FLUID MECHANICS & HYDRAULIC MACHINES

Lecture 1: Properties of FluidsEr. Deepak Kumar Mallick,

School of Civil Engineering.

What is a Fluid?A fluid is a substance that deforms continuously when subjected to a shear stress, no matter how small that shear stress may be.

”or”If a fluid is at rest, there can be no shearing forces acting and, therefore, all forces in the fluid must be perpendicular to the planes upon which they act.

• A solid can resist a shear stress by a static deformation, a fluid cannot.

• Liquid & Gases.• Water, Milk, Petrol, Air, etc.

Fluid Properties• Density (ρ) = M/V = Mass per unit volume. (Kg/m3).

• Specific Weight (γ ) = ρg = Weight of fluid per unit volume (N/m3).

• Specific Volume (ν) = = Volume occupied by mass of fluid (m3/kg).

• Specific Gravity (s) = = Ratio of the specific weight of the fluid to

the specific weight of pure water at 40C.

• Viscosity (µ) = Property of a fluid which determines its resistance to shearing stresses.

• Kinematic Viscosity = = Ratio between dynamic viscosity and density of fluid.

1

0

f

w,4 C

Shear Stress

Newton’s Law• Newton’s law of viscosity:

The shear stress (τ) on a fluid is directly proportional to the rate of shear strain. The constant s called the co-efficient of viscosity.

• The fluids follow this law is called as Newtonian Fluid.

dudy

Types of Fluids• Ideal Fluids : τ = 0

• Newtonian Fluids :

• Ideal Plastics :

• Non-Newtonian Fluids :

dudy

duConstant

dy

ndudy

Newtonian Fluids vs Non-Newtonian Fluids

Effect of Temperature

For Liquids:

• The Viscosity of liquids decreases with increase in temperature.• Shear stress is due to the inter-molecular cohesion which decreases

with increase in temperature.

For Gases:

• The Viscosity of gases increases with increase in temperature.• Shear stress is due to the exchange of momentum of the molecules.

The inter-molecular cohesion is negligible in gases.

e

2ba

1T

Compressibility & Bulk Modulus

• Compressibility: Change in volume under the action of external force.Compressibility = 1/K,

• Bulk modulus (K) : The substance's resistance to uniform compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.

• K increases with increase in pressure.• For liquid K decreases with increase in temperature and for

gases K increases with increase in temperature.• At NTP, Kair = 101.3 KN/m2 and Kwater = 2.07x106 KN/m2

dPK

dV / V

Surface Tension• Cohesion: The force of attraction between the molecules of a liquid

by virtue of which they are bound to each other to remain as one assemblage of particles is known as the force of cohesion. This property enables the liquid to resist tensile stress.

• Adhesion: This force enables two different liquids to adhere to each other or a liquid to adhere to a solid body or surface.

• Surface Tension: Surface tension is a property of the surface of a liquid that allows it to resist an external force. This property is caused by cohesion of similar molecules.

Water Droplets, Soap Bubble, Liquid Jet

• Water Droplets:

• Soap Bubbles:

• Liquid:

4P

d

Pd

Pd

Capillary

Capillarity: This is the ability of a liquid to flow in narrow spaces without the assistance of, and in opposition to external forces like gravity.

For water & Glass tube

4 cosh

gd

4h

gd

Vapor Pressure & Cavitation• Liquids evaporate because of molecules escaping from the liquid

surface. The vapor molecules exert a partial pressure in the space, known as vapor pressure.

• The vapor pressure increases with increase in temperature.• When the pressure above a liquid equals the vapor pressure of the

liquid, boiling occurs.

• In many situations involving the flow of liquids it is possible that very low pressure are produced as certain locations in the system. Under such circumstances the pressures may be equal to or less than the vapor pressure. When this occurs, the liquid flashes into vapor. This phenomenon is called cavitation.

• The growth and decay of vapor bubbles affects the operating performance of hydraulic pumps and turbines and can result in erosion of the metal parts in the region of cavitation.

Pressure Scale

• In fluid mechanics the pressure results from a normal compressive force acting on an area. The pressure p is defined as force per unit area.

• The standard atmospheric pressure at sea level is 101.3 kPa.• The gauge pressure is the pressure recorded by the gauge or

manometer.• Absolute pressure = gauge pressure + atmospheric pressure

Pa = Pg + Patm

• Zero gauge pressure is atmospheric pressure. Also, zero absolute pressure in ideal vacuum.

Pressure Scale

Problems