Fluid Mechanics – NDA Physics Notes

Fill a glass with water. The water takes the shape of the glass. Pour it into a bowl and it takes the shape of the bowl.

This ability to flow and conform to any container is what makes a liquid a fluid. Gases also flow and conform. They too are fluids. Fluid mechanics is the study of how forces, pressure, and energy behave in fluids.

Fluid mechanics explains why ships float, why aeroplanes fly, why water rises in capillary tubes, why blood circulates through tiny vessels, and why a deep-sea diver risks eardrum injury. It connects pressure to depth, buoyancy to density, and flow speed to pressure, through Bernoulli’s principle.

NDA has tested this chapter 43 times since 2010. Buoyancy alone accounts for 10 PYQs, the highest concentration of any single concept in the entire Physics syllabus. Master this chapter and earn guaranteed marks every year.

1. What Is a Fluid?

A fluid is any substance that can flow and deform continuously under an applied shear stress. Liquids and gases are both fluids. Solids are not.

Unlike solids, fluids cannot resist shear forces. A small sideways force causes continuous flow. A block of steel resists shearing. A cup of water immediately flows when you tilt the cup.

The distinction matters in Physics: solids transmit forces through their rigid structure. Fluids transmit pressure, which is force distributed uniformly across surfaces.

2. Pressure: Definition and Scalar Nature

When a force acts on a surface, what matters physically is not just the magnitude of the force but how concentrated it is. A sharp knife cuts more easily than a blunt one, because the same force is concentrated over a smaller area. This concentration is measured by pressure.

P = F⊥ / A

P = pressure (Pa). F⊥ = component of force acting normal (perpendicular) to the surface (N). A = area of the surface (m²). SI unit: Pascal (Pa) = N m⁻².

Why Pressure Is a Scalar

Pressure is a scalar quantity. [NDA 2016-II] This surprises students because force is a vector. The reason: we take only the normal component of force, the component perpendicular to the surface. This component of a vector, divided by area, gives a scalar result. The directional information is absorbed into “normal to the surface.”

Correctly: pressure is the ratio of the component of force normal to the area, divided by the area. It is not the ratio of force magnitude to area, but specifically the normal component.

3. Pressure Exerted by Solids on Surfaces

When a solid object rests on a surface, it exerts a pressure equal to its weight divided by the contact area:

P = mg / A

m = mass of object (kg). g = acceleration due to gravity (m s⁻²). A = area in contact with surface (m²).

One Foot vs Two Feet

A person of weight mg stands on both feet (contact area = 2A). Pressure = mg/(2A) = P. The same person stands on one foot (contact area = A). Pressure = mg/A = 2P. Standing on one foot doubles the pressure. [NDA 2015-I] Weight mg is unchanged: only the contact area changes.

Wooden Block in Three Orientations

A wooden block of dimensions 40 cm × 20 cm × 10 cm has a fixed weight. When placed on different faces:

Face in Contact	Contact Area	Pressure (since P = mg/A)
20 cm × 10 cm (smallest face)	200 cm²	Pₐ: highest pressure
10 cm × 40 cm (medium face)	400 cm²	Pᴮ: middle pressure
40 cm × 20 cm (largest face)	800 cm²	Pᶜ: lowest pressure

Order: Pₐ > Pᴮ > Pᶜ. [NDA 2023-II] The block’s weight is always mg. Smaller contact area → greater pressure. Larger contact area → smaller pressure.

A wooden box (30 cm × 15 cm × 10 cm, mass 2 kg) resting on its 30 cm × 10 cm face: P = mg/A = (2 × 10)/(0.30 × 0.10) = 20/0.03 ≈ 667 N/m². [NDA 2022-I]

4. Pressure in Fluids at Rest: Hydrostatic Law

In a fluid at rest, pressure is not uniform. It depends on depth. A diver feels more pressure at 10 m than at 5 m below the surface. The deeper you go, the more fluid above you pushes down.

P = P₀ + ρgh

P = absolute pressure at depth h (Pa). P₀ = atmospheric pressure at the surface (Pa). ρ = density of the fluid (kg m⁻³). g = acceleration due to gravity (m s⁻²). h = depth below the surface (m).

Three Properties of Fluid Pressure at Rest

Property 1: Pressure is NOT the same at all points in a fluid at rest. It increases with depth.

