plotting based on the results of mathematical formulas

[Timur]

Good day to all! I'm asking for help. How to derive the graphical dependence of Rmin, Rmax from P1-Pmax with the following mathematical dependencies:

elif Kg == 3 and Kz == 3:
print('Expected cloud combustion mode - 4')
Upl = 200 # visible flame front velocity 200 m/s
for R in np.arange(Rmin, Rmax, Ri):
Rx1 = R / ((E1/Ratm)**0.333)
Rcr1 = 0.34
if 0 < Rx1 <= Rcp1:
Px1 = ((Upl ** 2) / (340 ** 2)) * ((7 - 1) / 7) * ((0.83 / 0.34) - (0.14 / (0.34 ** 2)))
Ix1 = ((Upl / 340) * ((7 - 1) / 7)) * (1 - 0.4 * (( Upl / 340) * ((7 - 1) / 7))) * ((0.06 / 0.34) + (0.01 / (0.34 ** 2)) - (0.0025 / (0.34 ** 3)))
P1 = Px1 * Ratm
I1 = Ix1 * (Ratm ** 1 / 3 ) * ((E1 ** 1 / 3 ) / 340)
else:
Px1 = ((Upl ** 2) / (340 ** 2)) * ((7 - 1) / 7) * ((0.83 / Rx1) - (0.14 / (Rx1 ** 2)))
Ix1 = ((Upl / 340) * ((7 - 1) / 7)) * (1 - 0.4 * (( Upl / 340) * ((7 - 1) / 7))) * ((0.06 / Rx1) + (0.01 / (Rx1 ** 2)) - (0.0025 / (Rx1 ** 3)))
P1 = Px1 * Ratm
I1 = Ix1 * (Ratm ** 1 / 3 ) * ((E1 ** 1 / 3 ) / 340)
Rx2 = R / ((E2/Ratm)**0.333)
Rcr2 = 0.34
if 0 < Rx2 <= Rcr2:
Px2 = ((Upl ** 2) / (340 ** 2)) * ((7 - 1) / 7) * ((0.83 / 0.34) - (0.14 / (0.34 ** 2)))
Ix2 = ((Upl / 340) * ((7 - 1) / 7)) * (1 - 0.4 * (( Upl / 340) * ((7 - 1) / 7))) * ((0.06 / 0.34) + (0.01 / (0.34 ** 2)) - (0.0025 / (0.34 ** 3)))
P2 = Px2 * Ratm
I2 = Ix2 * (Ratm ** 1 / 3 ) * ((E2 ** 1 / 3 ) / 340)
else:
Px2 = ((Upl ** 2) / (340 ** 2)) * ((7 - 1) / 7) * ((0.83 / Rx2) - (0.14 / (Rx2 ** 2)))
Ix2 = ((Upl / 340) * ((7 - 1) / 7)) * (1 - 0.4 * (( Upl / 340) * ((7 - 1) / 7))) * ((0.06 / Rx2) + (0.01 / (Rx2 ** 2)) - (0.0025 / (Rx2 ** 3)))
P2 = Px2 * Ratm
I2 = Ix2 * (Ratm ** 1 / 3 ) * ((E2 ** 1 / 3 ) / 340)
Rx3 = R / ((E3 / Ratm) ** 0.333)
Rcr3 = 0.34
if 0 < Rx3 <= Rcr3:
Px3 = ((Upl ** 2) / (340 ** 2)) * ((7 - 1) / 7) * ((0.83 / 0.34) - (0.14 / (0.34 ** 2)))
Ix3 = ((Upl / 340) * ((7 - 1) / 7)) * (1 - 0.4 * (( Upl / 340) * ((7 - 1) / 7))) * ((0.06 / 0.34) + (0.01 / (0.34 ** 2)) - (0.0025 / (0.34 ** 3)))
P3 = Px3 * Ratm
I3 = Ix3 * (Ratm ** 1 / 3 ) * ((E3 ** 1 / 3 ) / 340)
else:
Px3 = ((Upl ** 2) / (340 ** 2)) * ((7 - 1) / 7) * ((0.83 / Rx3) - (0.14 / (Rx3 ** 2)))
