Question

In which one of the following cases will the liquid flow in a pipe be most streamlined?
A. Liquids of high viscosity and high density flowing through a pipe of a small radius
B. Liquids of high viscosity and low density flowing through a pipe of a small radius
C. Liquids of low viscosity and low density flowing through a pipe of a large radius
D. Liquids of low viscosity and high density flowing through a pipe of a large radius

Answer 1

Hint: Before going to solve this question let us understand the streamlined flow. The streamlined flow is also referred to as laminar flow. When there is no turbulence and fluctuations in velocity then it is called streamlined flow. It is a path traced by a particle in a flow.

Complete step by step solution:
If you consider a streamlined body, it has a very small contact with the fluid which it is passing through. Hence it loses energy in the form of heat. Streamline flow is a kind of flow where the fluid flows separately without mixing and the velocity of each fluid particle flowing will remain constant with time.

For the streamlined flow, Reynolds's number $N_R \varpropto \dfrac{r\rho}{\eta}$ should be less. For the lesser value $N_R$, the radius and density should be small and viscosity should be high. Therefore, a liquid of high viscosity and low density flows through a pipe of a small radius.

Hence, option B is the correct answer.

Note: Streamlined curve is one in which the velocity vector is tangent to it. The streamline can graphically represent how the fluid gets passed (flow) at any instant.