Blood Flow, Pressure and Resistance: Why Vessel Radius Matters

Blood flow depends on a pressure difference and the resistance of the pathway. A high pressure at one point does not, on its own, tell you how much blood will flow. This guide separates the driving pressure, the resistance of one vessel and the resistance of a whole vascular bed.

For undergraduate medical study and postgraduate revision. Updated 6 November 2026.

Learning objectives

  • Use Q = ΔP/R with consistent units.
  • Predict how vessel radius affects resistance in an ideal laminar-flow model.
  • Distinguish a single segment from a series or parallel network.
  • State what must remain constant before making a flow prediction.

1. Compare upstream and downstream pressure

For a defined pathway, Q = (Pin − Pout)/R = ΔP/R. Q is volume flow per unit time; ΔP is the pressure difference between its ends; R is resistance to flow.

Imagine an organ supplied at 95 mmHg and draining at 5 mmHg. Its driving pressure is 90 mmHg. If resistance is 18 mmHg·min/L, flow is 90/18 = 5 L/min. These are invented values for arithmetic practice, not reference values for a particular organ.

If both pressures rise by 10 mmHg while resistance stays constant, their difference is still 90 mmHg, so calculated flow is unchanged. The difference matters, rather than either pressure alone.

2. Why radius has a powerful effect

For steady laminar flow of a Newtonian fluid through a straight, rigid, circular tube, Poiseuille's relation gives R = 8ηL/(πr4). Here η is viscosity, L is length and r is radius.

At fixed viscosity and length, halving radius makes that tube's resistance 16 times larger. If the pressure difference across that tube is also fixed, its flow becomes one-sixteenth of the original flow. Doubling length or viscosity doubles resistance in this model.

Always state the assumptions. Blood vessels are compliant, flow is pulsatile, and blood does not behave as a perfectly Newtonian fluid in every setting. The relation is a useful reasoning model, not an exact prediction for every vessel or lesion.

3. Worked comparison: one segment versus the whole pathway

Consider two resistances in series, expressed in mmHg·min/L. The first segment has R1 = 1 and the remaining bed has R2 = 9. Total resistance is 10. At a fixed total driving pressure of 100 mmHg, flow is 100/10 = 10 L/min.

Now halve the radius of the first segment only, using the ideal tube assumptions. Its resistance becomes 16, while the remaining bed stays at 9. Total resistance is now 25, so flow is 100/25 = 4 L/min.

The segment's resistance increased sixteenfold, but total resistance increased from 10 to 25: a factor of 2.5. Whole-pathway flow fell to 40% of its starting value, rather than to one-sixteenth. The pressure drop redistributes across the two segments.

These large, simplified teaching flows illustrate a network calculation. They are not measurements from a patient or predictions about a particular stenosis.

4. Series and parallel arrangements

In an unbranched series model, the same steady flow passes through each segment and resistances add: Rtotal = R1 + R2 + ….

Parallel branches connect the same upstream and downstream points. They share a pressure difference, but their individual flows may differ. Their conductances add: 1/Rtotal = 1/R1 + 1/R2 + …. Two parallel branches, each with resistance 12, have a combined resistance of 6 in the same units.

This helps explain why the resistance of one small vessel cannot simply be assigned to an entire organ containing many branching vessels.

5. Pressure and flow are not interchangeable

At fixed ΔP, increasing R decreases Q. At fixed Q, increasing R requires a larger ΔP. Those are different experimental conditions. Before answering a question about vasoconstriction, identify whether pressure, flow or neither is being held constant.

For the systemic circulation as a whole, the relevant mean driving pressure is mean arterial pressure minus right atrial pressure. For an individual organ, use that organ's arterial and venous pressures. Choose the boundaries of the pathway before choosing the pressures.

6. Common misconceptions

  • “Higher arterial pressure always means more flow.” Downstream pressure and resistance also matter.
  • “Half the radius means half the flow.” The ideal tube relation involves the fourth power, with other variables fixed.
  • “One narrowed segment sets the entire resistance.” Account for the rest of the network.
  • “Parallel resistances add directly.” Add reciprocals; direct addition applies to series resistance.

7. Revision questions with answers

  1. ΔP is 80 mmHg and R is 20 mmHg·min/L. What is Q? 4 L/min.
  2. If resistance doubles at fixed driving pressure, what happens to flow? It halves.
  3. Two series resistances are 3 and 7. What is their total? 10 in the same resistance units.
  4. Two parallel resistances are each 8. What is their combined resistance? 4 in the same units.
  5. Why might a sixteenfold change in one segment produce a smaller change in total resistance? Unchanged series segments also contribute to the original and final totals.

8. Choose your next resource

For focused reading, view the Haemodynamics PDF chapter. For a broader reference, compare the contents of Cardiovascular Physiology: A Clinically Integrated Approach. These are separate paid digital resources; check their listings for scope and current prices.

To try the teaching style on another foundational topic, explore the free Homeostasis sample. It covers homeostasis, rather than the calculations above. Find related free guides in the physiology resource hub.

References and further reading

These original notes teach physiological reasoning; use your course materials for the depth and terminology required by your curriculum.