Chapter 1 Fluid Properties - Fluid Mechanics, Mechanical Engineering Mechanical Engineering Notes | EduRev

FLUID PROPERTIES

Definition of Fluids:- A fluid is a substance which flow continuously under the action of shear force (however small the force may be), as long as shear force is there the fluid moves or deforms.
E.g: - Liquids, gases, vapour etc.
For a static fluid shear force = 0 

• Density or mass density (S):- Mass per unit volume of a fluid is called its density
  s = (m/v)
• Density of water is maximum at 4ºC. 
• Density of water at 4ºC = 1000 kg/m³.
   
• Ideal Fluid (Perfect Fluid)
  • Non-viscous, friction less & incompressible. 
  • Does not offer shear resistance against flow. 
  • Bulk modulus is infinite 
  • Used in mathematical analysis and flow problems. 
  • Ideal fluid has no surface tension
     
• Real Fluid 
  • Possess the properties such as viscosity, surface tension and compressibility. 
  • Offers resistance against flow.
     
• Specific gravity (G or S)
  • G or S = Density of substance / Density of water at 4⁰C
  • Specific gravity for water is 1.0 at 4ºC and  that of mercury is 13.6  
  • Specific gravity varies with temperature therefore it should be determined at specified temperature (4ºC)
     
• Specific weight (unit weight) or weight density (g')
  g'=rg
  r = mass density
  g = due to gravity, acceleration
   

Newton's Law of Viscosity

Non-Newtonian Fluids

• These do not follow Newton's law of viscosity. The relation between shear sterss and velocity gradient is

Where A and B are constants depending upon type of fluid and condition of flow.(i) For Dilatant Fluids: n > 1 & B = 0
Ex. Butter, Quick sand
(ii) For Bingham Plastic Fluids: n = 1 & B ¹ 0 Ex. Sewage sludge, Drilling mud These fluids always have certain minimum shear stress before they yield.
(iii) For Pseudoplastic Fluids: n < 1 & B = 0 Ex. Paper pulp, Rubber solution, Lipsticks, Paints, Blood, Polymetric solution etc.
(iv) For Thixotropic Fluids : n < 1 & B ¹ 0 Viscosity increase with time.
Ex. Printers ink and Enamels.
(v) For Rheopectic Fluids: n > 1 & B ¹ 0 Viscosity decreases with time
Ex. Gypsum solution in water & Bentonite solution.

• Viscosity 
  • Due to viscosity a fluid offers resistance to flow. It is due to cohesion and intermolecular attraction.
    (i) Dynamic Viscosity ( m) Its SI unit is Pascal second or N-s/m2 Its CGS unit is Poise = Dyne-sec/cm2 1 poise = 0.1 N–s/m²
    (ii) Kinematic Viscosity
     

Its SI unit is m²/s.
Its CGS unit is cm²/s or stoke
1 Stoke = 10^–4 m²/s 

• Viscosity of liquids decrease with temperature whereas viscosity of gases increase with temperature. 
• fluids with increasing order of viscosity are air, gasoline, water, crude oil, castor oil. 
• Viscosity of water at 1ºc is 1 centipoise. 
• Viscosity of fluids is due to cohesion and molecular momentum transfer.
   
• Surface Tension (S) 
  • Surface tensions is due to cohesion only. 
  • Surface tension decrease with increase in temperature and it alos act when fluid is at rest 
  • It is a surface phenomenon 
  • At critical point liquid and vapour are at same state thus suface tension is zero s_water = 0.0736 N/m at 20ºC
    S_mercury = 4.51 N/m
  • (i) Pressure inside a liquid drop, in excess of atmospheric pressure                                                                          

p= 4s/d,                                                                                                                                             where s is surface tension d is dia. of drop                                                                               

• (ii)Pressure inside a soap bubble, in excess of atmospheric pressure
  p= 8s/d                                                                                                                                                                                
• (iii) Pressure inside jct                                                                                                                                                      

     p = 2s/d

• Capillary Action 
  • Capillary action is due to adhesion and cohesion, both.
  • Height of water in capillary tube

where,
g = Specific weight,
h = rise in capillary

ρ = density of fluid
S = surface tension of water & glass
r = radius of tube
θ = angle of contact between the liquid and the material
θ — 0º for water and glass
θ — 128º for mercury and glass

For capillary action dia of tube should be less than 3cm. 

• When a liquid surface supports another liquid of density " r_b ", then rise in capillary is given as

Compressibility

• It refers to change in volume/density due to change in pressure. 
• The compressibility reciprocal of bulk modulus of elasticity (K).

Compressibility  = 1/k

• In compressible fluids the velocity of sound is given by

C = velocity of sound in fluid
K = Bulk modulus of fluid