Questions: Viscosity and Newtonian Fluid Behavior

Question 1

Ketchup flows very slowly when you gently tilt the bottle, but pours freely after you shake it vigorously. What type of fluid behavior does this describe, and what does it imply about ketchup's viscosity?

• A. Newtonian behavior — viscosity is constant, and shaking simply adds kinetic energy to help it flow
• B. Shear-thickening — the shear stress from shaking increases viscosity, making ketchup easier to pour
• C. Shear-thinning — viscosity decreases with increasing shear rate, so vigorous shaking reduces resistance to flow
• D. Bingham plastic behavior — shaking overcomes the yield stress, after which ketchup flows as a Newtonian fluid

Answer: (C)

Ketchup is a shear-thinning (pseudoplastic) non-Newtonian fluid: its viscosity decreases as shear rate increases. This means gentle tilting (low shear) produces high viscosity and little flow, while vigorous shaking (high shear) dramatically reduces viscosity and allows pouring. This directly violates Newton's law of viscosity, which predicts constant viscosity (linear τ–shear rate relationship) regardless of shear rate. Option D is a common near-miss — ketchup does have a slight yield stress, but the primary behavior is shear-thinning, not Bingham plastic.

Question 2

In a Newtonian fluid flow between two parallel plates (Couette flow), if you double the velocity of the moving plate while keeping all else constant, what happens to the shear stress on the plates?

• A. It remains the same — shear stress depends only on viscosity, not plate speed
• B. It doubles — because shear stress equals μ times the velocity gradient, which doubles
• C. It quadruples — because the kinetic energy of the flow increases with the square of velocity
• D. It halves — because the fluid becomes thinner as it flows faster between the plates

Answer: (B)

For a Newtonian fluid, τ = μ(du/dy). Doubling the plate velocity doubles the velocity gradient du/dy (the velocity profile remains linear in Couette flow), which doubles the shear stress τ. This linear proportionality is precisely what defines a Newtonian fluid — constant μ means shear stress and shear rate are directly proportional. Non-Newtonian fluids break this proportionality; for them, doubling the shear rate would produce something other than a doubling of shear stress.

Question 3

The no-slip condition means that fluid velocity at a solid boundary is zero in all engineering flows, which is why shear stress is maximized at walls rather than at the center of a flow.

• T. True
• F. False

Answer: True

The no-slip condition states that fluid at a solid boundary moves at exactly the boundary's velocity — zero for a stationary wall. This creates the steepest velocity gradient (du/dy) right at the wall, which by Newton's law means maximum shear stress there. In pipe flow, for example, velocity is zero at the wall and maximum at the centerline, making wall shear stress responsible for all pipe friction. Without the no-slip condition, there would be no velocity gradient at the wall, no wall shear stress, and the entire analysis of pipe friction, drag, and boundary layers would be impossible.

Question 4

Dynamic viscosity μ and kinematic viscosity ν = μ/ρ measure the same fluid property and can be used interchangeably in any calculation.

• T. True
• F. False

Answer: False

Dynamic viscosity μ (units: Pa·s) measures a fluid's intrinsic resistance to shear — it appears directly in Newton's law of viscosity τ = μ(du/dy). Kinematic viscosity ν = μ/ρ (units: m²/s) combines this with density and appears naturally when inertial forces matter, such as in the Reynolds number Re = VL/ν. They are not interchangeable: comparing μ values across fluids tells you about their shearing resistance; comparing ν values tells you about momentum diffusion relative to inertia. Two fluids with equal μ can have very different ν if their densities differ, leading to completely different flow behaviors.

Question 5

Why does water's dynamic viscosity decrease with increasing temperature, while most liquids behave similarly? What is the physical mechanism?

Model answer: In liquids, viscosity arises from intermolecular attractive forces that resist layer-by-layer sliding. As temperature rises, molecules gain kinetic energy, more readily overcoming these cohesive bonds, allowing layers to slide past each other more easily — reducing viscosity. For water specifically, hydrogen bonding is the dominant cohesive mechanism, and elevated temperature weakens hydrogen bond networks, dramatically reducing viscosity (a roughly threefold drop from 20°C to 70°C). This contrasts with gases, where viscosity arises from momentum exchange between molecules colliding across adjacent layers — more thermal energy means more collisions and higher momentum transfer, so gas viscosity increases with temperature.

The physical mechanism differs fundamentally between liquids (intermolecular cohesion) and gases (molecular collision frequency). This is why the temperature dependence of viscosity runs in opposite directions for the two phases — a fact that surprises students who assume 'hotter = less viscous' universally. The liquid mechanism (cohesion weakening) is correct for water and most engineering liquids; the gas mechanism (collision frequency increasing) governs air, steam, and other gases at engineering conditions.