1. Ideal Flow Rate Calculation

In an ideal scenario, the peristaltic pump generates a consistent flow rate with each rotation, independent of external factors. If the pump generates X ml per revolution, and the pump is running at a speed of N revolutions per minute (RPM), the flow rate is:

$\text{Flow Rate (ml/min)}=X\times N$

For example, if the pump delivers 10 ml per revolution and operates at 100 RPM, the flow rate would be:

$10\text{ml}\times 100\text{RPM}=1000\text{ml/min}$

2. Impact of Tube Diameter

The inner diameter of the pump tube plays a key role in determining the flow rate. A larger tube diameter allows for a greater volume of liquid to be pumped with each rotation, resulting in a higher flow rate. Conversely, a smaller diameter tube will reduce the flow rate.

3. Viscosity and Rebound Time

In real-world conditions, the flow rate can deviate from the ideal calculation due to factors like liquid viscosity and the tube’s rebound time. When liquid is pumped, the pump tube compresses and then rebounds to its original shape. For more viscous liquids, the tube takes longer to rebound, which can reduce the effective flow rate.

• Rebound time: The rebound time is the period it takes for the tube to return to its original shape after compression. If the liquid is too viscous, the tube may not fully rebound before the next compression occurs, which can result in a reduced flow rate.

• Speed and linear growth: The flow rate typically increases linearly with the rotational speed, but if the rebound time exceeds the time between rotations (single roller displacement time), the flow rate will be less than the ideal value due to insufficient rebound.

4. Outlet Pressure Effects

As the outlet pressure increases, it can impact the flow rate. If the pressure on the outlet side becomes higher than the pump’s internal pressure, the flow rate can be reduced due to backflow. Additionally, an increase in outlet pressure can cause the pump tube’s inner diameter to expand, leading to less liquid being transported with each revolution.

If the outlet pressure exceeds the pump’s pressure, a complete backflow may occur, disrupting the flow rate calculation and causing liquid to flow backward into the pump.

5. Conclusion

When calculating the flow rate of a peristaltic pump, consider the following:

• Speed and tube diameter: These are the primary factors in determining flow rate in ideal conditions.
• Viscosity: Higher viscosity liquids take longer to move through the tube, affecting the rebound time and reducing the effective flow rate.
• Outlet pressure: Increased outlet pressure can cause backflow and reduce the pump's efficiency.

In practice, flow rate can often be approximated by the simple product of the pump’s output per revolution and its rotational speed, particularly for liquids with low viscosity. However, for highly viscous liquids, the actual flow rate will be lower than calculated, as the pump’s rotational speed may slow down due to increased resistance.

Understanding these factors and using empirical data will help achieve more accurate flow rate calculations for peristaltic pumps in real-world applications.