MCAT Flashcards
Passage
A biomedical engineer models blood flow through a segment of artery containing a localized narrowing caused by plaque buildup, comparable in principle to a Venturi constriction. Blood, treated as an incompressible fluid with constant density and viscosity, flows steadily through three consecutive segments: a normal-diameter segment proximal to the narrowing, the stenotic segment itself, and a normal-diameter segment distal to the narrowing with the same radius as the proximal segment. The engineer uses Poiseuille's law, in which resistance to laminar flow through a vessel scales inversely with the fourth power of the vessel radius for a fixed length and viscosity, together with the continuity equation relating flow speed to cross-sectional area. Table 3 lists the radius of each segment, the flow speed calculated from the continuity equation assuming a constant volumetric flow rate throughout, and the pressure drop measured across each segment relative to the segment immediately upstream. The engineer notes that the pressure drop across the stenotic segment is dramatically larger than across either normal segment, despite the flow rate being identical throughout the vessel. The engineer also calculates the Reynolds number for flow through the narrowed segment and finds it substantially elevated compared to the normal segments, raising the possibility that flow in the stenotic region may no longer be purely laminar, an assumption on which Poiseuille's law depends. Table 3. Radius, flow speed, and pressure drop across three segments of a modeled artery (constant flow rate) Segment · Radius (mm) · Flow speed (cm/s) · Pressure drop (mmHg) · Proximal (normal) · 2.0 · 10 · 2 · Stenotic (50% radius reduction) · 1.0 · 40 · 32 · Distal (normal) · 2.0 · 10 · 2
Based on Table 3, the pressure drop across the stenotic segment is how many times greater than the pressure drop across a normal segment?
A. 2 times
B. 4 times
C. 16 times
D. 32 times
Rationale
The pressure drop rises from 2 mmHg in a normal segment to 32 mmHg in the stenotic segment, a sixteenfold increase, consistent with Poiseuille's law in which resistance scales as the inverse fourth power of radius. Wrong: A twofold increase drastically understates the change shown between the 2 mmHg and 32 mmHg values in Table 3. A fourfold increase would be expected if pressure drop scaled with the inverse square of radius, not the inverse fourth power actually governing laminar flow resistance. 32 times is the pressure drop value itself in mmHg, not the ratio between the two pressure drops.
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