16.3 Pressure and Flow

Time To Read

17–25 minutes

Date Last Modified

Blood Vessels · Chapter 3 of 7

Flow equals pressure over resistance, and radius rules resistance to the fourth power. Stina’s pressure is normal — which clears one suspect and sharpens the puzzle.

The question you will answer

If her blood pressure is a textbook 118/74, why are her arteries still aging too fast?

Opener · Flow, Pressure, Resistance · about 1¾ minutes

The opener is the same narrated animation you will watch in Scene 1.

Watch the opener first. It sets the question; the chapter answers it.

1

Read the chart

Patient chart · Stina

2020 · age 45

Vitals
BP 118/74 at every visit; mean arterial pressure about 89 mm Hg; pulse 70.

Meaning
Neural, hormonal and renal controls are all working.

Puzzle
Vessels aging fast without the high-pressure damage that usually explains it.


This chapter writes line 3 of Chart Clue #16.

Your prediction

Normal blood pressure, held there by three working control systems, should…

Open the one you’d bet on. Nothing is recorded, and the answer isn’t here — the scenes will test your bet.

Protect her vessels from aging early

The intuitive answer. Hold it while you see exactly what pressure does to a wall — and what it cannot do.

Tell us nothing either way

Fair. Keep it while you watch how pressure, resistance and flow are related.

Rule out pressure as the cause and point somewhere else

Hold that. The chapter measures what a normal pressure actually protects against.

From Stina’s diary

2020 · age 45 · “Quiet”

“It stopped the way a phone stops ringing: one day you notice it’s been quiet a long time.”

2

The story

Three short movements: the case, the anatomy and physiology, then the tie back to Stina. Each links to the scene where you’ll see it move.

I · A Normal Number, a Real Puzzle

Stina’s blood pressure was reliably normal, which made her vascular aging harder to explain. High blood pressure is a familiar way to batter a vessel wall, and she simply didn’t have it. Ruling pressure out is itself informative — but first the team had to understand what blood pressure is and how the body sets it.

See it move: Scene 1 · Flow = ΔP ÷ R · Scene 2 · Systolic, Diastolic, MAP

An arm with a blood-pressure cuff and gauge beside a reading of 118/74 mm Hg, marked normal.
Her pressure is normal, so it cannot explain her aging vessels.

II · Flow, Resistance, and the Fourth Power

Blood pressure is the force blood exerts on vessel walls, highest in the arteries and falling toward the veins. Flow equals the pressure difference divided by resistance, and resistance rises steeply as vessels narrow — halve the radius and resistance rises sixteen-fold, so arteriole diameter is the body’s main pressure dial. Baroreceptors, hormones and the kidneys (renin, angiotensin II, aldosterone, ADH) hold the set-point.

See it move: Scene 1 · Flow = ΔP ÷ R · Scene 2 · Systolic, Diastolic, MAP · Scene 3 · Three Levels of Control

Two arteriole cross-sections. The larger is labelled radius r, resistance ×1. The smaller, half the size, is labelled radius ½ r, resistance ×16.
Halve the radius and resistance rises sixteen-fold.

III · Control Without Protection

For Stina the hemodynamics deliver a crucial negative result: her pressure is a genuine 118/74, held by three control systems working as they should. Blood-pressure control protects against pressure, not against inflammation, so a perfectly regulated number does nothing to stop an inflamed endothelium from aging. Her normal number doesn’t solve the puzzle; it sharpens it.

See it move: Scene 3 · Three Levels of Control

The heart with its great vessels, labelled baroreceptors, seconds; and a kidney with the adrenal gland on top, labelled adrenal, minutes, and kidney, days.
Three controls hold her pressure steady. None of them targets inflammation.

3

Watch · explore · think · check

3 scenes. Each one has a short animation or a slide, something to explore, a true/false spot-check of your thinking, and a quick check. Every scene gives you an evidence card for your board.

How to read the scenes

  • Animation (dark teal) — a short animated explainer, one idea each
  • Slide (dark teal) — a still to study: a micrograph, a diagram or a map
  • Explore (purple) — something to push on while you watch
  • Game (purple) — a quick challenge
  • Think (gold) — reason it out, then spot-check yourself with a few true/false questions; not graded
  • Check (gold) — a quick H5P that scores itself

Scene 1 of 3

Flow = ΔP ÷ R

Her handwritten equation, animated.

