Properties of Fluids - 3 - GATE ME Fluid Mechanics Free MCQ Test with solutions

When adhesion force is more than cohesion force then fluid will wet the surface and angle of contact between fluid and surface will be less than 90° (acute).

Graphically Capillarity can be represented as:

Case – 1:

when contact angle θ is acute i.e. θ < 90° 

In case of wetting fluid, the level in the capillary tube will rise and the phenomenon is capillary rise. For water and clean glass tube θ = 0°.

Case – 2:

when contact angle θ is obtuse i.e. θ > 90°

In case of non – wetting fluid, the level in capillary tube will fall and the phenomenon is capillary fall. For mercury glass tube θ = 128°. 

μ ⇒ Pa.s
1 poise = Dyne-sec/cm²

Note that force between like molecules is known as cohesive force, and force between unlike molecules is known as adhesive force. Due to predominent cohesive force mercury posses non-wetting characteristic.

Since some initial force is required to have the flow of tooth paste hence it is example of bingham plastic.

Milk, Blood ..........Pseudo plastic

Absolute viscosity → unit is poise
Kinematic viscosity → unit is stroke
Newtonian fluid → du/dy is constant
Surface tension → unit is N/m

Capillary rise is due to adhesion and capillary depression is due to cohesion and capillarity is due to both cohesion and adhesion.

Weight of liquid raised or lowered in the capillary to be
= (area of tube x rise or fall) x specific weight


Vertical component of surface tension force
= σ cosθ x circumference
= σ cosθ x πd = πdσcosθ
In equilibrium, the downward weight of the liquid column h the balanced by the vertical component of the force of surface tension.

Height of capillarity

v = m²/s = L²T^-1

From the definition of viscosity, viscosity is the resistance offered by the one layer of fluid on another layer and opposes relative motion between.

Bulk modulus of elasticity (k)

Also,

It represents change in volume with pressure.

In any flow system, if the pressure at any point in the liquid approaches the vapour pressure, vaporization of liquid starts, resulting in the pockets of dissolved gasses and vapours. The bubbles of vapour thus formed are carried by the flowing liquid into a region of high pressure where they collapse, giving rise to high impact pressure. This phenomenon is known as cavitation.

A spherical soap bubble has surfaces in contact with air, one inside and the other outside, each one of which contributes the same amount of tensile force due to surface tension. As such on a hemispherical section of a soap bubble of radius r the tensile force due to surface tension in equal to 2σ(2πr). However, the pressure force acting on the hemispherical section of the soap bubble is same as in the case of a droplet and it is equal to ρ(πr²). Thus equating these two forces for equilibrium, we have

Consider a jet of liquid of radius r, length l and having internal pressure intensity p is excess of the outside presure intensity. If the jet is cut into two halves, then the forces acting on one half will be those due to pressure intensity p on the projected area (2rl) and the tensile force due to surface tension a acting along the two sides (2l).
These two forces will be equal and opposite for equilibrium and hence we have
ρ(2rl) = σ(2l)
or

Consider a spherical droplet of radius r having internal pressure intensity ρ in excess of the outside pressure intensity. If the droplet is cut into two halves, then the forces acting on one half will be those due to pressure intensity p on the projected area (πr²) and the tensile force due to surface tension a acting around the circumference (2πr). These two forces will be equal and opposite for equilibrium and hence we have

Ideal fluid is non-viscous and incompressible
For Newton ion fluid

Kinematic viscosity v = μ/ρ
Mercury in glass - Capillary depression