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 the oil is given by 𝜂=𝑃(𝑟²− 𝑥²)/4𝑣𝑙 Where v is the velocity of oil at a distance x from the axis of the tube. Determine the dimensions of η.

Answer 1

We have:

$$\eta=\frac{P(r^2-x^2)}{4vl}.$$

The unit of pressure is N/m², the units of r and x are m, velocity is measured in m/s, and length is in meters as well:

$$[\eta]=\frac{\text{N/m}^2·\text{m}}{\text{m/s}}=\text{N}·\text{s/m}^2$$