Animation · narrated, with captions

Flow, Pressure, Resistance

Module 16 · 16.3 · Opener and Scene 1 · 5 scenes · about 1¾ minutes · narrated. Press Play to start; the words appear in the caption box under the picture.

Animation: the equation F = ΔP ÷ R builds over a vessel with flowing blood; raising the pressure difference speeds the flow and raising resistance slows it. Resistance depends on viscosity (syrup vs milk), vessel length (short vs long hose) and, most of all, radius (halve it and resistance rises 16×), so the arterioles are the body’s pressure dial — where pressure falls off a cliff on the graph of blood pressure across the circulation. Animated scene. The caption below shows the narration for the current scene; a full scene-by-scene description follows the animation.
Scene 1

Paused

Keyboard: when the picture has focus, Space plays or pauses, the left/right arrow keys move between scenes, and M mutes or unmutes.

Text description and full narration

Five-scene narrated animation (about 1¾ minutes) with captions. The equation F = ΔP ÷ R stays across the top; the space below changes each scene.

  1. Scene 1 · The equation (0:00–0:15)

    On screen: A horizontal blood vessel with red blood cells and teal flow arrows moving left to right, labelled “Higher pressure” (left, red), “Lower pressure” (right, blue) and “pressure gradient → flow”. The equation appears symbol by symbol: F (“blood flow”) = ΔP (“pressure difference”) ÷ R (“resistance”).

    Narration: Blood flows because there’s a pressure difference — there’s a gradient. And it flows less when there’s something that resists that gradient. So flow equals the pressure difference divided by resistance.

  2. Scene 2 · Push and resist (0:15–0:25)

    On screen: A red up-arrow appears by ΔP and the cells and arrows speed up (“↑ ΔP → the flow speeds up”); then a purple up-arrow appears by R and the flow slows to a crawl (“↑ R → the flow slows down”).

    Narration: If you raise the pressure difference, the flow speeds up, but if you raise the resistance, the flow slows down.

  3. Scene 3 · Viscosity and length (0:25–0:49)

    On screen: The vessel clears. Three purple chips branch from R: viscosity, length, diameter (“Three things set resistance”). A jar of maple syrup and a glass of milk appear, each over a small tube: arrows crawl through the syrup tube (“Thick, like syrup: more resistance”) and race through the milk tube (“Thin, like milk: less resistance”). A short green hose with fast arrows (“Short hose: less resistance”) and a long hose with slow ones (“Longer hose: more resistance”). A small and a tall person icon: “Growing body → longer vessels → pressure rises.”

    Narration: There are three things that set resistance. The first is viscosity. Thick blood, like maple syrup — it resists flow more than thin blood, like milk. The second is vessel length. A longer hose resists more, which is one reason blood pressure rises as children grow.

  4. Scene 4 · Diameter (0:49–1:23)

    On screen: The diameter chip glows. “Resistance ∝ 1 / r⁴” (“viscosity and length × (1 ÷ radius⁴)”). An arteriole cross-section shrinks to half its size (label changes from “radius r” to “radius ½ r”) while a purple bar stretches and its label counts from “Resistance 1×” to “Resistance 16×”. On the right, a large muscular artery barely pulses (“Large arteries: hardly change”) while an arteriole keeps shrinking and widening (“Arterioles: change all the time”), with a swinging dial: “the main pressure dial”.

    Narration: And the third thing that determines resistance is vessel diameter, and that actually matters most of all. Resistance really depends on the fourth power of the radius: r to the fourth. So if you cut the radius in half, resistance goes up 16 times. Think about that. The large arteries near the heart — they hardly ever change diameter. The arterioles change their diameter constantly, which is what makes them the body’s main pressure dial.

  5. Scene 5 · The pressure cliff (1:23–1:47)

    On screen: Amy’s graph of average blood pressure (0–120 mm Hg) across elastic artery, muscular artery, arterioles, capillaries, venules, veins and vena cava. A white marker runs along the curve as labels appear: “Aorta and big arteries: starts high”, “Arterioles: falls off a cliff” (the arteriole section of the graph is highlighted yellow), “Venae cavae: close to zero”. A gold star marks the top of the curve and a card reads “Stina: 118/74 — normal, at the top of the cliff — held there by dials that are working”, with a steady dial.

