Question

The dimensional Formula for viscosity
of Fluids is eta=M1L-1T-1
Find how many poise (CGS unit of
viscosity) is equal
to 1 poiseuille (SI unit of viscosity).
​

Answer 1

Given that :-

$\eta=(M^1L^{-1}T^{-1})$

Now,

Let :-

1 poiseuille = n poise

$\rule{200}{2}$

Therefore :-

$1(M_1)^a(L_1)^b(T_1)^c = n(M_2)^a(L_2)^b(T_2)^c$

From here we get that :-

$n= {\dfrac{M_1}{M_2}}^a{\dfrac{L_1}{L_2}}^b{\dfrac{T_1}{T_2}}^c$

We know that:-

In SI units :-

M is mass (in kg)

L is Length (in m)

T is time (in seconds)

In CGS units:-

M is mass (in g)

L is length (in cm)

T is Time (in second)

$\rule{200}{2}$

$n= {\dfrac{1kg}{1g}}^a{\dfrac{1m}{1cm}}^b{\dfrac{1sec}{1sec}}^c$

$n= {\dfrac{1000g}{1g}}^a{\dfrac{100cm}{1cm}}^b{\dfrac{1sec}{1sec}}^c$

$n= {1000}^a {100}^b {1}^c$

On comparing the dimensions of eta and n we get the values of a, b and c as follows :-

a = 1

b =(-1)

c =(-1)

Thus,

$n = {(1000)}^{1} {(100)}^{( - 1)} {1}^{( - 1)} \\ \\ \\n = \frac{1000}{100} \\ \\ \\n = 10$

Hence,

1 poiseuille = 10 poise

$\rule{200}{2}$