Mechanical Properties of fluids

Thrust

The total force exerted by a liquid on any surface in contact perpendicularly is called thrust.

Pressure

Thrust per unit area

Density

Mass per unit volume

Specific gravity or relative density

the ratio of a substance to density of water at 4 degrees celsius

pascal's law

the law states that the pressure exerted at any point of an enclosed liquid is transmitted equally in all directions

Viscosity

property of fluids by virtue of which an internal force of friction comes into play when a fluid is in motion and opposes relative motion between its layers

Viscous force

Backwards dragging force that acts tangentially on the layers of the fluids in motion and tends to destroy its motion

velocity gradient

Rate of change of velocity with distance.

effect of temperature on viscosity

when a liquid is heated, the kinetic energy of the molecule increases, and the inter molecular force of attraction become weaker. Hence viscosity of the liquid decreases with the increase in temperature

Poiseuille's formula

The volume of a liquid, flowing out per second through a horizontal capillary tube of length l, radius r, under a pressure difference across its ends,

Assumptions used in the derivations of Poiseulle's formula

1. the flow of the liquid is steady and parallel to the axis of the tube

2. The pressure is constant over any cross-section of the tube

3. The liquid velocity is zero at the walls of the tube and increases towards the axis of the tube

4. the tube is held horizontally so that gravity doesn’t have an influence on the flow of liquid

Stoke’s law

According to this law, the backward viscous force acting on a small spherical body of radius r moving with uniform velocity v through fluid of viscosity eta is given by

conditions under which stoke’s law is valid

1. the body is perfectly rigid and smooth

2. there is no slip between the body and the fluid

3. the fluid through which the body moves has infinite extension

4. The motion of the body doesn’t give rise to turbulent motion and eddies. Hence motion is streamline

critical velocity

the critical velocity of a liquid that is that limiting value of its velocity of flow upto which the flow is streamlined and above the flow becomes turbulent

streamlined flow

a flow is said to be streamlined or laminar if every particle of the fluid follows exactly the path of the preceding particles and has the exact same velocity of the preceding particles when crossing that point

properties of streamlined flow

1. tangent at any point on the streamline gives the direction of velocity at that point

2. two streamlines will not intersect, if two streamlines intersect then it would have 2 different direction of velocity at a given point which is not physically possible

3. at a particular point on the streamline the velocity of the liquid is constant

4. crowding of streamlines represents a faster flow of liquid

turbulent flow

when the liquid velocity exceeds a certain limiting value called critical velocity the liquid flow becomes zigzag, the path and the velocity of the liquid particle changes continuously. This flow is called turbulent flow

terminal velocity

it is defined as the maximum velocity acquired by a spherical body while falling through a viscous force

principle of conservation of mass for incompressible fluids

It states that during the streamlined flow of an ideal fluid through a pipe of varying cross-section, the product of the area of cross-section and fluid velocity remains constant throughout the flow

ideal fluid

a non-viscous incompressible irrotational and streamlined flow liquid

kinetic energy

energy possessed by a liquid by virtue of its motion

velocity head

kinetic energy per unit weight

potential energy

It is the energy possessed by a liquid by virtue of its position

Potential head

potential energy per unit weight

pressure energy

Pressure * volume

pressure head

pressure energy per unit weight

bernoulli’s priniciple

For an ideal fluid, the sum of pressure energy, potential energy and kinetic energy per unit mass is always constant.

Limitations of Bernoulli’s principle

1. it applies only to non-viscous fluids. (in the case of viscous fluids we need to take into account the work done by viscous drag)

2. it is applicable only to streamlined flow and not to turbulent flow

3. applicable only to incompressible fluids because it doesn’t take into account the elastic energy of the fluid

4. has been derived on the assumption that there is no energy loss due to friction

5. doesn’t take into consideration of angular momentum so it can’t be used when the fluid moves along a circular path

toricelli’s law of efflux

the velocity of efflux of the liquid is equal to that of which a body would attain in falling freely from the free surface to the orifice

molecular range

it is the maximum distance upto which a molecule can exert some appreciable force of attraction on other molecules

cohesive force

the force of attraction between the molecules of the same substance

adhesive force

the force of attraction between the molecules of different substances

sphere of influence

a sphere drawn around a molecules at the centre and with radius equal to the molecular range

surface tension

it is the property by virtue of which free surface of a liquid at rest behaves like an elastic stretched membrane tending to contract so as to occupy minimum surface area

angle of contact

it is defined as the angle between the tangent of the liquid surface at the point of contact and the solid surface inside the liquid

miniscus

the curve in the upper part of the surface of the liquid produced by surface tension

when will a liquid have a concave miniscus

if the adhesive force is greater than cohesive force, liquid will wet the solid surface and have a concave miniscus

when will a liquid have a convex miniscus

if the cohesive force is greater than adhesive force, the liquid will not wet the solid surface and have a convex miniscus

when will a liquid have a plane miniscus

if adhesive force and cohesive force are same

Factors on which angle of contact depend on:

1. nature of the solid and liquid in contact

2. cleanliness of the surface in contact

3. medium above the free surface of the liquid

4. temperature of the liquid

capillarity

the phenomena of rise or fall in a liquid in a capillary tube in comparison to the surroundings

capillary tube

a tube of very fine bore is called capillary tube