    Narration: Now trace the pressure from the aorta outward. It starts high, it falls off a cliff exactly where arterioles are, and it’s close to zero by the time blood reaches the vena cava. Stina’s pressure sits at the top of that cliff, at a normal 118 over 74, and it’s held there by dials that are working.

Prefer the full lecture? Blood Flow and Pressure (original 2019 video)

Explore

Radius rules

Shrink one arteriole step by step and watch resistance climb — sixteen-fold at half the radius. Then thicken the blood and lengthen the vessel.

Think · not graded

Your notes say vessels lengthen as you grow, “and so BP ↑.” Which other factor could the body change day to day?

Spot-check your thinking: true or false?

Check · Single Choice

One question: the rule that governs flow.

Evidence card 1

Add it to your evidence board

Flow is pressure over resistance; arteriole diameter is the main dial — and hers is turning normally.

Scene 2 of 3

Systolic, Diastolic, MAP

120 over 80 — and about 93 in between.

Slide · a still to study

Pressure Across the Tree

Graph of average blood pressure along the vessel tree: highest at the elastic arteries, falling steeply through the muscular arteries and arterioles, low and level through the capillaries, venules and veins, and near zero at the venae cavae.

Pressure falls steeply through the arterioles and is close to zero by the time blood reaches the venae cavae.

Game

Compute a MAP

Drag the numbers: pulse pressure first, then diastolic + pulse pressure ÷ 3. Try 120/80, Stina’s 118/74 and 140/90.

Prefer the full lecture? Systolic and Diastolic Pressures (original 2019 video)

Think · not graded

Why is MAP not just the average of the two numbers?

Spot-check your thinking: true or false?

Check · Multiple Choice

Why MAP is the number organs feel — pick every true statement.

Evidence card 2

Add it to your evidence board

Her 118/74 is a normal, well-regulated pressure with a normal MAP.

Scene 3 of 3

Three Levels of Control

Nerves in seconds, hormones in minutes, kidneys in days.

Animation · narrated, with captions

Holding the Set-Point

Module 16 · 16.3 · Scene 3 · 6 scenes · about 2 minutes · narrated. Press Play to start; the words appear in the caption box under the picture.

Animation: blood pressure is held at a set point by three systems at three speeds. When a person stands up quickly the gauge dips; stretch receptors, the medulla’s vasomotor center and sympathetic nerves restore it in seconds; the adrenal medulla’s epinephrine works in minutes; the kidney’s renin-angiotensin system works over hours to days; ANP from stretched atria is the brake. All three of Stina’s work, so her 118/74 is normal. Animated scene. The caption below shows the narration for the current scene; a full scene-by-scene description follows the animation.
Scene 1

Paused

Keyboard: when the picture has focus, Space plays or pauses, the left/right arrow keys move between scenes, and M mutes or unmutes.

Text description and full narration

Six-scene narrated animation (about 2 minutes) with captions. Three timer chips run across the top (Seconds — nerves, Minutes — hormones, Hours to days — kidney) and a blood-pressure gauge with a needle sits on the right throughout.

  1. Scene 1 · Stand up fast (0:00–0:17)

    On screen: A person icon rises from a crouch to standing (“Stand up quickly”). Red dots slide down into the legs (“blood pools in the legs”) and the gauge needle swings left: “pressure dips ↓”.

    Narration: Blood pressure is held at a set point, really, by three systems working at three speeds. Okay, so stand up really quickly. I do it. When you do that, blood pools in your legs, so the pressure dips for a moment.

  2. Scene 2 · Seconds: the nerves (0:17–0:44)

    On screen: The Seconds timer glows. A heart with its aortic arch appears with two yellow stretch-receptor dots on the arch and carotid branch (“Stretch receptors: carotid sinus, aortic arch”); they blink, then dim (“fire less when pressure falls”). A gold line carries pulses up to the base of a brain in midsagittal section, where a red ring marks the “Vasomotor center (medulla oblongata)”. A red arrow carries pulses down to an arteriole (“Sympathetic signals”), which shrinks (“Arterioles narrow”). The pooled blood fades, the needle swings back to the green zone: “118/74 · normal — back within seconds”.

