1. The particle equation of motion considering only drag is
m(dup/dt) = ½CD(πdp2/4)ρf(uf - up)[uf - up]
which can be reduced to
dup/dt = (18μ/ρpdp2)(CDRer/24)(uf - up)
Rer = (ρfdp|uf - up|/μ)
a) Create a spreadsheet to solve the differential equation using Euler's method. Assume CD = 24/Rer + 0.44.
b) Use the spreadsheet to examine the particle motion for the following conditions:
Fluid density = 1000 kg/m3, fluid viscosity = 0.001 Pa s, particle density = 2650 kg/m3, particle diameter = 100 microns, fluid velocity = 0.01 m/s, initial particle velocity = 0 with a time step of 1e-5 s. Plot particle velocity for the time range from 0 to 4e-3 s.
c) Compare solution of part b with the exact solution for Stoke's flow.
up = uf(1 - e-t/τ_v)
τv = ρpdp2/18μ
d) Use the spreadsheet to examine the particle motion for the following conditions: Fluid density = 1000 kg/m3, fluid viscosity = 0.001 Pa s, particle density = 2650 kg/m3, particle diameter = 100 microns, fluid velocity = 2 m/s, initial particle velocity = 0 with a time step of le-5 s. Plot particle velocity for the time range from 0 to 4e-3 s.
e) Use the spreadsheet to examine the particle motion for the following conditions: Fluid density = 1.2 kg/m3, fluid viscosity = 1.8e-5 Pa s, particle density = 2650 kg/m3, particle diameter = 100 microns, fluid velocity = 10 m/s, initial particle velocity = 0 with a time step of le-3 s. Plot particle velocity for the time range from 0 to 0.3 s.