Property 2: Pressure is exerted on all container walls in contact with the fluid, from all sides, not just downward.

Property 3: Pressure exists everywhere throughout the fluid volume, not just near the walls or bottom.

Among these three: Property 1 is the incorrect statement if phrased as “pressure is the same at all points.” Properties 2 and 3 are correct. [NDA 2018-I]

Eardrum Risk for Deep-Sea Divers

A deep-sea diver risks eardrum injury because of high water pressure at depth. [NDA 2015-I] Total pressure at depth d = P₀ (atmospheric) + ρ_water × g × d. The eardrum separates high external water pressure from normal air pressure in the middle ear. If the pressure differential is too large, the eardrum can rupture.

5. The Hydrostatic Paradox

Fill three containers of completely different shapes: narrow, wide, funnel-shaped: to the same height with the same liquid. The pressure at the base of all three is identical.

This is called the hydrostatic paradox. Pressure at the base depends only on the liquid height (h), the liquid density (ρ), and g. It does not depend on the shape of the container or the total amount of liquid. [NDA 2020-I & II]

Intuition check: the narrow tube seems to have “less” liquid pushing down on its base, yet the base pressure equals that of the wide barrel. In the narrow tube, the walls also exert downward pressure on the liquid. The total effect at the base is always ρgh, regardless of shape.

6. Measuring Atmospheric Pressure: The Barometer

A barometer is the instrument used to measure atmospheric pressure. [NDA 2018-I] A simple mercury barometer: a glass tube closed at one end is filled with mercury and inverted into a mercury dish. The atmosphere pushes down on the mercury in the dish, supporting a column of mercury in the tube. The height of the mercury column gives atmospheric pressure: P₀ = ρ_mercury × g × h.

Common NDA Confusion: confuse barometer with other instruments: Ammeter measures electric current. Potentiometer measures potential difference (or emf). Lactometer measures the density or purity of milk.

7. Compressibility of Solids, Liquids, and Gases

Compressibility is the ease with which a material can be compressed, meaning its volume reduced by applying pressure. The correct order of compressibility among the three states of matter is:

Solid < Liquid < Gas   [NDA 2016-I]

State	Molecular Spacing	Compressibility	Physical Reason
Solid	Tightly packed (fixed lattice)	Least: almost incompressible	Molecules already close; repulsion resists further compression
Liquid	Close but mobile	Moderate: nearly incompressible	Molecules close but can move; small gaps allow slight compression
Gas	Widely spaced (free motion)	Highest: easily compressed	Large gaps between molecules; easy to reduce volume

Practical consequence: tyres use compressed gas (not liquid or solid) because gas is easily compressible and stores energy efficiently. Hydraulic systems use liquid because liquids are nearly incompressible. Pressure transmits without volume change.

8. Density and Relative Density

Density

Density is mass per unit volume: ρ = m/V. SI unit: kg m⁻³. Density of water at 4°C = 1000 kg/m³ = 1 g/cm³. This is the standard reference for relative density calculations.

Relative Density (Specific Gravity)

Relative density is the ratio of a substance’s density to the density of water at 4°C:

Relative density = ρ_substance / ρ_water(4°C)

Relative density is dimensionless. It has no unit. A relative density of 1 means the substance is as dense as water. Greater than 1 means denser than water; less than 1 means less dense. Relative density of silver with respect to iron: ρ_silver/ρ_iron = 11/8 ≈ 1.4. [NDA 2013-I]

Density of Mixtures

The formula for mixture density depends on how the substances are combined:

Mixing Condition	Formula	Type of Mean
Equal volumes mixed	ρ_mix = (ρ₁ + ρ₂)/2	Arithmetic mean
Equal masses mixed	ρ_mix = 2ρ₁ρ₂/(ρ₁ + ρ₂)	Harmonic mean

An object made of two equal volumes with densities ρ₀ and 2ρ₀: average density = (ρ₀ + 2ρ₀)/2 = (3/2)ρ₀. [NDA 2022-II]

Two substances (densities ρ₁ and ρ₂) mixed in equal volumes give relative density 4 and in equal masses give relative density 3. Setting up: (ρ₁ + ρ₂)/2 = 4 → ρ₁ + ρ₂ = 8. 2ρ₁ρ₂/(ρ₁ + ρ₂) = 3 → 2ρ₁ρ₂/8 = 3 → ρ₁ρ₂ = 12. Solving: ρ₁ = 6, ρ₂ = 2. [NDA 2019-II]

9. Anomalous Expansion of Water

Most liquids contract when cooled. Their density increases as temperature falls. Water is different.

