If a pipe with flowing water has a cross-sectional area nine times greater at point 2 than at point 1, what would be the relation of flow speed at the two points?

Diffusion can be defined as the net transfer of molecules down a gradient of differing concentrations. This is a passive and 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 unit of lung mechanics, to red blood cells in the capillaries.

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

ΔV = (Area/Thickness) · D_gas · (P_{1 –} P₂)

Where ΔV is flow rate and area and thickness refer to the permeable membrane through which the gas passes, in this case, the wall of the avlveoli. P₁ and P₂ refer to the partial pressures upstream and downstream, respectively. Further, D_gas­, the diffusion constant of the gas, is defined as:

D_gas = Solubility / (Molecular Weight)^(1/2)

During strenuous exercise, blood flow greatly increases. Compared to red blood cells traveling along the sides of the capillary, how will oxygen diffusion be affected for those red blood cells traveling towards the center of the capillary?

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.

Which of the following disorders would most likely cause an increase in turbulent flow?

I. Increased cardiac output

II. Anemia

III. Lung cancer

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.

Which of the following accurately demonstrates a relationship between critical velocity and 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:

During inspiration, the diaphragm contracts and allows oxygen to rush into the lungs. How would a change in average airway diameter affect the speed at which oxygen moves?

The law of Laplace states what relationship between that the tension in the wall of a bubble and the radius of the bubble?

A barrel of height 10m is filled with water to a height of 5m. If a hole is punctured 2m above the bottom of the barrel, what is the velocity of the water leaving the barrel?

A liquid of density  enters a pipe at velocity  and with pressure . The liquid then exits the pipe a height h above the starting point, at velocity . What is the pressure, , at this exit point, in terms of , , , and h?

What causes the lift experienced by the wing of an airplane in level flight?

Which of the following is the gravitational equivalent in mechanical energy to Bernoulli's equation for fluid mechanics?