Blood flows through a vessel in the leg at an average velocity of 10 cm/s. How much glucose passes by a segment of the blood vessel each second if the radius of the blood vessel is 0.20 cm and each 1.0 cm³ of blood contains 1.0 mg of dissolved glucose?

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11ecba2d_1325_c6cb_a3bf_61834bd391ed_MD0008_00 Fluid flow describes the motion of liquid or gas molecules. For a fluid traveling through a closed conduit (eg, pipe), the volume of fluid flowing past a fixed point per unit time is the volumetric flow rate (Q). Q is equal to the product of the velocity of the fluid (v) and the cross-sectional area (A) of the conduit at a given point: 11ecba2d_1325_eddc_a3bf_13654f673ecb_MD0008_00 Fluid flow may be further characterized by the movement of fluid mass per unit time. For a noncompressible, ideal fluid with constant density (ρ), the mass flow rate (m_f) quantifies the amount of mass flowing past a point within the conduit per unit time: 11ecba2d_1325_eddd_a3bf_e7ee8b54b8e8_MD0008_00 MassTime=VolumeTime⋅MassVolume 11ecba2d_1325_edde_a3bf_eff0d1f46c7d_MD0008_00 The concept of mass flow rate may also be extended to solutes within a fluid, provided that solutes are uniformly distributed through the fluid. In this question, blood with a glucose mass concentration of 1 mg/cm³ (ie, 1 cm³of blood contains 1mg of glucose) flows through a blood vessel with a radius (r) of 0.20 cm. Accordingly, the cross-sectional area of the artery is: 11ecba2d_1325_eddf_a3bf_731b48447a32_MD0008_00 11ecba2d_1325_ede0_a3bf_3dc67fe3c1c1_MD0008_00 Given a blood velocity of 10 cm/s, Q is: 11ecba2d_1325_ede1_a3bf_e925389a7454_MD0008_00 Furthermore, the mass flow rate of glucose (m_glucose) at a segment of the artery is equal to the product of the volumetric flow rate and the blood glucose mass concentration: 11ecba2d_1325_ede2_a3bf_1789ab7749fa_MD0008_00 11ecba2d_1325_ede3_a3bf_694eef678527_MD0008_00 Therefore, 1.3 mg of glucose passes by a segment of the artery each second (Choice D). Educational objective: A mass flow rate refers to the quantity of fluid or solute mass that flows past a fixed point per unit time. For solutes uniformly dissolved within fluids, the mass flow rate of the solute is equal to the product of volumetric flow rate and mass concentration of the solute (ie, mass of solute per unit volume of fluid).

Blood Flows Through a Vessel in the Leg at an Average