One possible way is to use the “Poiseuille equation” to calculate the plug length:
V = (ΔP dπ t)/(128 η L)

where V is volume of the injected plug, ΔP is pressure drop down the length of the capillary (pascals), d is the inside diameter (m), η is the fluid viscosity (Pascal-sec), t is time the pressure is applied (sec), and L is the length of the capillary (m). Here you solve for V to get the injected plug volume. From there, you simply use the cylinder volume equation to convert volume to length of the plug:
V = π r2 Lplug
Lplug = (V / (π r2))
Lplug = (V / (π (d/2)2))0

where r is the inside radius and Lplug is the length of the plug.

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