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# Basic Calculations

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The following equations are for the novice chromatographer. More advanced calculations can be found on the system suitability and pressure-flow pages. Please click on the corresponding tab below for the equations and details of how to calculate each one.

1. Total or empty column volume

2. Linear velocity

3. Mobile phase porosity

4. Calculation of empty column linear flow rate from volumetric flow rate

5. Calculation of volumetric flow rate from empty column flow rate

6. Relationship between linear velocity and empty column linear flow rate

Total or empty column volume

## Ve = π • R2 • L = 1/4 π • D2 • L

Ve = empty column volume
L = length of the column (or packed bed)
D = column diameter
If R (or D) and L are expressed in mm, Ve will be in µL. If in cm, then Ve in mL.

Linear velocity

The efficiency of an HPLC column varies with flow rate. Instead of expressing efficiency as a function of flow rate, it is easier to use linear velocity when comparing the efficiencies of columns with different internal diameter, Simply stated, linear velocity is the speed at which the solvent front travels the length of the column (L), and is calculated by dividing the column length by the retention time (t0) of an unretained component. By definition, an unretained compound has complete access to the volume of mobile phase between the particles and to the volume of mobile phase in the pores of the particles, while not interacting with the external or internal surface of the particles.

## v = L/ t0

v (or < v >) = linear velocity (cm/min or cm/hr or mm/s)
L = length of the column or packed bed (cm or mm)
t0 = retention time of an unretained compound (in min, hr or s)

Note: see also the Eq. 4 for an expression of the empty column linear flow rate or superficial velocity, which is commonly used to describe transport phenomena in open tubes, and is also used in process chromatography.

Mobile phase porosity

## εt = F • t0 / 1/4 π • D2 • L

εt = mobile phase porosity (fraction of the column occupied by mobile phase between the particles and in the pores); dimensionless parameter.
D and L are defined as in Eq. 1; t0 defined as in Eq. 2.
F = volumetric flow rate (mL/min)

Calculation of empty column linear flow rate from volumetric flow rate

## u = F/ π • R2

u = empty column linear flow rate or superficial velocity (cm/min or cm/hr)
F = volumetric flow rate (mL/min or mL/hr)
R as defined in Eq. 1.

Calculation of volumetric flow rate from empty column linear flow rate

Using Eq. 4, the volumetric flow rate can be obtained by multiplying the linear flow rate by the cross-sectional area of the column.

## F = u • π • R2

Relationship between linear velocity and empty column linear flow rate

Empty column linear flow rate or superficial velocity (u) relates to the linear velocity (v in Eq. 2 above) as:

## u = v • εt or, v = u /εt

u = empty column linear flow rate, or superficial velocity (see Eq. 4)
v = linear velocity (see Eq. 2)
εt = mobile phase porosity (see Eq. 3)