Answer to Question #198168 in Mechanics | Relativity for fara

Question

for low speed ( laminar) flow through a circular pipe, the velocity distribution takes the form v=(beta/

Answer 1

$v=B\dfrac{\Delta p}{\mu}(r_o^2-r^2)$

Dimension of $v=L/T=LT^{-1}$

Dimension of $\mu=\dfrac{\tau}{\dfrac{du}{dy}}$

$\mu=ML^{-1}T^{-1}$

Dimension of $\Delta p=ML^{-1}T^{-2}$

Dimension of $r=L$

Substituting all values in first equation

$LT^{-1}=B\times\dfrac{ML^{-1}T^{-2}}{ML^{-1}T^{-1}}\times L^2$

$B=L^{-1}$

Therefore, dimension of B = L^-1