Question

Turpentine oil is flowing through a tube of length $l$ and radius $r$. The pressure difference between the two ends of the tube is $P$. The viscosity of oil is given by $\eta=\frac{P(r^2-x^2)}{4vl}$ where $v$ is the velocity of oil at a distance $x$ from the axis of the tube. The dimensions of $\eta$ are

• A. $[M^0 L^0 T^0]$
• B. $[MLT^1]$
• C. $[ML^2T^{-2}]$
• D. $[ML^{-1}T^{-1}]$

Answer 1

Answer: (D)

$[ML^{-1}T^{-1}]$

Answer 2

Dimensions of $P=[ML^{-1}T^{-2}]$ Dimensions of $r = [L]$ Dimensions of $v = [LT^{-1}]$ Dimensions of $l = [L]$ $\therefore$ Dimensions of $\eta=\frac{[P][r^2-x^2]}{[4vl]}$ $=\frac{[ML^{-1}T^{-2}][L^2]}{[LT^{-1}][L]}$ $=[ML^{-1}T^{-1}]$