Question

In which one of the following cases will the liquid flow in a pipe be most streamlined :
(1) Liquid of high viscosity and high density flowing through a pipe of small radius
(2) Liquid of high viscosity and low density flowing through a pipe of small radius
(3) Liquid of low viscosity and low density flowing through a pipe of large radius
(4) Liquid of low viscosity and high density flowing through a pipe of large radius

Answer 1

Answer on Question #41318, Physics, Mechanics

In which one of the following cases will the liquid flow in a pipe be most streamlined?

(1) Liquid of high viscosity and high density flowing through a pipe of small radius

(2) Liquid of high viscosity and low density flowing through a pipe of small radius

(3) Liquid of low viscosity and low density flowing through a pipe of large radius

(4) Liquid of low viscosity and high density flowing through a pipe of large radius

Solution

The liquid flow in a pipe is most streamlined if the Reynolds number would be lesser.

For flow in a pipe or tube, the Reynolds number is generally defined as:

$$Re = \frac {\rho v \cdot (2 r)}{\mu},$$

where $r$ is the radius of a pipe, $v$ is the mean velocity of the fluid, $\rho$ is the density of the fluid, $\mu$ is the dynamic viscosity of the fluid.

We can see from this formula that the Reynolds number would be lesser when liquid of high viscosity and low density flowing through a pipe of small radius.

Answer: (2) Liquid of high viscosity and low density flowing through a pipe of small radius.

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