Ix3 = ((Upl / 340) * ((7 - 1) / 7)) * (1 - 0.4 * (( Upl / 340) * ((7 - 1) / 7))) * ((0.06 / Rx3) + (0.01 / (Rx3 ** 2)) - (0.0025 / (Rx3 ** 3)))
P3 = Px3 * Ratm
I3 = Ix3 * (Ratm ** 1 / 3 ) * ((E3 ** 1 / 3 ) / 340)
Rx4 = R / ((E4/Ratm)**0.333)
Rcp4 = 0.34
if 0 < Rx4 <= Rcp4:
Px4 = ((Upl ** 2) / (340 ** 2)) * ((7 - 1) / 7) * ((0.83 / 0.34) - (0.14 / (0.34 ** 2)))
Ix4 = ((Upl / 340) * ((7 - 1) / 7)) * (1 - 0.4 * (( Upl / 340) * ((7 - 1) / 7))) * ((0.06 / 0.34) + (0.01 / (0.34 ** 2)) - (0.0025 / (0.34 ** 3)))
P4 = Px4 * Ratm
I4 = Ix4 * (Ratm ** 1 / 3 ) * ((E4 ** 1 / 3 ) / 340)
else:
Px4 = ((Upl ** 2) / (340 ** 2)) * ((7 - 1) / 7) * ((0.83 / Rx4) - (0.14 / (Rx4 ** 2)))
Ix4 = ((Upl / 340) * ((7 - 1) / 7)) * (1 - 0.4 * (( Upl / 340) * ((7 - 1) / 7))) * ((0.06 / Rx4) + (0.01 / (Rx4 ** 2)) - (0.0025 / (Rx4 ** 3)))
P4 = Px4 * Ratm
I4 = Ix4 * (Ratm ** 1 / 3 ) * ((E4 ** 1 / 3 ) / 340)
Rxmax = R / ((Emax / Ratm) ** 0.333)
Rxmax = 0.34
if 0 < Rxmax <= Rxmax:
Pxmax = ((Upl ** 2) / (340 ** 2)) * ((7 - 1) / 7) * ((0.83 / 0.34) - (0.14 / (0.34 ** 2)))
Ixmax = ((Upl / 340) * ((7 - 1) / 7)) * (1 - 0.4 * (( Upl / 340) * ((7 - 1) / 7))) * ((0.06 / 0.34) + (0.01 / (0.34 ** 2)) - (0.0025 / (0.34 ** 3)))
Pmax = Pxmax * Ratm
Imax = Ixmax * (Ratm ** 1 / 3 ) * ((Emax ** 1 / 3 ) / 340)
else:
Pxmax = ((Upl ** 2) / (340 ** 2)) * ((7 - 1) / 7) * ((0.83 / Rxmax) - (0.14 / (Rxmax ** 2)))
Ixmax = ((Upl / 340) * ((7 - 1) / 7)) * (1 - 0.4 * (( Upl / 340) * ((7 - 1) / 7))) * ((0.06 / Rxmax) + (0.01 / (Rxmax ** 2)) - (0.0025 / (Rxmax ** 3)))
Pmax = Pxmax * Ratm
Imax = Ixmax * (Ratm ** 1 / 3 ) * ((Emax ** 1 / 3 ) / 340)
print(f"at {dot1} m R = {R} m, Rx1 = {Rx1}, P1 = {P1/1000} kPa, I1 = {I1} Pa * s,\
\ppri {dot2} m and R = {R} m, Rx2 = {Rx2}, P2 = {P2/1000} kPa, I2 = {I2} Pa * s,\
\ppri {dot3} m and R = {R} m, Rx3 = {Rx3}, P3 = {P3/1000} kPa, I3 = {I3} Pa * s,\
\ppri {dot4} m and R = {R} m, Rx4 = {Rx4}, P4 = {P4/1000} kPa, I4 = {I4} Pa * s,\
\ppri {dmax} m and R = {R} m, Rxmax = {Rxmax}, Pmax = {Pmax/1000} kPa, Imax = {Imax} Pa*s")

Gribouillis write Feb-08-2024, 07:19 PM:
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[Gribouillis]

How to derive the graphical dependence of Rmin, Rmax from P1-Pmax

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