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

A lab compares two Newtonian fluids flowing through the same rigid cylindrical capillary (same $r$ and $L$) under the same pressure drop $\Delta P$. Fluid X has viscosity $\eta_X = 1.0\ \text{mPa}\cdot\text{s}$ and Fluid Y has viscosity $\eta_Y = 4.0\ \text{mPa}\cdot\text{s}$ at the measurement temperature. Flow is laminar for both. Based on Poiseuille flow, what is the expected ratio $Q_X/Q_Y$?

A researcher evaluates whether a capillary-flow assay is sensitive to small manufacturing variation in tube radius. Two nominally identical rigid cylindrical capillaries have the same length $L$ and are used with the same Newtonian fluid at the same temperature and the same applied pressure drop $\Delta P$. Capillary A has radius $r$, while Capillary B has radius $0.90r$. Assuming laminar Poiseuille flow, which outcome is most consistent with the expected change in volumetric flow rate?

To compare two capillaries, a student drives the same Newtonian fluid (viscosity $\eta$) through each under identical pressure drop $\Delta P = 1.0\ \text{kPa}$. Capillary 1 has length $L$ and radius $r$. Capillary 2 has length $2L$ and radius $r$. The flow is laminar in both. Based on Poiseuille's equation, which outcome is consistent with these conditions?

In a microfluidics experiment, a Newtonian buffer is driven through a straight cylindrical glass capillary of length $L = 10\ \text{cm}$ and radius $r = 0.50\ \text{mm}$ under a constant pressure drop $\Delta P = 2.0\ \text{kPa}$. The flow is verified to be laminar and fully developed. The same capillary is then used with a second buffer at the same temperature, identical except its dynamic viscosity is doubled (from $\eta$ to $2\eta$). Based on Poiseuille flow, what change in volumetric flow rate $Q$ is expected under the same $\Delta P$, $L$, and $r$?

A physiologist approximates flow through a small arteriole as steady laminar flow in a rigid cylindrical tube. A vasodilator increases the arteriole radius by 10% (from $r$ to $1.10r$) without changing $\Delta P$ across the segment, its length $L$, or blood viscosity $\eta$. Based on Poiseuille's equation, which change in flow rate is most consistent with this model?

A device uses laminar flow through a cylindrical capillary to deliver a drug solution. The designer can change only one parameter while keeping the others constant: pressure drop $\Delta P$, tube length $L$, and fluid viscosity $\eta$ remain fixed. Which modification is most effective for increasing the volumetric flow rate $Q$ by approximately an order of magnitude (about $10\times$) while remaining within the Poiseuille-flow model?

A physiology lab models blood flow through a small artery as steady, laminar Poiseuille flow in a rigid cylindrical vessel. During a cold-pressor test, sympathetic activation causes the artery radius to decrease from $r$ to $0.90r$ while mean arterial pressure and vessel length remain approximately constant over the short interval. Viscosity is assumed unchanged. Based on Poiseuille's relationship $Q \propto r^4$, what is the expected change in flow rate through that artery?

(You may use: $(0.90)^4 \approx 0.66$.)

In a capillary viscometry setup, a constant pressure source applies $\Delta P$ across a rigid tube of radius $r$ and length $L$. The fluid is Newtonian and the flow is verified to be laminar. The investigator accidentally records the tube diameter $d$ as if it were the radius when predicting the effect of changing tube size. If the true radius is doubled (from $r$ to $2r$) while $\Delta P$, $L$, and $\eta$ are held constant, which prediction for the change in $Q$ is consistent with Poiseuille flow?

A lab uses the same capillary (fixed $r$ and $L$) to measure flow of a Newtonian fluid at two temperatures. At $20^\circ\text{C}$, the viscosity is $\eta_{20}$ and the measured flow rate is $Q_{20}$. At $37^\circ\text{C}$, the viscosity decreases to $0.75\eta_{20}$ while the applied pressure drop $\Delta P$ is kept constant and the flow remains laminar. Based on Poiseuille flow, what is the expected $Q_{37}$ relative to $Q_{20}$?

