lecture 2 : Fundamental Concepts

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lecture 2 : Fundamental Concepts

Source:- https://fluidscience.blogspot.com

 Property: Any characteristic of a system.

 Some familiar properties are pressure P, temperature T, volume V, and mass   

 Properties are considered to be either intensive or extensive.

 Intensive properties: Those that are independent of the mass of a system, such as temperature, pressure,     and density.

 Extensive properties: Those whose values depend on the size—or extent—of the system.

 Specific properties: Extensive properties per unit mass.

Couses of Viscosity

 Matter is made up of atoms that are widely spaced in the gas phase. Yet it is very convenient to disregard the atomic nature of a substance and view it as a continuous, homogeneous matter with no holes, that is, a continuum. 

  The continuum idealization allows us to treat properties as point functions and to assume the properties vary continually in space with no jump discontinuities. 

 This idealization is valid as long as the size of the system we deal with is large relative to the space between the molecules. 

  This is the case in practically all problems. 

 In this text we will limit our consideration to substances that can be modeled as a continuum

No slip condition 

 The layer of the fluid in contact with the solid boundary has the velocity of the boundary itself. In other words, the layer of the fluid sticks to the solid surface in contact and there is “NO SLIP” at the surface.

Lets take a example of pipe  Inside a pipe or tube a very thin layer of fluid right near the walls of the tube are motionless because they get caught up in the microscopic ridges of the tube. Layers closer to the centre move faster and the fluid sheers. The middle layer moves the fastest

Specific mass or density (𝞺) 

 The “mass per unit volume” is mass density. Hence it has units of kilograms per cubic meter (kg/m3 ). Specific mass or density (𝞺) = 𝑀𝑎𝑠𝑠/ 𝑉𝑜𝑙𝑢𝑚𝑒 𝑘𝑔 𝑚3

 The mass density of water at 4 oC is 1000 kg/m3 while it is 1.20 kg/m3 for air at 20oC at standard pressure

Specific weight or weight density (𝟂 or 𝞬) 

 It is the ratio between the weight of a fluid to its volume. It is also termed as weight per unit volume of a fluid. Its unit is N/m3 .

 Specific Weight (𝟂) = 𝑊𝑒𝑖𝑔ℎ𝑡 

/ 𝑉𝑜𝑙𝑢𝑚𝑒 = 𝑚𝑎𝑠𝑠 ×𝑔𝑟𝑎𝑣𝑖𝑡𝑦 𝑣𝑜𝑙𝑢𝑚𝑒 = 𝞺𝒈 (𝑁/ 𝑚3)

 Problem: 1. What is the specific weight for water at 4 oC is …….. 2. What is the specific weight for air ………. 

Specific volume (𝞶)

  It is defined as the volume of a fluid occupied by a unit mass or volume per unit mass of a fluid is called specific volume. 

Specific volume (𝞶) = 𝑉𝑜𝑙𝑢𝑚𝑒 / 

 𝑀𝑎𝑠𝑠 = 1 𝞺 ( 𝑚3/ 𝑘𝑔 )

Problem: 1. What is the specific volume of water at 4 oC is …….. 2. What is the specific volume for air ……….

Specific gravity (S) 

 The ratio of specific mass (density) of a given liquid to the specific mass (density) of water (standard fluid) at a standard reference temperature (4 oC) is defined as specific gravity (S). 

Specific gravity (S) = 𝐷𝑒𝑛𝑠𝑖𝑠𝑖𝑡𝑦𝑡𝑒𝑠𝑖𝑛𝑔 𝑓𝑙𝑢𝑖𝑑 / 𝐷𝑒𝑛𝑠𝑖𝑠𝑖𝑡𝑦𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑓𝑙𝑢𝑖𝑑 (𝑁𝑜 𝑢𝑛𝑖𝑡𝑠 )

Example: 

 Density of mercury is 13600 kg/m3 . What is the specific gravity. 𝑆𝐻𝑔 = 13600  / 1000 = 13.6 Problem: 1. Find out the specific gravity of oil having density of 800 kg/ m3? 2. If the specific weight of oil is 8829 N/m3 . Find its specific gravity, density and specific volume?

VISCOSITY 

Viscosity: A property that represents the internal resistance of a fluid to motion or the “fluidity”. Drag force: The force a flowing fluid exerts on a body in the flow direction. The magnitude of this force depends, in part, on viscosity

Viscosity

  Different kinds of fluids flow more easily than others. Water, for example, flows more easily than honey. This is because honey has a higher viscosity. 

 Viscosity is a property of fluid by virtue of which a fluid offers resistance to the relative movement of one layer to the other layer adjacent to the first layer.

Cohesion force of attraction 

 Particle of a layer attracts the particles of other adjacent layer. 

 As a result net force in the backward direction for upper later and forward direction for lower layer. So, the net velocity of upper layer decreases and lower layer increases.

Molecular momentum exchange 

 Particles of one layer jumps into the other adjacent layer and vice versa. 

 As a result the particles in the upper layer consists of some slower particles and in the lower layer we have some fast moving particles. So, the net velocity of upper layer decreases and lower layer increases.

Newton’s Law of Viscosity: It says that the shear stress is proportional to the velocity gradient or shear strain rate.

 Dynamic viscosity: Units or Units of dynamic viscosity are Poise.

 Kinematic viscosity (𝝂) : It is defined as the ratio between the dynamic viscosity and density of the fluid. μ = Fh VA = 𝑁 ×𝑚 𝑚 𝑠𝑒𝑐 ×𝑚2 = 𝑁𝑠𝑒𝑐 𝑚2 = Pa-sec F = μAV h 1 Poise =0.1 Pa-sec ν = μ ρ = 𝑁.𝑠𝑒𝑐 𝑚2 𝑘𝑔 𝑚3 = 𝑘𝑔.𝑚 𝑠𝑒𝑐2 𝑠𝑒𝑐 𝑚2 𝑘𝑔 𝑚3 = 𝑚^2/𝑠𝑒c

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