Question

A large plate is at rest in water at 15?C. The plate is suddenly translated parallel to itself, at 1.5 m/s. The resulting fluid movement is not exactly like that in a b.l. because the velocity profile builds up uniformly, all over, instead of from an edge. The governing transient momentum equation, Du/Dt = ?(?2u/?y2), takes the form 1 ? ?u ?t = ?2u ?y2

`Determine u at 0.015 m from the plate for t = 1, 10, and 1000 s. Do this by first posing the problem fully and then comparing it with the solution in Section 5.6. [u 0.003 m/s after 10 s.]

Answer 1

Answer: (a) = 3.8187m/s, (b) =24.0858m/s (c) = = 3220.071m/s

Step-by-step explanation:

du/u² = dt = ∫du/2.3183 = ∫dt

0.4313 u = t + c

(a) t = 0, u= 15m/s, c = 0.647

u = t+c/0.4313 = t + 0.647/0.4313

(a) when t= 1 u = 1+ 0.647/0.4313 = 3.8187m/s

(b) when t= 10 u = 10 + 0.647/0.4313 = 24.0858m/s

(c)when t= 1000 u = 1000 + 0.647/0.4313 = 3220.071m/s