In a microfluidics study, researchers drive an incompressible Newtonian fluid through a straight glass capillary under steady, laminar conditions. The capillary length is held constant at $L = 10\ \text{cm}$ and the pressure drop is fixed at $\Delta P = 20\ \text{kPa}$. The temperature is kept constant so viscosity does not change during a run. The team replaces Fluid 1 (viscosity $\eta_1 = 1.0\ \text{mPa}\cdot\text{s}$) with Fluid 2 (viscosity $\eta_2 = 2.0\ \text{mPa}\cdot\text{s}$) while keeping the same capillary radius. Based on Poiseuille flow, what change in volumetric flow rate $Q$ is expected?

(Use Poiseuille proportionality: $Q \propto \frac{\Delta P\, r^4}{\eta L}$.)

A student uses a syringe pump to generate steady laminar flow of a Newtonian fluid through a capillary. For a given trial, $\Delta P$, $r$, and $\eta$ are held constant while the student compares two capillary lengths: $L_1 = 4\ \text{cm}$ and $L_2 = 12\ \text{cm}$. Which statement is consistent with Poiseuille flow for the ratio of flow rates $Q_1/Q_2$?

An investigator models blood flow through a straight artery segment as laminar Poiseuille flow. During mild hypothermia, plasma viscosity increases by 25% (from $\eta$ to $1.25\eta$) while arterial radius, length, and the pressure drop across the segment are assumed unchanged. Under these assumptions, which statement best describes the influence of viscosity in this system?

In an experiment, laminar flow of a Newtonian fluid is established through a cylindrical capillary. The operator accidentally increases the pressure drop from $\Delta P$ to $2\Delta P$ while simultaneously switching to a fluid with twice the viscosity (from $\eta$ to $2\eta$). The tube radius $r$ and length $L$ are unchanged. Under Poiseuille flow, what is the expected net effect on the volumetric flow rate $Q$?

A researcher measures laminar flow of a glycerol–water mixture through a rigid cylindrical capillary at constant temperature. The capillary length is held fixed at $L = 5.0\ \text{cm}$ and the applied pressure drop is held fixed at $\Delta P = 1.5\ \text{kPa}$. The capillary radius is increased from $r$ to $2r$ by switching to a wider tube of the same length. Assuming Poiseuille flow applies, what change in volumetric flow rate $Q$ is expected?

In a microfluidics experiment, a Newtonian buffer is driven through a straight glass capillary (length $L = 10\ \text{cm}$, radius $r = 0.50\ \text{mm}$) under a constant pressure drop $\Delta P = 2.0\ \text{kPa}$. Flow is confirmed laminar (Re $< 200$). The buffer is then replaced with a glycerol-water mixture whose dynamic viscosity is 4 times higher, while $\Delta P$, $L$, and $r$ are held constant. Based on Poiseuille flow, what change in volumetric flow rate $Q$ is expected?

A capillary viscometer uses a fixed glass tube (radius $r$, length $L$) and measures flow rate $Q$ under a known pressure drop $\Delta P$. A student accidentally uses a tube of the same radius but half the length ($L/2$), keeping $\Delta P$ and fluid viscosity $\eta$ the same. Under laminar conditions, what outcome is consistent with Poiseuille flow?

A lab measures laminar flow of a Newtonian fluid through a capillary at constant $\Delta P$, $L$, and $r$. Temperature is increased from $20^\circ\text{C}$ to $40^\circ\text{C}$, and the fluid's dynamic viscosity decreases by 30% (to $0.70\eta_0$). All other parameters are unchanged. What change in $Q$ is expected from Poiseuille flow?

In an in vitro model of an arteriole, researchers keep the same blood-mimicking fluid (constant $\eta$) and the same tube radius $r$, but double the tube length from $L$ to $2L$ while maintaining the same pressure drop $\Delta P$. Flow remains laminar. What change in $Q$ is expected?

A physiology lab compares two arterioles with the same radius and viscosity but different lengths: Vessel X has length $L$, Vessel Y has length $3L$. Both experience the same pressure drop and exhibit laminar flow. What is the expected ratio $Q_Y/Q_X$?

A device measures flow through a rigid capillary for two conditions. Condition 1: $\Delta P_1$, viscosity $\eta$, radius $r$, length $L$, flow $Q_1$. Condition 2: pressure drop is reduced to $0.80\Delta P_1$ and radius is increased to $1.10r$ with $\eta$ and $L$ unchanged (laminar). Which prediction for $Q_2/Q_1$ is most consistent with Poiseuille flow?