I’m trying to set up the following differential equation in excel. The aim is to calculate Aair. This is one part of a model of how particles being sprayed in the air change over time due to gravity.
I don’t think we need to worry too much about the background of this but here is a link if interested. See section 4.1.2.2 Equation 20a.
https://www.rivm.nl/bibliotheek/rapporten/2017-0197.pdf
I think I have achieved this using the following setup in excel:
Where the formulas for each part of the expression are:
I think this is correct (though please let me know if you think I have done something wrong mimicking the equation.
I decided to break the equation into two parts to simplify the issue.
So Initially I work out dAir/dt and then multiply this by the current time to get Aair.
In reality I have many particle sizes I need to apply this to simultaneously and dont want to have two components for each. Is it possible to somehow calculate Aair in a single column? I have tried this but as they seem to rely on each other this seems… difficult.. It is even possible? MI feel saying circular reference but Im not convinced and its breaking my head
Any thoughts would be much appreciated.
DATA to copy:
Particle Size Qvent Room Volume Floor Surface Area Vs Rairbone
0.19 0.000555556 10 4 1.96E-06 1.23E-08
TIME (s) dair/dt Aair
0 1.23E-08 0.00E+00
7.80 1.22E-08 9.57E-08
15.60 1.22E-08 1.91E-07
23.40 1.21E-08 2.85E-07
31.20 1.21E-08 3.78E-07
39.00 1.20E-08 4.70E-07
46.80 1.20E-08 5.62E-07
54.60 1.19E-08 6.53E-07
62.40 1.19E-08 7.43E-07
70.20 1.18E-08 8.33E-07
78.00 1.18E-08 9.21E-07
85.80 1.17E-08 1.01E-06
93.60 1.17E-08 1.10E-06
101.40 1.16E-08 1.18E-06
109.20 1.16E-08 1.27E-06
117.00 1.15E-08 1.35E-06
124.80 1.15E-08 1.44E-06
132.60 1.14E-08 1.52E-06
140.40 1.14E-08 1.60E-06
dair/dt = =-Table8[Qvent]*J40-$L$37*Table8[Floor Surface Area]*(J40/Table8[Room Volume])+$M$37
Aair = I40*H41 (dair/dt multiplied by time)