The flow rate of a specific peristatic pump is determined by three major parameters: the rotation speed (N rpm) of the rotor shaft, the inner diameter (d cm) of the hose, and the diameter (D cm) of the roller assembly. The flow rate V (mL/min) can be expressed in the following formula.

                    V = [p (d/2)2] [p(D+2T-d)b]N

Where T is the wall thickness of hose in cm (centimeter), which is usually much smaller than D, and b is the effective fraction for a cycle of rotor rotation. The flow rate formula above indicates the following general conclusions under normal run conditions:

  • The volume flow rate is proportional to the rotor speed N.
  • The volume flow rate is proportional to the square of the hose diameter.
  • The volume flow rate is closely proportional to the diameter of the roller track arc.

However, other factors need to be considered, since the effective fraction b is dependent on the number of rollers and roller diameters, the back pressure of the inlet side (hose diameter and length, viscosity of fluid, and hose material, etc.), and the rotation speed N when N is too big.

As a numerical example, we can consider a system when being operated at N = 10 rpm; suppose the tubing inner diameter is d = 0.48 cm, wall thickness 0.16 cm, and the diameter of the roller assembly D = 4.0 cm, and b = 0.8 (typically b in the range of 0.6-0.8). So the flow rate is: 

                              V = 3.14 x (0.48/2)2 x 3.14 x (4.0 +2x0.16- 0.48) x 0.8 x 10 = 17.46 mL/min

In application practice, the flow rate for a specific pump system should be calibrated, so a calibration curve can be plotted as shown in the following example. A simplified flow rate formula can be obtained:

                             V = kN

where k is the slope of the calibration curve, and the relation is trust-worthy in the linearity range.