    Narration: The fastest system is called the neural system. Stretch receptors in the carotid sinuses and in that aortic arch — those stretch receptors fire less when pressure falls, and they report to the vasomotor center in the medulla oblongata. The center sends sympathetic signals that narrow the arterioles, and pressure recovers within seconds of you standing up.

  3. Scene 3 · Minutes: the adrenal medulla (0:44–0:59)

    On screen: The Minutes timer glows. A kidney with the adrenal gland on top (“Adrenal medulla”) releases small orange triangles (“Epinephrine + norepinephrine”) that fly to the heart, which beats rapidly (“Heart beats faster and harder”), and the arteriole tightens (“Vessels tighten”).

    Narration: The second system that controls blood pressure is hormonal. The adrenal medulla releases epinephrine and norepinephrine. Within minutes, the heart beats faster and harder, and the vessels tighten.

  4. Scene 4 · Hours to days: the kidney (0:59–1:28)

    On screen: The Hours-to-days timer glows. Amy’s renin-angiotensin system chart fills the centre and a gold frame moves through it as each step is named: blood pressure down; kidney → renin; angiotensinogen, angiotensin I, ACE from the lungs; angiotensin II; vascular smooth muscle → vasoconstriction; adrenal cortex → aldosterone; posterior pituitary → ADH; kidney → H₂O and Na⁺ reabsorption; blood pressure up. A list builds on the left: Pressure drops; Kidney → renin; → angiotensin II; narrows vessels; aldosterone + ADH; kidney keeps salt + water; blood volume ↑ over hours and days. The needle rises a little: “blood volume ↑”.

    Narration: The slowest and most powerful system of blood vessel control is the renal system. When pressure drops, the kidney releases renin, which leads to angiotensin II. And angiotensin II does everything to raise blood pressure. It narrows vessels, it triggers aldosterone and ADH, so the kidney keeps salt and water. Over hours and days, blood volume rises — very slowly.

  5. Scene 5 · The brake: ANP (1:28–1:42)

    On screen: “ANP: the brake.” The heart returns with a gold ring pulsing over its atria (“Stretched atria”); teal dots (“ANP (atrial natriuretic peptide)”) travel to a kidney, which releases water drops and Na⁺ chips downward (“Kidney lets go of salt + water”). The needle settles back: “pressure comes down”.

    Narration: When volume is too high, the heart does the reverse. Stretched atria release ANP, atrial natriuretic peptide, and the kidney lets go of salt and water, bringing your blood pressure down.

  6. Scene 6 · One set-point (1:42–2:04)

    On screen: The three timers glow in turn and arrows run from each to the gauge; “✓ working” appears under each. “Three systems, one set point.” “All three of Stina’s are working: 118/74.” A card: “Pressure control is not what’s aging her vessels.”

    Narration: Seconds, minutes, and days. Three systems, one set point. All three of Stina’s systems are working just fine, which is why her pressure is the normal 118 over 74. It’s also why pressure control is not the place to look for what’s aging her vessels.

Prefer the full lecture? Controls of Blood Pressure (original 2019 video)

Explore

Drop the pressure

When you stand up, about half a liter of blood drops into your legs. Clinicians test how well the body copes with a simple bedside check: blood pressure and heart rate lying down, then 1 and 3 minutes after standing. Four people take the test.

Read two numbers: how far the top blood-pressure number falls, and how much the heart rate climbs. A fall of 20 or more in the top number, or 10 or more in the bottom one, counts as a real drop.

Choose a person
Tilt table The person lies flat on a tilt table. Lying flat
Orthostatic vitals
Orthostatic vital signs for the chosen person
PositionBlood pressureHeart rateChange

Press Stand them up to run the test.

Choose a person, then stand them up.

What does this result show?

Why this matters for Stina

Her test is normal: her top number barely moves and her heart rate rises a little. All three controls are doing their job, which is why her 118/74 is a true normal. But these controls guard pressure, not the lining. They cannot stop an inflamed endothelium from aging.

Text description of this activity

A bedside test of the blood-pressure controls. Choose one of four people: Stina; a 72-year-old with diabetes for 25 years who gets dizzy on standing; a 19-year-old after two days of stomach flu; and a 34-year-old who gave blood an hour ago. Pressing Stand them up tilts a drawn tilt table from flat to upright and fills in a vital-signs sheet for lying down, 1 minute standing and 3 minutes standing. Then choose what the result shows: all three controls are keeping up; the nerve reflex is not firing; or the nerves are firing but there is not enough blood volume.