Water contracts as it cools from 100°C down to 4°C. Its density increases normally over this range. But below 4°C, water begins to expand as it cools further. This means water reaches its maximum density at 4°C, then becomes less dense both above and below this temperature.

Maximum density of water = 1000 kg/m³ at 4°C = 277 K. [NDA 2021-I | NDA 2024-II]

This anomalous behaviour has profound consequences. In winter, the surface of a pond cools to 4°C first. The denser water sinks. As the surface cools further below 4°C, the water expands and stays at the surface (being less dense). Ice forms on top while the bottom remains at 4°C. Aquatic life survives under the ice in the 4°C water.

10. Buoyancy and Archimedes’ Principle

★  IMPORTANT This is the highest-frequency topic in NDA Physics, with 10 PYQs across 16 years. Learn every layer of this section carefully.

Why Does a Submerged Object Experience an Upward Force?

Imagine a cube submerged in water. Water pressure acts on all six faces. The pressure on the bottom face (deeper) is greater than the pressure on the top face (shallower). This pressure difference creates a net upward force on the cube: this is the buoyant force.

Archimedes’ Principle: Precise Statement

When a body is partially or fully immersed in a fluid, the fluid exerts an upward force (buoyant force or upthrust) on the body equal in magnitude to the weight of the fluid displaced by the body. [NDA 2021-II | NDA 2022-I | NDA 2025-I]

Buoyant force = weight of displaced fluid = ρ_fluid × V_submerged × g

Critical precision: the buoyant force equals the weight of displaced fluid, not the mass. Weight = mass × g. Confusing the two introduces a factor of ~10 error.

Also critical: buoyancy is a force (measured in Newtons), not a pressure (measured in Pascals). The two are not interchangeable. [NDA 2021-II | NDA 2022-I]

Apparent Weight

When a solid object is submerged in a fluid, the fluid pushes up (buoyancy) while gravity pulls down (weight). The net downward force felt is the apparent weight:

Apparent weight = Actual weight − Buoyant force

A submerged object always weighs less than in air. The apparent weight loss equals the weight of the displaced fluid. [NDA 2012-I | NDA 2017-II]

Four Key Facts About Buoyancy

Fact	Correct Statement	Common Wrong Version
Type of quantity	Buoyancy is an upward FORCE (Newtons)	Buoyancy is an upward pressure (wrong units)
Magnitude	Equals WEIGHT of displaced fluid	Equals mass of displaced fluid (wrong: omits g)
Apparent weight	Actual weight − Buoyancy	Always equal to actual weight (wrong)
Floating body	Displaces fluid equal to own WEIGHT	Displaces fluid equal to own volume (only true when fully submerged)

11. Floating and Sinking: The Average Density Rule

Whether a body floats or sinks depends on one thing: how its average density compares to the density of the fluid.

Condition	Result	Physical Reason
Average density of body > density of fluid	Body SINKS	Weight > buoyant force at full submersion
Average density of body < density of fluid	Body FLOATS (partially submerged)	Buoyant force = weight before full submersion
Average density of body = density of fluid	Body is NEUTRALLY BUOYANT (suspended anywhere)	Buoyant force = weight at any submersion depth

Mass alone, shape alone, or mass + shape are all insufficient criteria for floating or sinking. Only the average density matters. [NDA 2018-I | NDA 2025-II]

The Floating Body Rule

A floating body displaces fluid equal in weight to its own weight. [NDA 2010-II | NDA 2012-I] A steel ship floating on water: the weight of water displaced equals the weight of the ship, not more, not less.

Iron Nail vs Iron Ship

An iron nail sinks because its average density (≈ 7800 kg/m³) >> density of water (1000 kg/m³). An iron ship floats because it encloses a large air volume. The average density of (steel hull + air) is less than 1000 kg/m³. [NDA 2023-II] The two correct statements: average density of iron nail > water (it sinks) AND average density of ship < water (it floats).

