Question

Determine the transition length at the entrance to a 10 mm tube through which 100 percent glycerol at 60 C is flowing at a velocity of 0.5 m/s. The density of a glycerol is 1240 kg/m Data: The dynamic viscosity is 0.0813 Pa-s. a) 18.13 mm b) 50 mm c) 45.43 mm d) 38.13 mm

Answer 1

Answer: Option (d) is the correct answer.

Explanation:

The given data is as follows.

Tube diameter d = 10 mm = 0.01 m

Velocity of glycerol, v = 0.5 m/s

Density of glycerol ($\rho$) = 1240 kg/m3

Dynamic viscosity of glycerol ($\mu$) = 0.0813 pa.s

Reynolds number (Re) = $\rho \times velocity \times \frac{density}{\mu}$

                                     = $1240 \times 0.5 \times \frac{0.01}{0.0813}$

                                     = 76.26

Therefore, according to Reynolds number we can say that flow is laminar.

                     Lt = $0.05 \times Re \times d$

                         = $0.05 \times 76.26 \times 0.01$

                         = $0.03813 m$

As it is known that 1 m = 1000 mm. Hence, in 0.03813 m will be equal to $0.03813 m \times \frac{1000 mm}{1 m}$

                         = 38.13 mm

Thus, we can conclude that the transition length of glycerol is 38.13 mm.