My quick answer is that I do not know of a time-dilation experiment for the classroom.
The laws of Physics tell us that time indeed advances differently in moving frames (spaceship),
this is a measurable effect only at relativistic speeds approaching the speed of light;
It has nothing to do with the method by which time is measured, which might only confuse students.
The simplest example I describe to students is that the lifetime of a particle as
measured in the lab
is shorter when it is at rest, but longer when moving very fast.
As for Newtonian or non-Newtonian fluid, I am not sure I see the connection to relativity?
If a fluid changes its flow qualities, such as viscosity, under an external force, it is non-Newtonian.
Taking a fluid to space could represent a change in pressure, but what was the idea to use it for time measurements?
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