Sealed Packet Calculation

A sealed packet: volume = 1 litre = 1000 cm³, mass = 800 g. Average density = 800/1000 = 0.8 g/cm³. Since 0.8 < 1.0 (water), the packet floats in water. Since 0.8 < 1.5 (liquid B), the packet also floats in liquid B. A body floats in any liquid with greater density than itself. [NDA 2022-II]

Balloon Rises in Air

A balloon rises in air only if the density of its fill gas is less than the density of air. [NDA 2014-I] The buoyant force (weight of air displaced) must exceed the total weight of the balloon (gas + envelope). Hydrogen and helium are lighter than air. They provide lift. Cold air, water vapour, or heavier gases do not.

Two Identical Ice Blocks

Two identical blocks of ice with the same mass floating in water in different orientations displace equal volumes of water. Archimedes’ Principle depends only on the weight of the floating body, not on orientation or shape. Both blocks have the same weight, so both displace the same weight of water. [NDA 2010-II]

12. Multi-Fluid and Composite Buoyancy

Sphere in Oil-Water System

A homogeneous sphere of volume V floats with half its volume in a denser liquid (density ρ₂) and half in oil (density ρ₁, lighter) above it. The total buoyant force equals the weight of the sphere:

Buoyant force = (V/2)ρ₂g + (V/2)ρ₁g = Vg(ρ₁ + ρ₂)/2

Weight of sphere W = Vg(ρ₁ + ρ₂)/2   [NDA 2010-I]

Pumpkin Density Calculation

A pumpkin weighs 7.5 N. When fully submerged in water, it displaces ¾ L = 7.5 × 10⁻⁴ m³ of water. Volume of pumpkin = 7.5 × 10⁻⁴ m³. Mass = W/g = 7.5/10 = 0.75 kg. Density = 0.75/(7.5 × 10⁻⁴) = 1000 kg/m³. [NDA 2024-II] The pumpkin is exactly as dense as water, making it neutrally buoyant.

Two Hollow Cubes at Different Fill Levels

Two hollow cubes C₁ and C₂ (negligible mass) are partially filled with liquids of densities ρ₁ and ρ₂ respectively, and float in water (density ρ_w). A cube floats when its average density < ρ_w. More submerged means average density is closer to ρ_w. The density relationship depends on the fill levels shown in the figure. [NDA 2024-II]

13. Stability of Floating Bodies: The Metacentre

When a ship tilts slightly, the geometry of submersion changes. The centre of buoyancy (the centroid of displaced water) shifts sideways. The new buoyant force acts from this shifted centre. If the resulting restoring torque brings the ship back to upright, the ship is stable.

The metacentre (M) is the point at which the line of action of the buoyant force (when tilted) intersects the ship’s original vertical axis. For stable floating:

Stable floating: Centre of gravity (G) must be below the metacentre (M).

If G is below M: tilting generates a restoring torque that returns the body to upright, giving stable equilibrium. [NDA 2026-I] If G is above M: tilting generates a torque that tips the body further. The body capsizes.

14. Streamline Flow and Bernoulli’s Principle

Streamline (Steady) Flow

In steady (streamline) flow, every fluid particle passing through a given point follows exactly the same path and has exactly the same velocity at that point. The velocity at any fixed point does not change with time.

The incorrect statement: “each particle may not follow the same path as a previous particle passing through that point.” In steady flow, they always follow the same path. [NDA 2015-II] The velocity of all fluid particles crossing a given position is constant in steady flow. [NDA 2016-II]

Two streamlines can never intersect. Intersection would imply two different velocities at one point, which violates the definition of steady flow.

Bernoulli’s Principle

Bernoulli’s principle is conservation of energy applied to fluid flow. For an ideal (incompressible, non-viscous) fluid in steady flow along a streamline:

P + ½ρv² + ρgh = constant

P = pressure at the point. ρ = fluid density. v = fluid speed at the point. h = height above reference level. Bernoulli’s principle is based on conservation of energy, not conservation of mass (that is the continuity equation) and not conservation of momentum. [NDA 2014-I]

Key consequence: where fluid moves faster (narrow section of a pipe), pressure is lower. Where it moves slower (wide section), pressure is higher.

Applications of Bernoulli’s Principle

Aerofoil lift: The wing of an aircraft is shaped so air flows faster over the top surface than below. Faster flow → lower pressure on top → net upward force (lift).

Venturimeter: A device with a narrowed throat. Measures flow rate from the pressure difference between wide and narrow sections.

Spray gun: Fast-moving air over a liquid surface creates low pressure, drawing liquid up into the spray.

