As I was digging through some of the research material that I have amassed throughout the years, I came across this one (see attached)― Non-Newtonian Behavior of Ballistic Gelatin at High Shear Rates, Experimental Mechanics (2012) 52:551–560. I thought that you might like to see it.
Attachment 37318
In the attached paper there is a simple power law that allows for the adjustment of dynamic viscosity at high shear rates which is really useful for calculating Reynolds Numbers (R
e = ρVD/μ) for high-velocity penetration events in the 10
-4 seconds range. The coefficients for the power law were fitted against the empirical data using the 'least squares' method.
The equation is:
μ =
αγ(n-1)
where μ = dynamic viscosity in centipoise (cp) for 10% gelatin
γ = shear strain rate in s
-1
α = 4.5 x 10
-3 kg∙s
(n-2)
n = 2.22
As stated in the paper above, when the dynamic viscosity for a projectile is calculated for shear strains of 2,000s
-1 and 8,000s
-1, dynamic viscosity increases about 5 times as shown below:
4.5 x 10
-3 kg∙s
(2.22-2) x 2,000s
-1(2.22-1) = μ = 3,243 cp
4.5 x 10
-3 kg∙s
(2.22-2) x 8,000s
-1(2.22-1) = μ = 17,598 cp
Of course, the Q-model can be used to compute such time frames.
For the latest test that I conducted here:
https://pistol-forum.com/showthread....slug-(P152XT1) ―
―the computed duration for that test was on the order of 4.858 milliseconds, so dynamic viscosity would have been on the order of―
4.5 x 10
-3 kg∙s
(2.22-2) x 2,058s
-1(2.22-1) = μ = 3,716 cp
―which means that the average Reynolds Number (R
e = ρVD/μ) for this event would be R
e = 29.211 indicating that turbulence would be very low since R
e < 2,000.
ETA: This paper might also add some valuable insight:
Attachment 37324