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Chapter 9: Problem 9

Typical values of the Reynolds number for various animals moving through air or water are listed below, For which cases is inertia of the fluid important? For which cases do viscous effects dominate? For which cases would the flow be laminar; turbulent? Explain. . $$\begin{array}{lcc} \text { Animal } & \text { Speed } & \text { Re } \\ \hline \text { (a) large whale } & 10 \mathrm{m} / \mathrm{s} & 300,000,000 \\\ \text { (b) flying duck } & 20 \mathrm{m} / \mathrm{s} & 300,000 \\ \text { (c) large dragonfly } & 7 \mathrm{m} / \mathrm{s} & 30,000 \\ \text { (d) invertebrate larva } & 1 \mathrm{mm} / \mathrm{s} & 0.3 \\ \text { (e) bacterium } & 0.01 \mathrm{mm} / \mathrm{s} & 0.00003 \end{array}$$

Short Answer

Expert verified
For (a) large whale, (b) flying duck, and (c) large dragonfly, inertia forces dominate leading to turbulent flows whereas for the (d) invertebrate larva and (e) bacterium, viscous forces dominate creating laminar flows.

Step by step solution

01

Analyzing the Reynolds numbers

Take each case and analyze it based on its Reynolds number.
02

Case (a) large whale

With Re = 300,000,000, the inertia forces would be significantly prominent, rendering the fluid's flow to be turbulent.
03

Case (b) flying duck

Despite having a considerably smaller Re (300,000) than the large whale, inertia forces would still dominate and lead to a turbulent flow.
04

Case (c) large dragonfly

This case represents a Re of 30,000. It's on the higher side, meaning turbulence due to inertia dominates over viscous forces.
05

Case (d) invertebrate larva

Here, Re = 0.3 indicates a predominantly viscous effect, resulting in laminar flow.
06

Case (e) bacterium

Lastly, with Re = 0.00003, viscous forces largely dominate, and the flow is laminar.

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