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Write names of four dimensionless quantities. If y = A sin(wt - kx) then find out dimension of w/k.

Write names of four dimensionless quantities. If y = A sin(wt - kx) then find out dimension of w/k.

Grade:11

3 Answers

Ramesh V
70 Points
11 years ago

The dimensionless quantities are

Coefficient of static friction(μs)

coefficient of kinetic friction(μk)

Decibels(dB)

Poissons ratio

Stokes number

 

for Sin X , X should be dimensionless

here wt-kx should be dimensionless , so dimension of w/k is equal to dimension of x/t which is m/sec or LT-1

 
AskIITianExpert Srijan.iitd
8 Points
11 years ago

since the argument of any trignometric quantity have to be neccessarily a radian hence it implies dimention of wt-kx has to be the dimention of radian that is dimentionless.hence dimention of w is T-1and dimention of k is L-1 hence dimention of w/k is L1T -1.

AskiitianExpert Shine
10 Points
11 years ago

Hi

There are infinitely many dimensionless quantities and they are often called numbers. very few of them has been listed below:

Name Standard Symbol Field of application
Abbe number V optics (dispersion in optical materials)
Albedo α climatology, astronomy (reflectivity of surfaces or bodies)
Archimedes number Ar motion of fluids due to density differences
Atomic weight M chemistry
Bagnold number Ba flow of bulk solids such as grain and sand. [5]
Biot number Bi surface vs. volume conductivity of solids
Bodenstein number   residence-time distribution
Bond number Bo capillary action driven by buoyancy [6]
Brinkman number Br heat transfer by conduction from the wall to a viscous fluid
Brownell Katz number   combination of capillary number and Bond number
Capillary number Ca fluid flow influenced by surface tension
Coefficient of static friction μs friction of solid bodies at rest
Coefficient of kinetic friction μk friction of solid bodies in translational motion
Colburn j factor   dimensionless heat transfer coefficient
Courant-Friedrich-Levy number ν numerical solutions of hyperbolic PDEs [7]
Damkohler number Da reaction time scales vs. transport phenomena
Darcy friction factor Cf or f fluid flow
Dean number D vortices in curved ducts
Deborah number De rheology of viscoelastic fluids
Decibel dB ratio of two intensities of sound

y = A sin (wt-kx)
According to dimensional analysis , in any term sin ø, ø should be dimensionless
Hence, the term wt-kx is also dimensionless
 where t= time (sec)
            x= distance (m)

for the term to be dimensionless, wt has no units
      units of  w = s^(-1)
                    k = m^(-1)

Now, units of w/k = m/s

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