MCAT Chemical and Physical Foundations of Biological Systems Flashcards: 4b Viscosity Poiseuille Flow

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This deck focuses on 4b Viscosity Poiseuille Flow, giving you a quick way to review the definitions, rules, and examples that matter most for MCAT Chemical and Physical Foundations of Biological Systems.

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Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: If viscosity triples ($\eta\to 3\eta$), by what factor does $Q$ change (Poiseuille, constant $\Delta P$)?

Answer: $Q$ decreases by a factor of $3$. Tripling viscosity reduces flow rate to one-third, as it inversely scales in Poiseuille flow under constant conditions.

Flashcard 2: What SI unit is used for kinematic viscosity $\nu$?

Answer: $\frac{\text{m}^2}{\text{s}}$. Kinematic viscosity's SI unit is area per time, reflecting its role in momentum diffusion without density dependence.

Flashcard 3: What is the relationship between maximum and average speed in Poiseuille flow?

Answer: $v_{\max}=2v_{\text{avg}}$. In parabolic laminar flow, the centerline maximum velocity is twice the cross-sectional average due to the velocity distribution.

Flashcard 4: What SI unit is used for dynamic viscosity $\eta$?

Answer: $\text{Pa}\cdot\text{s}=\frac{\text{N}\cdot\text{s}}{\text{m}^2}=\frac{\text{kg}}{\text{m}\cdot\text{s}}$. The SI unit for dynamic viscosity derives from force per area times time, equivalent to pascal-seconds or its breakdowns in base units.

Flashcard 5: State the hydraulic resistance $R$ for laminar flow in a cylindrical tube, defined by $\Delta P=QR$.

Answer: $R=\frac{8\eta L}{\pi r^4}$. Hydraulic resistance analogs to electrical resistance, where flow rate relates to pressure drop, incorporating geometric and viscous factors for cylindrical tubes.

Flashcard 6: Two identical tubes are placed in series; by what factor does total resistance $R$ change versus one tube?

Answer: Total $R$ increases by a factor of $2$. Series connection adds resistances linearly, doubling total resistance for identical tubes analogous to electrical circuits.

Flashcard 7: What boundary condition at the wall is assumed in Poiseuille flow (name the condition)?

Answer: No-slip condition: $v=0$ at the wall. The no-slip condition assumes fluid adheres to solid surfaces, leading to zero velocity at tube walls in viscous flows.

Flashcard 8: Which flow regime is typically assumed for Poiseuille flow: laminar or turbulent?

Answer: Laminar flow. Poiseuille flow derives under assumptions of steady, incompressible, laminar conditions with fully developed velocity profiles.

Flashcard 9: What is the Reynolds number formula for flow in a tube using density $\rho$, speed $v$, diameter $D$, and viscosity $\eta$?

Answer: $\text{Re}=\frac{\rho v D}{\eta}$. Reynolds number quantifies the ratio of inertial to viscous forces, using diameter for pipe flow characterization.

Flashcard 10: What does it mean for a fluid to be Newtonian regarding the relation between $\tau$ and $\frac{dv}{dy}$?

Answer: $\tau\propto\frac{dv}{dy}$ with constant $\eta$. Newtonian fluids exhibit a linear relationship between shear stress and velocity gradient, maintaining constant viscosity independent of shear rate.

Flashcard 11: What is the velocity profile $v(r)$ for laminar Poiseuille flow in a tube of radius $R$?

Answer: $v(r)=\frac{\Delta P}{4\eta L}\left(R^2-r^2\right)$. The parabolic profile results from viscous drag, with velocity maximum at the center and zero at walls due to no-slip.

Flashcard 12: If tube radius doubles ($r\to 2r$), by what factor does $Q$ change (Poiseuille, constant $\Delta P$)?

Answer: $Q$ increases by a factor of $16$. Doubling radius raises flow rate by $2^4=16$ due to the strong geometric dependence in Poiseuille's equation.

