Physics, asked by akshatmathur606, 18 days ago

The Reynold number(N) for a liquid flowing through a pipe depends upon diameter(D) of pipe, speed (v), density (d) and coefficient of viscosity (n) of liquid. Derive the expression for Reynold number.​

Answers

Answered by Saby123
9

Reynold number , R_é = rho vd)μ. It's a dimensionless constant showing the ratio between the inertial force and viscous force on a body .

Here, we have to derive an expression for the number.

N ∝ D

N ∝ V

N ∝rho(density)

N ∝ n( coefficient of viscosity)

[ D ] = l

[ V ] = LT^-1

[ n ] = ML^-1T^-1

[ rho ] = ML^-3

N = [D]^a . [ V]^b. [ n ]^c . [ rho]^d

> N = l^a . [ LT^-1]^b . [ ML^-1T^-1]^c. [ML^-3]^d

> N = l^a. l^b . t^-b . m^c . t^-c. m^d . l^-3d

But N = l^0 . m^0 . t^0 ( As reynold's number is a dimensionless constant mentioned above)

> l^a+b-3d = l^0

> m^c+d = m^0

> t^-b-c = t^0

a + b - 3d = 0

c + d = 0

-b -c = 0

>> a + b = 3d ; c + d = 0, b = -c

d = -c (2nd eqn) and b = -c. So b = d

a + d = 3d

>> a = 2d = 2b .

This is the required expression .

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Answered by rohithkrhoypuc1
5

Answer:

Answered by Rohith kumar. R.

Renoyld number.It is a dimensionless constant showing the ratio between the inertial force and viscous force on the object.

N is proportional to D

N is proportional to V

N is proportional to density

N is proportional ton (viscosity)

[D]=1

[V]=LT^-1

[n]=ML^-1T^-1

[rho]=ML^-3

N=1^a×1^b.t^-b.m^c.t^-c.m^d

But we know that

N= 1^0.t^0.m^0

=1^a+b-3d=1^0

=m^c+d=m^0

=t^-c-c=t^0

=a+b-3d=0

=c+d=0

=-b-c=0

=a+b=3d,c+d=0,b=-c

=d=-c.and b=-c

so we can tell that b=d

Therefore a=2d=2b.

Hope it helps u mate.

Thank you.

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