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  • Critical velocity depends upon coefficient of viscosity, density and radius and is given by the relation: <img alt="V_c\alpha\ \eta^x \rho^y r^z" src="http://entrancecorner.oncodecogs.com

Critical velocity depends upon coefficient of viscosity, density and radius and is given by the relation:

V_c\alpha\ \eta^x \rho^y r^z, where \eta =coefficient \ of\ viscosity, \rho =density, r=radius

Find value of x,y,z

Option: 1

x = 1 , y = 1 , z = -1 


Option: 2

x=1 , y= -1 , z = -1 


Option: 3

x= 0 , y= 1/2  ,z = -1/2 


Option: 4

x= 0  y= -1/2,  z = +1/2 


Answers (1)

best_answer

We can write the relation as:

V_c=K\eta^x \rho^y r^z, where K is a constan

Dimension of coefficient of viscosity: [\eta ]=[ML^{-1}T^{-1}]

Dimension of density: [\rho]=[ML^{-3}]

[V_c]=[\eta ]^x [\rho]^y [r]^z

\Rightarrow[LT^{-1}]=[ML^{-1}T^{-1}]^x [ML^{-3}]^y [L]^z

\Rightarrow[LT^{-1}]=[M]^{x+y}[L]^{-x-3y+z}[T]^{-x}

so, -x-3y+z=1

x+y=0\Rightarrow x=-y

-x=-1⇒x=1, y=-1, z=-1

so, [V_c]\alpha [\eta ]^1 [\rho]^{-1} [r]^{-1}

Posted by

Nehul

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