Gradients, pressure and flow

Blood moving through your arteries, air moving into your lungs, and fluid running from an IV bag into a vein all follow one rule. A pressure gradient pushes the fluid, and resistance holds it back. This page builds that rule from the ground up: what a gradient is, what pressure is, why flow depends on a pressure difference, what sets resistance, and why narrowing a tube by half cuts its flow to one-sixteenth. These ideas return in almost every chapter of this course.

Gradients: a difference across a distance

Wrap your hands around a hot mug. Heat moves from the mug into your hands, never the other way, and it moves faster when the mug is hotter. That is a gradient at work.

A gradient (grad- = step) is a difference in some quantity between two places. Two kinds matter most to you now.

• A concentration gradient is a difference in the concentration of a substance between two places. For example, just after a cell uses oxygen, the fluid around it holds more dissolved oxygen than the cell does. Between the air in your lungs and your blood, the difference that sets the direction is oxygen's pressure, not its amount: oxygen moves from the air into your blood because its pressure is higher in the air, even though the arriving blood holds more oxygen per liter. A later topic on breathing explains why.
• A temperature gradient is a difference in temperature between two places. Your core is warmer than your skin, and on a cold day your skin is warmer than the air.

Things tend to move from where there is more to where there is less. Heat moves from warm to cool, and dissolved substances tend to spread from high concentration toward low. This is called moving down the gradient. It needs no outside energy, because a gradient is itself a form of potential energy: the difference is what drives the movement. Moving something up a gradient, from low to high, does take energy, and in your cells that energy usually comes from ATP.

How steep a gradient is depends on two things: the size of the difference, and the distance over which it occurs. A difference of 10 units across 1 millimeter is ten times steeper than the same difference across 10 millimeters. The steeper the gradient, the faster things move down it (Figure 1).

You will meet gradients again and again: in the next topic, as substances spread and water moves across membranes; in the topic after that, as charged particles move; and later in your lungs, kidneys and brain.

Pressure

Press your thumb on the back of your hand. The same push feels sharper through a fingernail than through the pad of your thumb, because the force is concentrated on a smaller area. Pressure is force per unit area: how hard something pushes on each bit of a surface.

Millimeters of mercury

In physiology, pressure is usually measured in millimeters of mercury (mm Hg; Hg is the chemical symbol for mercury). The unit comes from an old way of measuring: a pressure is described by how high it can push a column of mercury up a tube. Mercury is very dense, about 13.6 times denser than water, so the column stays short enough to read.

Atmospheric pressure

Atmospheric pressure (atmo- = vapor, sphere = ball) is the pressure of the air around you, caused by the weight of the air above. At sea level it is about 760 mm Hg. It falls as you climb, because there is less air above you.

Pressures in your body are almost always given relative to atmospheric pressure. A blood pressure of 120 mm Hg means 120 mm Hg above the pressure of the surrounding air. A pressure of 0 means "the same as the air outside", and a negative pressure means "below the air outside".

Pressure gradients drive flow

Turn on a garden hose. Water is under pressure at the tap end, and the open end is at atmospheric pressure. Water flows from the high-pressure end to the low-pressure end. Close the nozzle and the pressure inside the hose rises, yet the water stops. The pressure is high everywhere inside, so there is no difference to push it.

A pressure gradient is a difference in pressure between two points. It is often written ΔP (Δ, the Greek letter delta, means "difference" or "change"). Fluids, both liquids and gases, flow from higher pressure toward lower pressure, and the flow depends on the difference, not on how high the pressures are. A tube with 100 mm Hg at one end and 90 at the other has the same ΔP (10 mm Hg) as a tube with 20 at one end and 10 at the other.

In your body, the heart pumps blood into your large arteries, where the pressure averages roughly 90 mm Hg. By the time blood returns to your heart through the large veins, its pressure is close to 0. That difference of about 90 mm Hg is what drives blood all the way around your body.

Bulk flow

When blood moves along an artery, everything in it moves together: water, dissolved glucose and salts, proteins and cells. Bulk flow is the movement of a whole fluid, with everything dissolved or carried in it, driven by a pressure gradient. Other examples:

• Air moves into your lungs when you breathe in, because the pressure inside your lungs drops a little below atmospheric pressure.
• Fluid runs from an IV bag into a vein, because the pressure at the bag end is higher than the pressure in the vein.

Bulk flow is fast and carries materials over long distances: blood makes a full circuit of your body in about a minute. In the next topic you will meet a different kind of movement, in which individual particles spread on their own down their concentration gradients. That kind works over tiny distances. Bulk flow is what carries materials the long way.

Hydrostatic pressure

Dive to the bottom of a swimming pool and your ears hurt: the deeper you go, the more water sits above you. Hydrostatic pressure (hydro- = water, stat- = standing) is the pressure a fluid exerts, for example on the walls of its container. In a column of fluid, it rises with depth, because each layer carries the weight of the fluid above it.

For water, each centimeter of depth adds about 0.74 mm Hg. Two body examples show why this matters.