  • Stina: lying 118/74, heart rate 68; 1 minute 114/76, 78; 3 minutes 117/76, 75. Normal: the controls are keeping up.
  • 72, diabetes for 25 years: lying 146/84, 72; 1 minute 110/70, 74; 3 minutes 102/64, 75. The top number falls 44 while the heart rate barely rises: the nerve reflex is not firing. Long-standing diabetes can damage the autonomic nerves that carry it.
  • 19, two days of stomach flu: lying 104/68, 94; 1 minute 90/62, 122; 3 minutes 86/58, 128. The pressure falls and the heart races: the nerves are firing flat out, but there is not enough blood volume. Fluids help fast; the kidney rebuilds volume over hours to days.
  • 34, gave blood an hour ago: lying 118/76, 74; 1 minute 114/78, 86; 3 minutes 116/78, 82. Normal: the nerves narrow the arterioles and nudge the heart rate up, and the kidney keeps salt and water to refill the plasma over a day or two.

The numbers are illustrative. The cut-offs follow the consensus definition of orthostatic hypotension (a fall of at least 20 in systolic or 10 in diastolic pressure within 3 minutes of standing), and a small heart-rate rise alongside a large pressure fall points to a nerve (neurogenic) cause. Sources: Freeman R, et al. Consensus statement on the definition of orthostatic hypotension, neurally mediated syncope and the postural tachycardia syndrome. Clin Auton Res. 2011;21:69–72. Gibbons CH, et al. The recommendations of a consensus panel for the screening, diagnosis, and treatment of neurogenic orthostatic hypotension and associated supine hypertension. J Neurol. 2017;264:1567–1582.

Think · not graded

If all three systems are working, what does that say about where her problem is not?

Spot-check your thinking: true or false?

Check · Fill in the Blanks

Five blanks: why standing up doesn’t drop you.

Evidence card 3

Add it to your evidence board

Her pressure controls are intact — control protects against pressure, not against an inflamed lining.

4

Your evidence board

Every scene gave you an evidence card, and the chart adds more. Drag each card to the column it supports: Clears pressure, Neither on its own, or Pressure protects her. Some cards can honestly go in more than one place — that’s allowed, and the feedback tells you which cards decide the case.

5

Your verdict

Time to decide. Look back at your bet, then build your verdict from statements that hold up — no writing needed.

Look back at your prediction

Normal blood pressure, held there by three working control systems, should…

Open the one you chose at the top. Does the evidence support it, refute it, or revise it?

If you bet: Protect her vessels from aging early

It protects them from one thing: pressure injury. The scenes showed that control systems hold a number steady; they don’t stop an inflamed lining from aging.

If you bet: Tell us nothing either way

It tells us something useful: hypertension is off the suspect list. A negative result still narrows the search.

If you bet: Rule out pressure as the cause and point somewhere else

Your bet held. Three working control systems and a normal MAP clear pressure — and point the search at something pressure control can’t reach.

Build your verdict · no writing

Choose the statement that holds in each set. The ones you keep become your argument.

6

The finding

Sign · normal, well-controlled blood pressure

Normal, Well-Controlled Blood Pressure (118/74)

A normal, well-regulated pressure: 118/74, a mean arterial pressure near 89 mm Hg, held steady by intact neural, hormonal and renal control. Blood flow is pressure divided by resistance, controlled chiefly through arteriole diameter. Chart entry: hypertension is off the suspect list, and pressure control offers no protection against an inflamed endothelium.

Next · Chapter 4

The Body’s Highways

Her cholesterol story is really a liver story. Follow the circuits — especially the one that sends everything from the gut through the liver first.

Reliable information on rare diseases

NORD · NIH GARD · Orphanet · MedlinePlus Genetics: FMF · FMF & AID Global Association · Autoinflammatory Alliance · Global Genes · Amyloidosis Foundation

Stina has one rare disease. In the United States, about 1 in 10 people live with one of the more than 7,000 known rare diseases. These organizations are where patients, families and clinicians go for trustworthy information.

List of terms