**General Calculation**

- Calculation of total column volume (also used for calculating bed volume)
- Calculation of empty column linear flow rate from a volumetric flow rate
- 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)

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**Pressure Flow Calculations**

- Theoretical changes in pressure after changing particle size
- Ergun Modification of the Blake-Kozeny Equation for Pressure-Flow
- Pressure conversions starting with psi
- Pressure conversions starting with bar
- Pressure conversions starting with kg/cm2
- Pressure conversions starting with kPa
- Pressure conversions starting with MPa

1. Theoretical changes in pressure after changing particle size:

Where: Î”P1 = Initial pressure (any pressure units)

Î”P2 = Calculated pressure (same pressure units as P1)

dp1 = Initial mean particle size (any units but typically Âµm)

dp2 = Mean particle size of new resin (same units at dp1)

2. Ergun Modification of the Blake-Kozeny Equation for Pressure-Flow:

Where:

Î”P = Change in pressure

L = Column Length

Î· = Mobile phase viscosity

u = Empty column linear velocity (cm/hr)

dp2 = Mean particle size

Îµ = 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

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