Estimating the Flow Rate in Capillary: Flow Rate in Capillaries

When a viscous fluid flows through a tube of fixed length and ID, a resistance to fluid flow exists. So long as the Reynolds Number is less than 2000 and the fluid is considered to be Newtonian, some relatively simple equations can be used to describe the system. Under these conditions, the maximum speed is at the center and near the walls the fluid tends to remain nearly stationary. In terms of the viscosity, the resistance to fluid flow, R, for steady flow through a circular tube of radius, r, can be shown to be:

(eq. 3-1)

where h is the coefficient of viscosity, and L is the length. The SI unit for the coefficient of viscosity is poise, after the French physician Jean Poiseuille (1797-1869), who is often credited with deriving the above expression.

As can be seen, the resistance is inversely proportional to the square of the radius of the tube. For example, a change from 200mm inside diameter capillary to 100mm inside diameter means an increase in resistance to flow by a factor of 4.

By rearrangement of Equation 3-1 above, Poiseuille’s Equation is derived.  It follows that the flow rate through a capillary can be expressed in terms of pressure drop. More importantly, the flow rate is expressed in terms of the capillary ID, and is given by:

(eq. 3-2)

The flow rate, F (sometimes expressed as v), varies as the 4th power of the radius, i.e., a 2-fold change in radius creates a 16-fold change in flow rate. Equation 3-3 offers an easy to use version that gives the flow rate, F, in mL/min:

Technical Data Disclaimer

The information given herein, including drawings, illustrations and schematics (that are intended for illustration purposes only), is believed to be reliable.  However, Polymicro Technologies makes no warranties as to its accuracy or completeness and disclaims any liability in connection with its use.  Polymicro Technologies only obligation shall be as set forth in Polymicro Technologies' standard terms and conditions of sale for this product and in no way will Polymicro Technologies be liable of any incidental, indirect or consequential damages arising out of the sale, resale, use or misuse of the product.  Users of Polymicro Technologies' products should make their own evaluation to determine the suitability of each such product for the specific application.