Lecture-8

# J i it l c tar y v i cj a ni l go s e i

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Unformatted text preview: t: ç- ftiL l t- ¿ l!J /Z / A.u ,7' è) ., ( 22 Surface of Rotating Bucket 1. Draw a picture. 2. Dynamic or Static? 3. Coordinate system? …Static …co-rotating cylindrical 4. Can you apply conservation principles? (no ﬂow in this frame) …Bernoulli’s 5. Use your intuition. 23 Co-Rotating Frame ⌅u + u · ⌅u ⌅t = g (1/⇥)⌅p + ⌅2 u ⌅ uR + uR · ⌅uR ⌅t = g (1/⇥)⌅p + ⌅2 uR + R 2 2 ⇤ uR with Centrifugal and Coriolis “apparent” forces. ( Very convenient when uR = 0.) 24 L- \1 &quot;: ~ ~ \! () .. \- u- ~ u ~ Co-Rotating With Bucket ~ v ~ 'ù ~ \!; \L '0 ~ \L \) 'l ~ ~ U. ~ ., .. ~ () C: , 0 \J 0 K t.. ù ~ .. \0 ~ \c ~ ~ l. \1 ~ I ~ '3 I- q. ~ ~ \I \L C: l :s i '0 r: \) ~ led l') + 1\ï -l ~ D \~ l (( () U I :: 'l. lo J\) l:: . &quot;&quot; ~ 'J ~ ~ :) ~ \Ù i ~ &quot; .. d 'U ~ ( '\ &quot;) -l '&quot; . .. .J Force balance: ~ I. \l 'J ~ '- r' ~ .. ~~ '- I C: \\ ~ \~ l \i l~ Q (W (V tL\~ \~ '- -l .. c: J ~ ~ li ~ 0 LA i f. V ~ '\ \I ~ ~ t I.. l ~ t; 0 V 25 ~ tJ d ., ~ r...
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