Use the following information to answer questions 1-6:

The circulatory system of humans is a closed system consisting of a pump that moves blood throughout the body through arteries, capillaries, and veins. The capillaries are small and thin, allowing blood to easily perfuse the organ systems. Being a closed system, we can model the human circulatory system like an electrical circuit, making modifications for the use of a fluid rather than electrons. The heart acts as the primary force for movement of the fluid, the fluid moves through arteries and veins, and resistance to blood flow occurs depending on perfusion rates.

To model the behavior of fluids in the circulatory system, we can modify Ohm’s law of V = IR to ∆P = FR where ∆P is the change in pressure (mmHg), F is the rate of flow (ml/min), and R is resistance to flow (mm Hg/ml/min). Resistance to fluid flow in a tube is described by Poiseuille’s law: R = 8hl/πr⁴ where l is the length of the tube, h is the viscosity of the fluid, and r is the radius of the tube. Viscosity of blood is higher than water due to the presence of blood cells such as erythrocytes, leukocytes, and thrombocytes.

The above equations hold true for smooth, laminar flow. Deviations occur, however, when turbulent flow is present. Turbulent flow can be described as nonlinear or tumultuous, with whirling, glugging or otherwise unpredictable flow rates. Turbulence can occur when the anatomy of the tube deviates, for example during sharp bends or compressions. We can also get turbulent flow when the velocity exceeds critical velocity v_c, defined below.

 v_c = N_Rh/ρD

N_R is Reynold’s constant, h is the viscosity of the fluid, ρ is the density of the fluid, and D is the diameter of the tube. The density of blood is measured to be 1060 kg/m³.

Another key feature of the circulatory system is that it is set up such that the organ systems act in parallel rather than in series. This allows the body to modify how much blood is flowing to each organ system, which would not be possible under a serial construction. This setup is represented in Figure 1.

One of the effects of norepinephrine is vasoconstriction of peripheral blood vessels. If the medication reduces the diameter of a peripheral vessel in the hands by ½, what effect does this have on the flow of blood to hands?

Which change will produce the greatest increase to flow rate through a tube?

Which of the following would tend to decrease the viscosity of a liquid flowing through a pipe?

A variation of Poiseuille's law, a relationship that helps explain fluid resistance in a pipe, is given by:

In the formula, is viscosity,  is the length of the pipe, and  is the diameter of the pipe.

Which one of the following effects would decrease resistance?

Diffusion can be defined as the net transfer of molecules down a gradient created by differing concentrations of the molecule in different locations. This is a passive, spontaneous process and relies on the random movement of molecules and Brownian motion. Diffusion is an important biological process, especially in the respiratory system where oxygen diffuses from alveoli, the basic units of lung mechanics, to red blood cells in the capillaries.

Figure 1 depicts this process, showing an alveolus separated from neighboring cells by a capillary with red blood cells. The partial pressures of oxygen and carbon dioxide are given. One equation used in determining gas exchange is Fick's law, given by:

In this equation,  is the flow rate. Area and thickness refer to the permeable membrane through which the gas passes—in this case, the wall of the alveolus.  and refer to the partial pressures upstream and downstream, respectively. , the diffusion constant of the gas, is defined as:

At high altitudes, the partial pressure of oxygen quickly drops while that of carbon dioxide decreases by much less. Given the following table, at what elevation is the pressure gradient of oxygen equal to half that of carbon dioxide, assuming constant capillary partial pressures of oxygen and carbon dioxide of 50mmHg and 40mmHg, respectively?

Diffusion can be defined as the net transfer of molecules down a gradient created by differing concentrations of the molecule in different locations. This is a passive, spontaneous process and relies on the random movement of molecules and Brownian motion. Diffusion is an important biological process, especially in the respiratory system where oxygen diffuses from alveoli, the basic units of lung mechanics, to red blood cells in the capillaries.

Figure 1 depicts this process, showing an alveolus separated from neighboring cells by a capillary with red blood cells. The partial pressures of oxygen and carbon dioxide are given. One equation used in determining gas exchange is Fick's law, given by:

In this equation,  is the flow rate. Area and thickness refer to the permeable membrane through which the gas passes—in this case, the wall of the alveolus.  and refer to the partial pressures upstream and downstream, respectively. , the diffusion constant of the gas, is defined as:

Using the values from Figure 1, what is the flow rate of oxygen in terms of the flow rate of carbon dioxide, given that oxygen and carbon dioxide have equal permeability?

A liquid flows through a pipe with a diameter of 10cm at a velocity of 9cm/s. If the diameter of the pipe then decreases to 6cm, what is the new velocity of the liquid?

If blood flows through the aorta with velocity, , with what velocity would blood flow through the capillaries in the body?

Which will produce the greatest increase in flow velocity through a tube?

A pipe with a diameter of 4 centimeters is attached to a garden hose with a nozzle. If the velocity of flow in the pipe is , what is the velocity of the flow at the nozzle when it is adjusted to have a diameter of 8 millimeters?