2.2.1 · D5Fluid Mechanics
Question bank — Fluid definition — shear stress, no fixed shape
Before we start, one reminder of the vocabulary, so no symbol is used unexplained:
Recall The four words every question below leans on
- Shear stress ::: a sideways (tangential) force spread over an area — the push that tries to slide one layer of stuff over the next.
- Normal stress ::: a perpendicular force spread over an area — a straight push or pull into/out of a surface.
- Strain ::: how much something has been tilted/deformed (an angle).
- Rate of strain ::: how fast that tilt is growing right now (a velocity gradient, units ).
True or false — justify
A fluid can never carry any shear stress at all.
False. It carries zero shear only at rest; a moving fluid carries , which is exactly what makes honey hard to stir.
Gases are not fluids because they don't pour like water.
False. "Fluid" is defined by giving way to any shear, and gases flow and fill their container just like liquids — so both are fluids.
A solid also deforms under shear, so a solid is a kind of fluid.
False. A solid reaches a fixed tilt and stops (), storing the stress like a spring; a fluid never stops tilting, so the two are fundamentally different.
If you apply a tiny enough shear stress, a fluid will resist it and hold still.
False. The definition says "any shear, however small" makes it flow — there is no threshold below which a (Newtonian) fluid stays put.
For a fluid at rest, the only stresses present are normal (pressure-like).
True. With zero shear at static equilibrium, only perpendicular pushes remain — this is why Hydrostatics — Fluids at Rest deals in pressure alone.
"No fixed shape" and "cannot resist shear" are two independent properties of a fluid.
False. They are the same fact: holding a shape against gravity needs shear support on slanted surfaces, which a fluid cannot give — so no-shape follows from no-shear.
Doubling the shear stress on a Newtonian fluid doubles how far it has deformed.
False. For a fluid, sets the rate , so doubling doubles the speed of shearing, not the accumulated angle — the angle keeps growing regardless.
A more viscous fluid can support a static shear stress that a thin fluid cannot.
False. Any Newtonian fluid supports zero static shear; high viscosity only means it flows slowly, not that it stops.
Spot the error
"Water on a table keeps its shape until a big enough breeze blows it."
The error: fluids have no shear threshold. Even a gentle breeze gives ; water spreads because for static shear, so it never truly "held" a self-made shape.
", so shear stress is viscosity times the tilt angle."
The error: it should be — the rate of tilt, not the tilt . That form belongs to Stress and Strain in Solids.
"Since stress is force over area, a bigger plate feels a bigger shear stress for the same drag force."
The error: decreases with area for fixed force. Bigger area spreads the same force thinner, so the intensity (stress) drops.
"At rest a fluid has zero stress of any kind."
The error: only shear stress is zero at rest; normal stress (pressure) is very much present — it holds up the column of fluid above.
"Velocity gradient has units of velocity."
The error: it is velocity per distance, — an inverse time, the rate at which the shear angle grows.
"Because gases flow, they must be more viscous than liquids."
The error: flowing is not viscosity. Gases actually have much smaller than most liquids; both flow simply because both are fluids.
Why questions
Why does a fluid take the shape of its container from the bottom up?
Because it cannot balance shear on slanted surfaces, it collapses under gravity until every surface is horizontal (or matches the walls), filling low points first.
Why do we divide force by area to define stress instead of just using force?
Deformation depends on the intensity of the push, not the total force — the same force is crushing on a pinpoint but gentle spread over a wall.
Why does Newton's law use rather than the strain like solids do?
A fluid's tilt never settles to a fixed , so isn't a stable quantity to relate stress to; the rate is well-defined and constant in steady flow. See Velocity Profile and No-Slip Condition.
Why does a fluid at static equilibrium carry only normal stress?
Any leftover shear would keep deforming it, so it can't be at rest until all shear has driven the fluid to a shape where shear vanishes — leaving only perpendicular pushes.
Why is honey harder to stir than water even though both obey ?
Honey's viscosity is far larger, so to make the same you must supply a much larger — see Viscosity and Newtonian vs Non-Newtonian Fluids.
Why does calling pressure a "normal stress" connect fluids to Pressure in Fluids?
Pressure is the normal-stress that a fluid pushes with; since fluids at rest have only normal stress, pressure is the entire story of static fluids.
Edge cases
What is the shear stress when the velocity gradient is exactly zero?
Zero — no relative sliding between layers means no shear, which is precisely the static-rest condition of any fluid.
A fluid film has both plates moving at the same speed. Is there shear stress?
No — the whole film moves together as a block, so and ; motion alone doesn't create shear, only relative motion does.
As viscosity (an "ideal" fluid), what happens to the shear stress at a given ?
: the fluid slides with no resistance, an idealization where layers never grip each other — a useful limiting model, not a real substance.
As viscosity , does the fluid become a solid?
Not quite — it flows ever more slowly and looks solid on short timescales, but given enough time any Newtonian fluid still flows, since it still cannot hold a static shear.
A blob of steel and a blob of water both feel a tiny breeze. What is the key difference in outcome?
Steel resists via , tilting imperceptibly and keeping shape; water has for static shear, so and it spreads — it can never reach static equilibrium in that shape.
Right at the moment shear is first applied to still water, is the velocity gradient large or small?
Initially small (the fluid was at rest), but it grows immediately because any forces — the fluid begins and keeps deforming with no settling point.
Connections
- Parent topic (Hinglish)
- Pressure in Fluids — the normal stress that survives at rest.
- Viscosity and Newtonian vs Non-Newtonian Fluids — the role of .
- Hydrostatics — Fluids at Rest — why only normal forces at rest.
- Stress and Strain in Solids — the contrasting law.
- Velocity Profile and No-Slip Condition — origin of .