# Syringe Pump Linear Force

When selecting the syringe pump for your application you may have pressure as an important factor, but how to know which pump will fulfill your requirements? Either using a single syringe or a multi-channel can affect the pressure. To calculate the final pressure, we need to know the linear force of the pump which is directly related to the pressure the syringe will receive. Therefore, in this article, we will talk about linear force, what it is? How to calculate it? And why it is important.

We will present the linear force fundamentals to understand the mechanics behind syringe pumps; we also will calculate the force and pressure with examples. Hopefully, after this small review, you will have a better insight into how your syringe pump works.

## Linear Force Fundamentals

Syringe pumps use stepper motor-linear actuators that convert rotary-to-linear motion, which means that the force of the motor will be transferred from torque to linear force. To calculate the linear force in a given device, we have to consider four contributions: force from friction, acceleration force, the force due to gravity and the applied force. Then, a linear force is defined as follow:

Total Linear Force = F (friction) + F (acceleration) + F (gravity) + F (applied).

The applied force is that provided by the stepper motor, however, the net force decrease due to the friction (at higher speed lower force). In practical terms, the friction force is taken as a factor correcting the maximum force of the motor reflected in terms of efficiency. The efficiency is also affected by the lead screw used in the actuator (length and pitch), which modify the velocity of the nut that moves the syringe plunger. Considering these characteristics, we can calculate the linear force with the following formula.

Linear Force = (Maximum force of the motor × 2π × efficiency)/pitch

For example, the linear force of a linear actuator with a motor of 0.5 Nm and a lead screw with a 1 mm pitch, and a 0.8 efficiency at a 1 mm/s speed is:

Linear force= (0.5 Nm × 2(3.14) ×0.8)/0.001 m = 2512 N = 564.69 lbf

As we mentioned previously, the pressure in the syringe is related to the linear force of the pump. Recall that pressure is the amount of force exerted in a given area, for example, in this case, if we use a syringe of 0.3-inch diameter the final pressure will be:

Pressure = 564.69 lbf/(π/4 × (0.3)2) = 7998.44 psi

Since the pressure is related to the area, if we use two syringes of 0.3-inch diameter, the force and the pressure received by each syringe is half of the calculated pressure. One of the advantages of the syringe pumps is that we can have high pressure due to the small area in the syringe, which makes critical the use of high-quality syringes (stainless steel for high pressure).

## Concluding Remarks

In conclusion, we can say that it is important to know the linear force of the syringe pump to choose the correct model for our application, for example, viscous liquids required higher pressure, or maybe you want to use a multichannel. Chemyx syringe pumps offer a variety of models with linear forces ranging from 35 to 500 lbf that make them suitable for many applications.

## Do you need more specialized information?

You can also find more exciting subjects regarding syringe pumps and their application in your field of study; please visit the Chemyx website to learn more about microfluidics, chemical synthesis, biochemical reactions, and materials synthesis among others. 