Fluid velocity through a capillary? 1

[Partington]

I wish to use a capillary tube to dose a fluid and so need to calclate the fluid velocity through the capillary.

How do I do this?

I know the pressure differential, fluid viscosity and the capillary dimension may be set according to need.

Hope you can help

Tom

 

[25362]

If the flow is considered "laminar", the net [Δ]P is known, and the velocity (i.e., kinetic energy) of the fluid leaving the capillary is zero, or negligibly small, use the Poiseuille formula:

Volume, m³/s = [π] r⁴[Δ]P/(8 [η]L)​

r: tube radius, m
[Δ]P: pressure differential N/m²
[η]: absolute(=dynamic) viscosity of the fluid, Ns/m²
L: tube length, m

Any consistent set of units may be used.

BTW, this equation serves to measure fluid viscosities by gravity flows through capillary tubes, from the times [τ] taken by equal volumes of the liquids, that of unknown viscosity when compared with another, say, water, taken as reference, the viscosity of which is known.

Since [Δ]P is proportional to the density [ρ] of the fluids:

[η] = [[η]/([τ] [ρ])]_ref ([τ] [ρ])​