Syringe Flow Rate Calculator
Calculate volumetric flow rate based on syringe diameter and pump linear speed.
Calculation Results
Understanding Syringe Flow Rate Calculations
In microfluidics, chemistry, and medical infusion therapy, precise fluid delivery is often controlled by syringe pumps. These pumps operate by pushing the plunger of a syringe at a constant linear velocity. To determine the actual volume of fluid being dispensed per unit of time (the volumetric flow rate), one must consider the physical dimensions of the syringe.
The Math Behind the Calculator
The calculation assumes the syringe barrel is a perfect cylinder. The relationship between the linear speed of the pump and the volumetric flow rate is defined by the cross-sectional area of the syringe.
1. Calculate the Radius ($r$):
$$ r = \frac{\text{Diameter}}{2} $$
2. Calculate Cross-Sectional Area ($A$):
$$ A = \pi \times r^2 $$
If the diameter is in millimeters (mm), the area is in square millimeters (mm²).
3. Calculate Flow Rate ($Q$):
$$ Q = A \times v $$
Where $v$ is the linear velocity of the plunger.
Note: Since $1 \text{ mm}^3$ is equivalent to $1 \text{ microliter (\mu L)}$, calculating with mm and mm/min directly gives the flow rate in $\mu L/\text{min}$.
Common Syringe Inner Diameters
The inner diameter varies by manufacturer (e.g., BD, Hamilton, Terumo). Below are approximate values for standard plastic syringes (BD Plastipak):
| Syringe Size | Approx. Inner Diameter (mm) |
|---|---|
| 1 mL | 4.69 mm |
| 3 mL | 8.59 mm |
| 5 mL | 11.99 mm |
| 10 mL | 14.48 mm |
| 20 mL | 19.05 mm |
| 60 mL | 26.59 mm |
Always verify the diameter with calipers or the manufacturer's datasheet for critical applications.
Why is this calculation important?
Syringe pumps often display units in linear steps or speed (mm/min) depending on the motor configuration, while experimental protocols require volumetric rates (mL/hr). This calculator bridges that gap, ensuring accurate dosing for drug delivery, chemical synthesis, or electrospinning applications.