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# Chromatographic Calculations

General Calculation

1. Calculation of total column volume (also used for calculating bed volume)
2. Calculation of empty column linear flow rate from a volumetric flow rate
3. Calculation of volumetric flow rate from empty column linear flow rate

1. Calculation of total column volume (also used for calculating bed volume): Where:
V = calculated column volume
r = column radius
L = length of the column (or packed bed)

2. Calculation of empty column linear flow rate from volumetric flow rate: Where:
u = Linear flow rate (cm/hr)
F = volumetric flow rate (mL/hr) [multiply mL/min x 60 min/hr]
r = column radius (cm)

3. Calculation of volumetric flow rate from empty column linear flow rate Where:
F = volumetric flow rate (mL/hr) [divide by 60 min/hr to get mL/min]
u = Linear flow rate (cm/hr)
r = column radius (cm)

Pressure Flow Calculations
1. Theoretical changes in pressure after changing particle size
2. Ergun Modification of the Blake-Kozeny Equation for Pressure-Flow
3. Pressure conversions starting with psi
4. Pressure conversions starting with bar
5. Pressure conversions starting with kg/cm2
6. Pressure conversions starting with kPa
7. Pressure conversions starting with MPa
1. Theoretical changes in pressure after changing particle size: Where: ΔP1 = Initial pressure (any pressure units)
ΔP2 = Calculated pressure (same pressure units as P1)
dp1 = Initial mean particle size (any units but typically µm)
dp2 = Mean particle size of new resin (same units at dp1)

2. Ergun Modification of the Blake-Kozeny Equation for Pressure-Flow: Where:
ΔP = Change in pressure
L = Column Length
η = Mobile phase viscosity
u = Empty column linear velocity (cm/hr)
dp2 = Mean particle size
ε = Interstitial void volume intrinsic to each resin

3. Pressure conversions starting with psi:
• To convert to kg/cm2 from psi multiply by 0.0703
• To convert to bar from psi multiply by 0.0690
• To convert to kPa from psi multiply by 6.895
• To convert to MPa from psi multiply by 0.00690

4. Pressure conversions starting with bar:
• To convert to kg/cm2 from bar multiply by 1.0197
• To convert to psi from bar multiply by 14.504
• To convert to kPa from bar multiply by 100
• To convert to MPa from bar multiply by 0.100

5. Pressure conversions starting with kg/cm2: To convert to psi from kg/cm2 multiply by 14.223
• To convert to bar from kg/cm2 multiply by 0.981
• To convert to kPa from kg/cm2 multiply by 98.067
• To convert to MPa from kg/cm2 multiply by 0.0981

6. Pressure conversions starting with kPa: To convert to kg/cm2 from kPa multiply by 0.0102
• To convert to bar from kPa multiply by 0.01
• To convert to psi from kPa multiply by 0.1450
• To convert to MPa from kPa multiply by 0.001

7. Pressure conversions starting with MPa:
• To convert to kg/cm2 from MPa multiply by 10.197
• To convert to bar from MPa multiply by 10
• To convert to kPa from MPa multiply by 1000
• To convert to psi from MPa multiply by 145.04