Example 12.9 from College Physics, 12.5 The Onset of Turbulence

Is This Flow Laminar or Turbulent?

Calculate the Reynolds number for flow in the needle considered in Example 12.8 to verify the assumption that the flow is laminar. Assume that the density of the saline solution is $1025 kg/ m^{3}$ .

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We have all of the information needed, except the fluid speed $v$ , which can be calculated from $\bar{v} = Q / A = 1.70 m/s$ (verification of this is in this chapter’s Problems and Exercises).
Solution
Entering the known values into $N_{R} = \frac{2 ρ vr}{η}$ gives
$\begin{array}{l} N_{R} & = & \frac{2 ρ vr}{η} \\ = & \frac{2 ({1025 kg/m}^{3}) (1.70 m/s) (0.150 \times 10^{- 3} m)}{1 . 00 \times 10^{- 3} N \cdot {s/m}^{2}} \\ = & 523 . \end{array}$
12.54
Discussion
Since $N_{R}$ is well below 2000, the flow should indeed be laminar.

0 of 3 steps open

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