I am using a device to push small volumes (60-100cc) through a plastic tube with a length of approx 24 and a diameter of 1mm or less. I can control flow rate, generally 2-4cc/sec. The liquid has a higher viscosity than water. I am trying to determine the difference in pressure on the piston face (which remains a constant size) using different fluids with slightly different viscosities through tubing of the same length, and differences in pressure using the same fluid through different tubing lengths. Ie; Fluid A and Fluid B through Tube 1, and Fluid A through Tube 1 and 2. The tubes are the same material, same diameter, regardless of length. The pressure used to push the piston remains the same across all fluid/tubing combinations.
If the flow is not turbulent (no high speeds) and incompressible, and the tube is of circular cross section, then Poiseuille Law flow will ensue. In Poiseuille flow through a cylindrical pipe the velocity is largest along the centerline of the tube and diminishes to zero at the inner wall quadratically with distance r: v(r) = c (R^2 - r^2) with c a constant for given viscosity and pressure gradient ( delta(p) / L ) In Poiseuille flow through a cylindrical pipe the rate of flow (volume/second) is given by Qdot, where Qdot = ( Delta(p) pi R^4 ) /(8 eta L). (where eta is the dynamic viscosity of the fluid) Since the pressure difference Delta(p) is the pressure on the piston face - ambient pressure , let's call this (p - p0) , you have p - p0 = ( 8 eta L) * Qdot /(pi R^4) Using this Poiseuille' s Law you can calculate the pressure on the piston. You say at the end of your question that the pressure used to push is kept constant. In that case the flow rate you measure should be inversely proportional to eta and L.
