Suppose that two disks of indefinitely large radius are separated by a distance H, as in Fig. P5.6. One is porous and the other solid. Fluid is injected from the porous disk into the intervening space at a constant velocity v₀, such that Re = v₀H/ν ≪ 1. The radial velocity averaged over the height H is u(r).

(a) Use a shell balance to determine u(r).

(b) It is shown in Example 8.3-1 that

Determine the stream function and plot streamlines corresponding to several values of ψ⁄(H²v₀). The expression for ψ is simplest if the dimensionless coordinates η = r/H and ζ = z/H are used.

Transcribed Image Text:

H N Side View Porous r u(r) Solid Vo u(r + Ar) Figure P5.6 Flow between porous and solid disks. Top View u(r); u(r + Ar)