defined? I wonder if the graph would look straighter if you were to take y0 as being a bit less.