Passage
The flow of blood through the human body is typically laminar, but in certain conditions, as when blood flows through the aorta during a period of heightened physical activity, the flow can become turbulent. Blood flow can also become turbulent in abnormal cases in which the passage of blood is obstructed by constrictions within the blood vessel. The energy generated by blood turbulence creates sound vibrations that can be heard with a stethoscope.Using the technique of laser Doppler velocimetry, researchers recorded the blood velocity v at a point in the aorta of an experimental subject at different times during aerobic exercise. Table 1 shows the blood velocities observed over a 400 ms time interval.Table 1 Blood Velocity within the Aorta of an Experimental Subject (mean velocity v̅ = 101 cm/s)
Turbulent kinetic energy (TKE) is the kinetic energy per unit mass associated with turbulence within flowing fluids and is defined as:
Equation 1where σ_v is the standard deviation of the fluctuating fluid velocities at a point within the turbulent flow.Reynolds number Re is the quantity that ultimately measures whether a flow is turbulent or laminar. Re is defined in terms of the fluid density ρ, mean velocity of the flow v̅, conduit diameter d, and dynamic viscosity η of the fluid, as given by:
Equation 2In the context of blood flow, d is the diameter of the blood vessel, and blood has a fluid density of about 1,060 kg∙m⁻³ with a dynamic viscosity of about 0.003 kg∙m⁻¹∙s⁻¹.
-The diameter of a segment of an artery is reduced by a factor of two due to an obstruction. Assume that the flow is incompressible and laminar. Compared to an unobstructed segment of the artery, the velocity of blood in the obstructed segment of the artery is:

Question

Passage
The flow of blood through the human body is typically laminar, but in certain conditions, as when blood flows through the aorta during a period of heightened physical activity, the flow can become turbulent. Blood flow can also become turbulent in abnormal cases in which the passage of blood is obstructed by constrictions within the blood vessel. The energy generated by blood turbulence creates sound vibrations that can be heard with a stethoscope.Using the technique of laser Doppler velocimetry, researchers recorded the blood velocity v at a point in the aorta of an experimental subject at different times during aerobic exercise. Table 1 shows the blood velocities observed over a 400 ms time interval.Table 1 Blood Velocity within the Aorta of an Experimental Subject (mean velocity v̅ = 101 cm/s)

Turbulent kinetic energy (TKE) is the kinetic energy per unit mass associated with turbulence within flowing fluids and is defined as:

Equation 1where σ_v is the standard deviation of the fluctuating fluid velocities at a point within the turbulent flow.Reynolds number Re is the quantity that ultimately measures whether a flow is turbulent or laminar. Re is defined in terms of the fluid density ρ, mean velocity of the flow v̅, conduit diameter d, and dynamic viscosity η of the fluid, as given by:

Equation 2In the context of blood flow, d is the diameter of the blood vessel, and blood has a fluid density of about 1,060 kg∙m⁻³ with a dynamic viscosity of about 0.003 kg∙m⁻¹∙s⁻¹.
-The diameter of a segment of an artery is reduced by a factor of two due to an obstruction. Assume that the flow is incompressible and laminar. Compared to an unobstructed segment of the artery, the velocity of blood in the obstructed segment of the artery is:

Quizplus · Accepted Answer

11ecba2d_1328_fa3a_a3bf_43648a836aa6_MD0008_00 The flow of a fluid refers to the motion of many individual particles that make up the fluid. If the flow lines used to conceptualize the flow of the particles remain parallel to each other and do not change over time (ie, each of the fluid layers move past each other with little friction), the flow is referred to as laminar. For incompressible laminar flows traveling at velocity v between two regions of a conduit (eg, pipe) with cross-sectional area A, the quantity of mass entering one portion of a pipe over a period of time must equal the quantity of mass exiting that region simultaneously during that period. This relationship is stated by the continuity equation: 11ecba2d_1328_fa3b_a3bf_7d4975a341d1_MD0008_00 For a circular conduit (eg, pipe, blood vessel), A can be expressed in terms of the diameter d: 11ecba2d_1329_214c_a3bf_33452fe4f694_MD0008_00 Substituting the expression for A into the continuity equation and then simplifying yields the relationship between v₁ and v₂ in terms of the respective diameters: 11ecba2d_1329_214d_a3bf_259151c1a46e_MD0008_00 11ecba2d_1329_214e_a3bf_a3612a1c3056_MD0008_00 In this question, the diameter of the blood vessel is halved as it flows from one segment to the next (d₂ = 0.5∙d₁). Using these proportions, the relationship between v₁ and v₂ simplifies to: 11ecba2d_1329_214f_a3bf_c35c8ac312ff_MD0008_00 Therefore, the continuity equation implies v is inversely proportional to the square of conduit diameter and increases by a factor of four as conduit diameter is halved. (Choices A and B) v in a laminar flow is inversely proportional to the square of flow diameter. Therefore, velocity must increase if the diameter of the flow is reduced. (Choice C) v is inversely proportional to the square of diameter, not the diameter. Consequently, v must increase by a factor of four. Educational objective: The continuity equation expresses the conservation of mass observed as fluids flow through a conduit. The continuity equation indicates that velocity is inversely proportional to the square of diameter.

Passage The Flow of Blood Through the Human Body Is Typically