• An IV bag. Hang a bag of fluid 1 meter (100 cm) above an IV site, and the weight of that column adds about 74 mm Hg of pressure at the catheter. That is more than the pressure in the vein, so fluid flows in. Raise the bag, and the gradient and the flow increase. Lower it below the vein, and blood can flow back into the tubing.
• Standing up. When you stand, the column of blood between your heart and your feet adds roughly 90 mm Hg to the pressure in the vessels of your feet. That is one reason feet swell after a long day of standing.

Blood pressure is itself a hydrostatic pressure: the pressure of the blood against the walls of your vessels.

Blood pressure and blood volume: the short version

Blood pressure is the pressure blood exerts against the walls of your blood vessels. Unless someone says otherwise, it means the pressure in a large artery, usually measured with a cuff on your upper arm. It rises and falls with each heartbeat, so it is written as two numbers: the peak pressure during a beat over the lowest pressure between beats, for example 120/80 mm Hg.

Blood volume is the total amount of blood in your body: about 5 liters in an average adult, or roughly 70 mL for each kilogram of body weight.

The two are linked because your blood vessels form a closed, stretchy system. More blood stretches the vessel walls more, and stretched walls push back harder, so pressure rises. After heavy bleeding, less blood fills the same vessels, the walls are stretched less, and blood pressure falls. That is why a person who is bleeding heavily has a falling blood pressure.

That is all you need for now. The chapter on blood vessels returns to blood pressure in full in the topic "Blood pressure, flow and resistance", including how your heart and vessels set it and how your body keeps it steady.

Resistance

Try drinking a thick milkshake through a thin straw. You suck hard, and very little comes up. Swap to a wide straw and it flows easily. Swap the milkshake for water and it is easier still.

Resistance is anything that opposes flow. In a tube, it comes from friction: between the fluid and the tube wall, and between layers of fluid sliding past each other. Three things set it.

• Radius. A narrower tube has more resistance. This is by far the strongest effect, as the next sections show.
• Length. A longer tube has more resistance, in direct proportion: double the length, double the resistance.
• Viscosity. Viscosity (viscos- = sticky) is a fluid's thickness, its internal friction. Honey is more viscous than water. Blood is about three to four times as viscous as water, mostly because of the cells it carries. More cells per liter of blood make it more viscous; fewer make it less viscous.

In your body, the length of your vessels hardly changes from day to day, and viscosity changes slowly. The radius of your small arteries, though, changes from moment to moment, which makes radius your body's main way to control resistance.

The flow equation

Put the pressure gradient and resistance together and you get the rule behind this whole topic:

F = ΔP / R: flow equals the pressure gradient divided by resistance.

• F is flow: the volume of fluid that passes a point each minute, for example in mL/min.
• ΔP is the pressure gradient: the pressure at the start minus the pressure at the end, in mm Hg.
• R is resistance, in mm Hg for each mL/min of flow.

Read it as two plain rules: a bigger pressure difference pushes more flow, and a bigger resistance lets less through. Double ΔP and flow doubles. Double R and flow halves. Figure 2 shows the pieces.

Radius and resistance: the fourth-power rule

In the 1840s, the French physician Jean Poiseuille measured how liquids flow through fine glass tubes. His result, now called Poiseuille's law, shows how resistance depends on the tube and the fluid:

R = 8 × viscosity × length ÷ (π × radius⁴)

You do not need to use the whole formula. The part that matters is on the bottom: resistance depends on the fourth power of the radius, the radius multiplied by itself four times (r × r × r × r). Because radius is on the bottom, a smaller radius means a larger resistance, and because it is raised to the fourth power, small changes in radius make big changes in resistance. Viscosity and length are on the top, so resistance rises in direct proportion to each of them.

The same rule works in the other direction and for small changes (Figure 3).

• Double the radius: radius⁴ becomes 2 × 2 × 2 × 2 = 16 times larger, resistance becomes 1/16, and flow at the same ΔP becomes 16 times larger.
• Narrow the radius by 10%: radius⁴ becomes 0.9 × 0.9 × 0.9 × 0.9 ≈ 0.66 of the original, resistance rises about 1.5-fold, and flow falls to about two-thirds.

Why this matters in your body

• Controlling blood flow. Your small arteries have a ring of muscle in their walls. When that muscle tightens a little, the radius shrinks a little and resistance rises a lot. This is how your body sends more blood to working muscles and less to resting organs, without changing the pressure your heart makes. You will see it in the topics "Structure of blood vessels" and "Blood pressure, flow and resistance".
• Breathing. Air flowing through your airways follows the same rule, so a small narrowing of the airways makes breathing much harder. That returns in the chapter on breathing.
• IV catheters. A catheter with a slightly larger internal radius delivers far more fluid per minute. A short, wide catheter is the fastest.

Putting it together: fast fluid for a bleeding patient

Picture a paramedic starting an IV on a patient who is bleeding heavily. Every choice raises flow through the IV line, and each one maps onto F = ΔP / R.

• A large-bore catheter lowers R through the fourth-power rule. This is the biggest single gain.
• A short catheter lowers R in proportion to length.
• Hanging the bag high raises the hydrostatic pressure at the catheter, which raises ΔP.
• Squeezing the bag in a pressure bag raises ΔP further.
• Warm, thin fluids run faster than thick ones, because viscosity is part of R.