Torricelli’s theorem: Speed of fluid escaping from a hole in a tank (at depth h below surface) = √(2gh). A direct application of Bernoulli’s principle.

15. Surface Tension

The surface of a liquid behaves like a stretched elastic membrane. It tries to minimise its area. This behaviour is caused by surface tension: the net inward attractive force on surface molecules from molecules below. Surface molecules are attracted downward and sideways but not upward (no liquid above them). This net inward pull makes the surface contract.

Four Phenomena Caused by Surface Tension

1. Near-spherical raindrops: A sphere has the minimum surface area for a given volume. Surface tension minimises area → drops form spheres.

2. Capillary rise: Water rises in narrow tubes against gravity. Surface tension pulls the water up.

3. Soap and detergent cleaning: Soap lowers the surface tension of water, allowing it to wet oily surfaces and carry dirt away.

4. Soap bubbles: Bubbles form spherical shapes for the same reason as raindrops: minimum surface area.

Flow of a liquid under gravity is NOT caused by surface tension: it results from gravitational force and viscosity. [NDA 2015-I] Surface tension produces capillary rise, not bulk flow under gravity.

Temperature Dependence

Surface tension decreases as temperature increases. [NDA 2025-II] At higher temperatures, molecules have greater kinetic energy. The net inward attractive force at the surface is weaker. At the boiling point, surface tension approaches zero. This is why hot water cleans better than cold water. Lower surface tension allows better wetting.

16. Capillary Rise

When a narrow tube (capillary tube) is placed in a liquid that wets glass (like water), the liquid rises inside the tube above the level of the surrounding liquid. This is capillary rise. The rise occurs because surface tension pulls the liquid up along the glass walls. The narrower the tube, the higher the rise. Capillary rise explains how water travels upward through plant stems and soil.

Effect of Inclination

When a capillary tube is inclined at angle θ to the vertical, the vertical height of liquid rise remains the same as in the vertical tube. However, the length of the liquid column along the tube increases:

L = h / cos θ

h = vertical height of liquid rise (same as for vertical tube). θ = angle between the tube and vertical. L = actual length of liquid column along the inclined tube. At θ = 45°: L = h/cos 45° = h√2. The column is longer than in the vertical tube. [NDA 2011-I] The vertical height h is the same: only the slant length changes.

17. Viscosity and Terminal Velocity

What Is Viscosity?

Viscosity is the internal friction of a fluid, its resistance to flow. Honey has high viscosity; water has low viscosity. Viscosity causes faster-moving layers of fluid to drag on slower-moving layers. The coefficient of viscosity η is measured in Pascal-seconds (Pa s) or Poise.

Stokes’ Law

For a sphere moving slowly through a viscous fluid (laminar flow), the drag force is given by Stokes’ Law:

F_drag = 6πηrv

η = coefficient of viscosity (Pa s). r = radius of the sphere (m). v = speed of the sphere (m s⁻¹).

Terminal Velocity

When an object falls through a viscous fluid, three forces act: (1) Weight downward (mg). (2) Buoyancy upward (ρ_fluid × V × g). (3) Viscous drag upward (6πηrv), which increases as speed increases. Initially, weight > buoyancy + drag, so the object accelerates. As speed increases, drag increases. Eventually, when weight = buoyancy + drag, net force = 0. The object moves at constant speed, called terminal velocity.

v_terminal = 2r²(ρ_sphere − ρ_fluid)g / (9η)

v_terminal increases with: larger radius r, greater density difference (ρ_sphere − ρ_fluid), smaller viscosity η. Terminal velocity is faster in less viscous fluids and for denser, larger objects.

18. Boiling Point, Vapour Pressure, and Altitude

★  IMPORTANT This is the three-way misconception: the most persistently tested conceptual confusion in this chapter. Read this section with extra care.

What Is Vapour Pressure?

Every liquid continuously evaporates. Surface molecules escape into the space above the liquid. These vapour molecules exert a pressure called vapour pressure. Vapour pressure increases with temperature: the hotter the liquid, the more molecules escape.

What Is Boiling?

Boiling occurs when the vapour pressure of the liquid reaches and equals the atmospheric pressure above it. At this exact equality, vapour bubbles form throughout the liquid and escape freely.

