— Series & Parallel Resistance

Everything you add
slows the flow.

Every extension set, filter, and needleless connector is a resistor in your IV circuit. The Hagen-Poiseuille equation gives each component a resistance value — and the laws of fluid circuits determine how they combine.

R =
8ηLπr⁴
Component Resistance
Rs = R₁ + R₂ + ···
Series (additive)
1Rp
=
1R₁
+
1R₂
Parallel (reciprocal sum)
Quick Scenarios
IV Line Resistance Network
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Series Always Increases Resistance
Every component in series adds its resistance to the total. A 0.2μm inline filter can have 3–10× the resistance of the catheter itself, dramatically reducing flow.
⚖️
Parallel Lines Are Powerful
Two identical lines in parallel halve the total resistance (double the flow). Three lines reduce resistance to one-third. This is the math behind running two large-bore IVs in trauma.
🚧
The Bottleneck Rule
In a series circuit, the component with the highest resistance dominates. A tiny catheter after huge tubing still limits flow to the catheter's capacity. Always identify your bottleneck.
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Needleless Connectors
Mechanical valve connectors (e.g., Maximus, Tego) can add significant resistance — some equivalent to a 2–4cm length of narrow tubing. Use split-septum connectors for high-flow needs.
Historical Origin · Ohm → Physiology
An electrical law becomes hemodynamics.

Georg Ohm's 1827 law (V = IR) was adapted directly to blood flow: ΔP = Q × R. Voltage became pressure gradient; current became flow; resistance stayed resistance. The circuit metaphor is not an approximation — it's the same mathematics, rescaled.

Electrical: V = I · R
Hemodynamic: ΔP = Q · R
Hydraulic: R = 8ηL / πr⁴
Intracav Opportunity · Graph-Based Vascular Model
Model the vascular system as a weighted graph.

Every access point, junction, and vessel segment can be represented as a graph where resistance is the edge weight. This enables computation of optimal access points and predicted flow distribution before insertion.

Nodes = junctions & bifurcations
Edges = vessel segments
Weights = resistance (8ηL/πr⁴)
Output = optimal access point + flow distribution
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Flow Dynamics
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Turbulence