Help understanding the Viscosity Formula

[cpscdave]

1.

Hi there,
We have some questions regarding the force it would take to keep a shaft moving in a tube at a constant velocity.

I gather the formula we should use is:

$$F/A=u*dux/dy$$

My understanding is that in this formula
$$F$$ is the force required
$$A$$ is the parallel surface area
$$u$$ is the viscosity of the fluid
and
$$dux/dy$$ is the slope of the velocity gradient.
Since in the question the shaft is up to speed $$dux/dy=1$$
I punch in the numbers and the result I'm getting have been nonsensical so any clarification would be fantastic!

 

[KataKoniK]

Hello,

Thank you for your question. The formula you have provided is the correct one for calculating the force required to keep a shaft moving at a constant velocity in a tube. However, there are a few factors that may be affecting your results.

First, make sure that you are using consistent units for all of your variables. The force, F, should be in Newtons (N), the area, A, should be in square meters (m^2), the viscosity, u, should be in Pascal-seconds (Pa*s), and the velocity gradient, dux/dy, should be in meters per second per meter (m/s/m).

Additionally, it is important to consider the type of fluid that is present in the tube. Different fluids have different viscosities, and this can greatly affect the force required to keep the shaft moving. For example, water has a lower viscosity than honey, so the force required to keep a shaft moving in water will be lower than in honey.

Finally, keep in mind that this formula assumes that the tube is completely straight and the shaft is moving in a straight line. If there are any bends or curves in the tube, this will affect the force required.

I hope this helps clarify any confusion. If you have any further questions, please don't hesitate to ask. Best of luck with your calculations!