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.
-Blood flow in the aorta becomes turbulent at a Reynolds number of approximately 6,000. If the diameter of the aorta is approximately 2 cm, what is the average velocity of blood at this Reynolds number?

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.
-Blood flow in the aorta becomes turbulent at a Reynolds number of approximately 6,000. If the diameter of the aorta is approximately 2 cm, what is the average velocity of blood at this Reynolds number?

Quizplus · Accepted Answer

11ecba2d_1328_36e5_a3bf_5bb782a49d1f_MD0008_00 A flowing fluid can be conceptualized as a collection of packets traveling within the same conduit (ie, a pipe or container through which fluid flows). The flow of these packets can be described as either laminar or turbulent. In the case of laminar flow, the packets move together in a layered, uniform manner, and the flow is smooth. In cases of turbulent flow, the motion of the packets becomes highly nonuniform, and the resulting flow is more chaotic. The transition from laminar to turbulent flow in a fluid is indicated by the Reynolds number Re of a flow. Large values of Reynolds number (ie, Re > 2,000) are associated with the onset of turbulence because, like the onset of turbulence, Re depends on both the characteristics of the fluid and the fluid flow. In blood flows, the value of Reynolds number at which the transition between laminar and smooth flow takes place is measured to be about 6,000. A rearrangement of Equation 2 may be used to express the velocity (v_critical) associated with the transition: 11ecba2d_1328_5df6_a3bf_672af79b9713_MD0008_00 where η is the dynamic viscosity of blood, ρ is the density of blood, and d is the diameter of the vessel through which blood flows. In this question, the diameter of the conduit (a blood vessel) is 2 cm (0.02 m), and the passage states that the density and viscosity of blood are 1,060 kg/m³ and 0.003 kg/m∙s, respectively. Substituting these values into the equation above yields the value of v_critical: 11ecba2d_1328_5df7_a3bf_077ba45f9a0f_MD0008_00 The value of v_critical can be approximated as: 11ecba2d_1328_5df8_a3bf_05f6715e1b78_MD0008_00 which is slightly larger than the exact value: 11ecba2d_1328_5df9_a3bf_bb7f7499dcb0_MD0008_00 Therefore, in this case the blood flow will transition from a laminar to a turbulent flow at a velocity of 85.0 cm/s (Choice B). Educational objective: Reynolds number indicates the transition from laminar to turbulent flows. The critical velocity at which the onset of turbulence occurs can be calculated using the Reynolds number, the conduit diameter, and the density, as well as the dynamic viscosity, of the fluid.

Passage The Flow of Blood Through the Human Body Is Typically