Chapter 1.1, Problem 26E

Reminder Round all answers to two decimal places unless otherwise indicated.

Note Some of the formulas below use the special number $e$, which was presented in the Prologue.

Reynolds Number The Reynolds number is very important in such fields as fluid flow and aerodynamics. In the case of a fluid flowing through a pipe, the Reynolds’s number $R$ is given by

$R=\frac{vdD}{\mu }$.

Here $v$ is the velocity of the fluid in meters per second, $d$ is the diameter of the pipe in meters, $D$ is the density of the fluid in kilograms per cubic meter, and $\mu$ is the viscosity of the fluid measured in Newton-seconds per square meter. Generally, when the Reynolds number is above $2000$, the flow becomes turbulent, and rapid mixing occurs. When the Reynolds number is less than $2000$, the flow is streamline. Consider a fluid flowing through a pipe diameter $0.05$ meter at a velocity of $0.2$ meter per second.

a. If the fluid in the pipe is toluene, its viscosity is $0.00059$ newton-seconds per square meter, and its density is $867$ kilograms per cubic meter. Is the flow turbulent or streamline?

b. If the toluene is replaced by glycerol, then the viscosity is $1.49$ newton-seconds per square meter, and the density is $1216.3$ kilograms per cubic meter. Is the glycerol flow turbulent or streamline?