Boiling occurs when: vapour pressure = atmospheric pressure

[NDA 2023-II | NDA 2025-II] The boiling point is the temperature at which this equality is achieved. Water boils at 100°C at sea level (1 atm) precisely because its vapour pressure reaches 1 atm at that temperature.

Effect of Altitude

At high altitude (mountaintop), atmospheric pressure is lower than at sea level. Vapour pressure equals atmospheric pressure at a lower temperature, so the liquid boils at a lower temperature. Water on a mountaintop might boil at 85°C or 90°C. [NDA 2017-II]

Does this mean food cooks faster at altitude? No. The opposite is true. The cooking temperature is lower, so food takes longer to cook, despite the water boiling sooner.

19. The Pressure Cooker: The Boiling Point Connection

A pressure cooker is a sealed vessel that traps steam. As water boils, steam builds up inside and cannot escape. The pressure inside rises above atmospheric pressure.

Since boiling occurs when vapour pressure = internal pressure, and the internal pressure is now higher than 1 atm, the water must reach a higher temperature for its vapour pressure to match the elevated internal pressure. Boiling point rises above 100°C, perhaps to 120°C or 130°C. At this higher temperature, food cooks much faster.

Pressure cooker: higher pressure → higher boiling point → higher cooking temperature → faster cooking   [NDA 2011-I | NDA 2022-II]

Situation	Atmospheric/Internal Pressure	Boiling Point of Water	Cooking Speed
Sea level (normal cooking)	1 atm (standard)	100°C	Normal
High altitude (open vessel)	< 1 atm (reduced)	< 100°C (e.g., 85°C)	Slower: lower temperature
Pressure cooker (sealed)	> 1 atm (elevated)	> 100°C (e.g., 120°C)	Faster: higher temperature

Common mistake: “Pressure cooker decreases the boiling point.” This is wrong. A pressure cooker increases the boiling point by increasing the internal pressure. Altitude decreases the boiling point, not the pressure cooker.

20. Elasticity: Stress, Strain, and Young’s Modulus

Hooke’s Law

Within the elastic limit, the extension of a solid is directly proportional to the applied force:

F = kx

F = applied force (N). k = spring constant / stiffness (N m⁻¹). x = extension from natural length (m). This linear relationship holds up to the elastic limit, beyond which the material does not return to its original shape.

Stress and Strain

Stress is the force per unit cross-sectional area inside a solid:

Stress (σ) = F / A   (Pa = N m⁻²)

Strain is the fractional change in dimension:

Strain (ε) = ΔL / L   (dimensionless)

Stress has units (Pa); strain has no units. Stress is the cause; strain is the effect.

Young’s Modulus

Young’s modulus measures the stiffness of a material under tensile (stretching or compressing) stress:

Y = Stress / Strain = (F × L) / (A × ΔL)

Y = Young’s modulus (Pa). Higher Y means stiffer material (less strain for the same stress). Steel: Y ≈ 2 × 10¹¹ Pa. Rubber: Y ≈ 10⁶ Pa.

Important Distinctions

Pressure vs Buoyancy

Pressure is force per unit area (Pa = N/m²). Buoyancy is a net upward force (N). Pressure causes buoyancy. It is not the same as buoyancy. Never call buoyancy an “upward pressure.” It is an upward force resulting from pressure differences.

Weight of Displaced Fluid vs Mass of Displaced Fluid

Buoyancy = weight of displaced fluid = m_displaced × g. Not mass of displaced fluid alone. The extra factor of g ≈ 10 changes the numerical value significantly. Archimedes wanted the weight (in Newtons), not the mass in kilograms.

Float/Sink: Average Density Only

Mass alone, shape alone, or material alone cannot determine float or sink. Only average density relative to fluid density determines this. A hollow iron sphere floats (average density < water); a solid iron sphere sinks (average density >> water). Same material, different average density gives different outcomes.

Altitude Boiling vs Pressure Cooker Boiling

Altitude reduces atmospheric pressure → reduces boiling point → reduces cooking temperature → food takes longer. Pressure cooker increases internal pressure → increases boiling point → increases cooking temperature → food cooks faster. These are exact opposites of each other.

Surface Tension vs Viscosity Surface tension is a property of the liquid surface. It acts in the plane of the surface, minimising area. Viscosity is a bulk property. It resists flow between adjacent layers throughout the fluid. Surface tension lifts liquid in capillary tubes. Viscosity resists that flow and determines terminal velocity.

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