- #1
SpaceDuck127
- 1
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- Homework Statement
- Done for a research essay on physics models for water filtration, and what I am focusing on is the change in speed after water passes through a porous material
- Relevant Equations
- q = -k*∆p/(µ*L) Darcy’s Law (flux rate)
∆p = f(L/D)(𝜌V^2/2) Darcy-Weisbach equation
Re = ρVD/µ Reynolds Number equation
f = 64/Re Friction factor equation
By substituting the darcy-weisbach equation into darcy’s law we get
q = -kf/µL * (L/D) * (𝜌V^2/2)
This can be further simplified by substituting the equation for friction factor for laminar flow, f = 64/Re , with the equation for reynolds number, Re = ρVD/µ substituted in such that:
q = (-k/µL)(64µ/ρVD)*(L/D)(𝜌V^2/2)
Which can be simplified from crossing out variables into:
q =-32kV/D^2
Based on physics and research i've done on filtration mechanics this makes kinda perfect sense, but I haven't found any evidence of this substitution online.
q = -kf/µL * (L/D) * (𝜌V^2/2)
This can be further simplified by substituting the equation for friction factor for laminar flow, f = 64/Re , with the equation for reynolds number, Re = ρVD/µ substituted in such that:
q = (-k/µL)(64µ/ρVD)*(L/D)(𝜌V^2/2)
Which can be simplified from crossing out variables into:
q =-32kV/D^2
Based on physics and research i've done on filtration mechanics this makes kinda perfect sense, but I haven't found any evidence of this substitution online.