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Chapter 15: Problem 19

In the study of flow characteristics in pipes, the relative effect of velocity to viscous effects is given by the Reynolds number, which is a dimensionless number. Reynolds number is given by: $$ R e=\frac{\rho V D}{\mu} $$ where \(\rho\) is the fluid density \(\left[\mathrm{kg} / \mathrm{m}^{3}\right], V\) is velocity \([\mathrm{m} / \mathrm{s}]\), and \(D\) is the pipe diameter [m]. What is the unit of absolute viscosity \((\mu)\), ?

Short Answer

Expert verified
Answer: The unit for absolute viscosity (μ) is [kg / (m · s)].

Step by step solution

01

Write down the given formula

The Reynolds number is given by the formula: $$ Re = \frac{\rho V D}{\mu} $$
02

Analyze the formula to isolate absolute viscosity \((\mu)\)

We need to find the unit of absolute viscosity \((\mu)\). First, isolate \(\mu\) in the Reynolds number formula: $$ \mu = \frac{\rho V D}{Re} $$
03

Identify the given units for each variable

The units for each variable are given as follows: - Fluid density \((\rho)\): \(\left[\mathrm{kg} / \mathrm{m}^{3}\right]\) - Velocity \((V)\): \(\left[\mathrm{m} / \mathrm{s}\right]\) - Pipe diameter \((D)\): \([\mathrm{m}]\) - Reynolds number \((Re)\): dimensionless number (no units)
04

Substitute the units in the formula for absolute viscosity \((\mu)\)

Plug in the units of each variable into the formula for absolute viscosity: $$ \mu = \frac{[\mathrm{kg} / \mathrm{m}^{3}] \cdot [\mathrm{m} / \mathrm{s}] \cdot [\mathrm{m}]}{\text{dimensionless number}} $$
05

Calculate the unit for absolute viscosity \((\mu)\)

Simplify the units by canceling out common units: $$ \mu = \frac{\mathrm{kg}}{\mathrm{m} \cdot \mathrm{s}} $$
06

Report the unit for absolute viscosity \((\mu)\)

The unit for absolute viscosity \((\mu)\) is \(\left[\mathrm{kg} / \mathrm{m} \cdot \mathrm{s}\right]\).

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