Note: This question is from the course 'Additive Manufacturing'.
In a printing process modeling, the resulting droplet must retain enough kinetic energy to propel the liquid from the nozzle towards the substrate. The following approximation for the gauge pressure required in the reservoir of a continuous jetting system is given by:
Ap = 20 * d^4 * dj^2
where,
Ap is the total gauge pressure required,
μ is the dynamic viscosity of the liquid,
Ï is the liquid's density,
σ is the liquid's surface tension,
d is the diameter of the resultant jet,
d' is the inner diameter of the nozzle or supply tubing,
v is the velocity of the resultant jet, and
l is the length of the nozzle or supply tubing.
The above equation can be evaluated analytically for simple nozzle shapes. Assume that the nozzle is conical with the entrance diameter of d and the exit diameter d'.
Q-Evaluate the integral analytically, use your integrated expression to compute pressure drop through the nozzle, for the following variable values:
d [mm] 0.04 0.04 0.04
d' [mm] 0.02 0.02 0.02
l [mm] 0.1 0.1 1.0
μ [cP] 1 40 1
Ï [kg/m^3] 1,000 1,000 1,000
σ [N/m] 0.072 0.072 0.072
v [m/s] 10 10 10