Given that , we have
, so that
Take the derivative and find the critical points of :
Take the second derivative and evaluate it at the critical point:
Since is positive for all
, the critical point is a minimum.
At the critical point, we get the minimum value .
Answer:
If we assume a temperature of 20ºc and the blood interfacial surface tension is similar to water interfacial surface tension, the diameter of the capillary tube should be 0.933mm.
Step-by-step explanation:
The Jurin law describes the height a fluid can reach in a capillary tube. This law can be written as:
where γ is the interfacial surface tension, θ is the contact angle with the fluid, ρ is the fluid density, g is the gravity acceleration and r is the tube radius.
If we assume that the interfacial surface tension of blood and water are almost the same, γ=0,0728 N/m at 20ºc. Therefore the diameter of the tube will be: