3 Fluids in Biological Systems

How Fluids Move

Fluids carry oxygen, nutrients, hormones, heat, and waste through the body. Their movement depends on pressure differences and the resistance of the pathways they travel through. These principles help explain circulation, ventilation, and exchanges between blood and tissues.

Pressure, Flow, and Tube Resistance

A pressure difference drives fluid through a pathway, while resistance opposes that movement. Volumetric flow rate, written as $Q$, is the volume passing a point per unit time. The relationship is:

Here, $\Delta P$ is the pressure drop along the pathway and $R$ is its resistance. Increasing the pressure difference increases flow; increasing resistance decreases it.

For steady, laminar flow of a Newtonian fluid through a rigid cylindrical tube, the Hagen–Poiseuille relation gives:

In these equations, $r$ is tube radius, $L$ is length, and $\eta$ is dynamic viscosity. The fourth-power dependence on radius makes small changes in diameter important: doubling the radius of an ideal tube increases flow sixteenfold when the pressure difference is unchanged. Likewise, if an arteriole’s radius falls to half its original value, the idealized model predicts a sixteenfold increase in resistance.

These relationships are models, not exact descriptions of every vessel or airway. Living pathways branch and expand, and flow can be pulsatile. Blood also does not behave as a perfectly Newtonian fluid in every vessel or flow condition.

Circulation and Branching Vessels

In vessels connected in series, resistance adds. Parallel pathways lower total resistance compared with any one branch, so adding parallel routes can increase total flow. At a branch, incoming flow equals the sum of outgoing flows.

For an incompressible fluid, the continuity principle relates flow to cross-sectional area and average speed:

Here, $A$ is cross-sectional area and $v$ is average speed.

The heart creates pressure differences that propel blood through the circulation. Arterioles are important resistance vessels: smooth muscle changes their radius, helping regulate blood flow to organs. The many capillaries in a tissue provide a large total cross-sectional area. Blood is distributed across that area, so its average speed is relatively low, allowing time for exchange with surrounding tissue.

Airflow and Lung Expansion

Air moves when pressure inside the lungs differs from atmospheric pressure. During inhalation, expansion of the chest lowers pressure in the lungs, drawing air inward. During exhalation, the pressure difference reverses and air flows outward.

Airway resistance opposes airflow. Under laminar-flow assumptions, narrowing airways can greatly increase resistance because of the strong dependence on airway radius described by the Hagen–Poiseuille relation. Smooth-muscle contraction, swelling, or mucus can narrow airways and make ventilation more difficult.

Compliance describes how readily the lungs and chest wall expand. It is the change in volume divided by the change in pressure:

Resistance concerns the pressure needed to maintain airflow; compliance concerns the pressure needed to change lung volume. Both affect the work of breathing.

Fluid Exchange Between Blood and Tissues

Water crosses microvascular walls in response to pressure differences and the properties of the barrier. The Starling equation provides a framework for understanding this movement:

Here, $J_v$ is fluid flux; $K_f$ combines hydraulic permeability and exchange area; $P_c$ and $P_i$ are capillary and interstitial hydrostatic pressures; $\pi_c$ and $\pi_i$ are their oncotic pressures; and $\sigma$ describes how effectively the barrier restricts proteins. Hydrostatic pressure tends to push fluid away from the compartment with higher pressure. Plasma proteins usually create an oncotic force that opposes filtration from blood.

The equation is a framework rather than a complete account of fluid exchange in every tissue. The endothelial glycocalyx affects the effective protein barrier. Lymphatic drainage returns filtered fluid and proteins to the circulation, and under many steady conditions it is a major route for fluid return. The simplified picture of routine filtration at one end of a capillary and reabsorption at the other does not capture the full process.

Edema can develop when filtration exceeds lymphatic removal. Contributing factors can include elevated capillary pressure, increased barrier permeability, reduced plasma protein concentration, or impaired lymphatic drainage.