Dimensional Analysis Civil Engineering (CE) Notes | EduRev

Civil Engineering SSC JE (Technical)

Civil Engineering (CE) : Dimensional Analysis Civil Engineering (CE) Notes | EduRev

The document Dimensional Analysis Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)

 Chapter 8 Dimensional Analysis

  •  Velocity potential = [L2 T–1]
    Stream function = [L2 T–1]
    Acceleration = [LT–2]
    Vorticity = [T–1] 
  • Total no. of variables influencing the problem is equal to the no. of independent variables plus one, one being the no. of dependent variable. 
  • Buckingham p theorem states that if all the n-variable are described by m fundamental dimensions, they may be grouped into (n - m) dimensions p terms. 
  • Selection of 3 repeating variables from the geometry of flow, fluid properties and fluid motion. 
  • Geometric similarity - similarity of shape
    Kinematic similarity - similarity of motion
    dynamic similarity - similarity of forces 
NumberEquationSignificance
Reynolds No.Dimensional Analysis Civil Engineering (CE) Notes | EduRevFlow in closed conduit pipe
Froude NoDimensional Analysis Civil Engineering (CE) Notes | EduRevwhere a free surface is present,structure eg. weirs spillway, channels, etc. w here gravity force is predominant.
Eulers No.Dimensional Analysis Civil Engineering (CE) Notes | EduRevIn cavitation studies.
Mach No.Dimensional Analysis Civil Engineering (CE) Notes | EduRevwhere fluid compressibility is important.
Weber No Dimensional Analysis Civil Engineering (CE) Notes | EduRevIn capillary studies.

Reynolds Model Law :

 Dimensional Analysis Civil Engineering (CE) Notes | EduRev

(i) Velocity ratio

 Dimensional Analysis Civil Engineering (CE) Notes | EduRev

(ii) Time ratio
Dimensional Analysis Civil Engineering (CE) Notes | EduRev

(iii) Acceleration ratio,
Dimensional Analysis Civil Engineering (CE) Notes | EduRev

(iv) Force ratio
Dimensional Analysis Civil Engineering (CE) Notes | EduRev

(v) Power ratio
Dimensional Analysis Civil Engineering (CE) Notes | EduRev

(vi) Discharge ratio

 Dimensional Analysis Civil Engineering (CE) Notes | EduRev

Applications of Reynold’s Model Law :-

  • Flow through small sized pipes 
  • Low velocity motion around automobiles and aeroplane. 
  • Submarines completely under water. 
  • Flow through low speed trubo machines. 
     
  • Froude’s Model law :

(Fr) m = (Fr
Dimensional Analysis Civil Engineering (CE) Notes | EduRev

(i) Time ratio
Tr = Lr1/2 gr–1/2 = Lr1/2

(ii) Acceleration ratio ar = gr = 1

(iii) Force ratio
Dimensional Analysis Civil Engineering (CE) Notes | EduRev

(iv) Power ratio
Dimensional Analysis Civil Engineering (CE) Notes | EduRev

(v) Discharge ratio

 Dimensional Analysis Civil Engineering (CE) Notes | EduRev

Applications : 

  • Open channels 
  • Notches & weirs 
  • Spill ways & dams 
  • Liquid jets from orifice 
  • Ship partially submerged in rough & turbulent sea
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