Flashcard 13: If tube length halves ($L\to \frac{L}{2}$), by what factor does $Q$ change (Poiseuille, constant $\Delta P$)?

Answer: $Q$ increases by a factor of $2$. Halving length halves resistance, doubling flow rate since flow is inversely proportional to length in Poiseuille's law.

Flashcard 14: What is the relation between average flow speed $v_{\text{avg}}$, flow rate $Q$, and radius $r$?

Answer: $v_{\text{avg}}=\frac{Q}{\pi r^2}$. Average flow speed equals volumetric flow rate divided by cross-sectional area, assuming uniform density in incompressible fluids.

Flashcard 15: If pressure difference doubles ($\Delta P\to 2\Delta P$), by what factor does $Q$ change (Poiseuille)?

Answer: $Q$ increases by a factor of $2$. Doubling pressure gradient linearly increases driving force, thus doubling volumetric flow rate in laminar flow.

Flashcard 16: What is the definition of kinematic viscosity $\nu$ in terms of $\eta$ and density $\rho$?

Answer: $\nu=\frac{\eta}{\rho}$. Kinematic viscosity represents the ratio of dynamic viscosity to fluid density, indicating momentum diffusivity.

Flashcard 17: State the volumetric flow rate (Poiseuille) equation for laminar flow in a cylindrical tube.

Answer: $Q=\frac{\pi r^4\Delta P}{8\eta L}$. Poiseuille's equation describes laminar flow rate driven by pressure difference, inversely affected by viscosity and length while strongly dependent on radius to the fourth power.

Flashcard 18: What is the definition of dynamic viscosity $\eta$ in terms of shear stress and velocity gradient?

Answer: $\eta=\frac{\tau}{\frac{dv}{dy}}$. Dynamic viscosity quantifies a fluid's resistance to shear, defined as the shear stress divided by the rate of change of velocity perpendicular to the flow direction.

Flashcard 19: Two identical tubes are placed in parallel; by what factor does total resistance $R$ change versus one tube?

Answer: Total $R$ decreases by a factor of $2$. Parallel connection halves effective resistance as reciprocals add, increasing overall flow capacity for identical tubes.

Flashcard 20: Using Poiseuille flow, how does $Q$ scale with viscosity $\eta$ (all else constant)?

Answer: $Q\propto\frac{1}{\eta}$. Viscosity resists fluid motion, so flow rate decreases inversely with increasing viscosity under constant pressure and geometry.

Flashcard 21: What is the shear stress magnitude at the tube wall in laminar flow with pressure drop $\Delta P$ over length $L$?

Answer: $\tau_w=\frac{\Delta P\,R}{2L}$. Wall shear stress balances the pressure force over the tube's length, derived from force equilibrium in cylindrical coordinates.

Flashcard 22: Identify the approximate Reynolds number threshold above which pipe flow tends to become turbulent.

Answer: Turbulence tends to occur for $\text{Re}\gtrsim 2000$. The threshold indicates transition from laminar to turbulent regimes, where inertial forces dominate viscous damping in pipe flows.

Flashcard 23: Using Poiseuille flow, how does $Q$ scale with tube radius $r$ (all else constant)?

Answer: $Q\propto r^4$. In Poiseuille flow, the fourth-power dependence on radius arises from the integration of the parabolic velocity profile over the tube's cross-section.

Flashcard 24: Using Poiseuille flow, how does $Q$ scale with pressure difference $\Delta P$ (all else constant)?

Answer: $Q\propto\Delta P$. Pressure difference drives flow, resulting in direct proportionality with flow rate in laminar conditions per Poiseuille's law.

Flashcard 25: Using Poiseuille flow, how does $Q$ scale with tube length $L$ (all else constant)?

Answer: $Q\propto\frac{1}{L}$. Longer tubes increase frictional losses, making flow rate inversely proportional to length for a given pressure drop.