Poiseuille's Equation gives the volume flow rate through a capillary as Q = (pi r^4 Delta P)/(8 eta l), so flow is directly proportional to pressure difference and fourth power of radius, and inversely proportional to viscosity and length.

• Use it for laminar flow through a long cylindrical tube of uniform radius.
• The same relation can be written as Q = Delta P / R, where R = 8 eta l / (pi r^4).
• The trap is to compare radius changes linearly when the law actually depends on r^4.

Series Combination of Capillary Tubes keeps the same flow rate through each tube, so the effective liquid resistance is R_eff = R1 + R2 and the total pressure drop is shared across the two capillaries.

• The same volume per second must pass through both capillaries in a series path.
• Equivalent resistance increases, so for the same applied Delta P the total flow decreases compared with a single tube.
• The trap is to use the parallel rule in a series question just because two tubes are mentioned together.

Parallel Combination of Capillary Tubes keeps the same pressure difference across each branch, while the total flow divides among them, so 1/R_eff = 1/R1 + 1/R2.

• Each branch experiences the same Delta P between the common inlet and outlet points.
• Equivalent resistance decreases, which makes the total flow larger than the flow through any single branch alone.
• The trap is to assume the flow is the same in each branch even when the branch resistances are different.