(Solved): Problem 3. Observations show that flow in a circular pipe of diameter D remains laminar up to a Re ...

Problem 3. Observations show that flow in a circular pipe of diameter $$D$$ remains laminar up to a Reynolds number $${\mathbf{R}}_{\text{pipe }}=?UD/?=2000$$ (Figure 3.10). What about flows in other flow in channels or pipes with different geometries? Consider the example of flow between two flat plates shown in Figure 3.1. In this case, the appropriate length scale for the Reynolds number is $$L=d$$. It also makes sense to use plate speed rather than mean flow velocity speed as the characteristic velocity in $$\mathbf{R}$$, giving $${\mathbf{R}}_{\text{plate }}=?u_{\text{plate }}d/?$$. Changes in length and velocity scales can alter the upper limit for laminar flow, but for the case of flow between two parallel plates, flow is again laminar up to $${\mathbf{R}}_{\text{plate }}=2000$$. (A parameter called the hydraulic radius [Chapter 4.5] can be used to find values of $$R$$ corresponding to the laminar-turbulent transition for different flow cross-sections. This is explored further in an example problem in Chapter 4.) A. For $$20^{?}\mathrm{C}$$ water between 2 plates separated by a distance of $$4.0\mathrm{mm}$$ (i.e., $$d=4.0\mathrm{mm}$$; Figure 3.1), what is the maximum speed that the upper plate can move and still maintain laminar flow? B. Is the flow in Problem 2 laminar? (Note: if not, Equation $$3.1$$ is no longer cor1