Transcription of 「管内の流れ」 - lemons.k.u-tokyo.ac.jp
1 10 cf.. a . y _. a u x x x .. x . dp = 0 . dp dx <0. dx 1 2.. dp 1 . 2 r = r 2. p {. p 12dx 3 r u log y . a y .. u . = u ' v'. 123. y { u = u ' v ' = u ' v'. y .. du du u a y dp = u ' v ' = l 2 l = y u ' v' = (1) dy dy y 2 dx = . w u u ' v' du du . = ( y ) = w 2. dy dy . 3 4. 1. w .. du 1. = w w dy y = ut . ut u * u + .. u u 1 u * =. = log y + C ( 2) u log y ut w C y ut . y ut y * =.. u * =. 1.. ( ) u . log y * log t + C. 4. 14 4 2 4 3. C . 1. u * = log y * + C.. C 1. u * = log y * + .. 5 log - low 6. log y* log y*. u* u*= + u* u*= + u*=y* .. u u*=y*. = u ' v' = w y 12 0. 3. u u 2. = w = t y* y*. y 0 0 10 100 1000.. ut 2. u = y y* < 4 . u u *. u = y *. = t y ut 4 < y* < 30 70. u * = y * . 30 70 < y*. 1. u * = log y* +.}}
2 7 8. 2.. dy 2 (a-y) dy y Q = 0 u 2 (a y )dy a . a . y (2a y ) 2 (a y )dy 1 dp u=- 1 dp y (2a - y) = 0 . 2a x 4 dx 4 dx . y a 4 dp = .. 8 dx Q a 2 dp U m = 2 = . a 8 dx 8 2a 64 64. = U m 2 = =. a 1 U 2 2a U m Re m 2.. dp D. = 14243 D = 2a . U m . dx 1 U 2 = / . m 9 10. 2. a ut . ut ut2. u=- 1 y ut umax = log + u=.. y . log . y (2a - y) .. u 1 y ut . = log + a ut . ut . umax u u m + = t log + . y = a u = U max umax - u u 1 au . u 1 a ut m = log t + max = log + ut . ut . dp D dp 2 m 2 ut 2. a y = =. , =. dx 1 u 2 dx a a u u 1 a m max = log 2. ut y u 8 aut . t = , = Re um 4 2. u u a . max m a 2 = log 2 (a y )dy = . a 1 y 8 1. 0 . = loge Re + . ut y a 4 2 . 2 . log (a a ) d . 1 dy ( ). a = 1. = log10 Re 0 d .. = a 2 log (1 ) d.
3 1 2 1 dy 0 d . 1444424444. 3 1.. (. = log10 Re ). umax = u m + 11 12. 3.. /a .. 64 . Re 3 Re=2300 4 5 6 logRe .. Re .. a .. y* = 5 .. ut <5. 13. 14. 3 4 5 6 logRe .. 1 1. V1 + P1 + gh1 = V2 + P2 + gh2 . 2 2. 2 2.. : Pa .. g 2 P 2 V2. 2 2. 1 P 1 V1. V P V P. 1 + 1 + h1 = 2 + 2 + h2. 2 g g 2 g g h1 h2. m .. 2 2. V P V P. 1 + 1 + gh1 = 2 + 2 + gh2. 2 2 .. N m W. 15. : m 2 / s 2 = = 16. kg kg 4. 2 P 2 V2. 1 P 1 V1 . V2. (1) E = . 1 2 P 1 2 P. L. h2 2. V1 + 1 + gh1 = V2 + 2 + gh2 + E h1. 2 2 .. v v v v . dp 1. = U 2 D U . dx D 2 = = = ~ = 1. L (2) . dp L 1. L = U 2. dx D 2 A2. v2 v1 v2. = E A1 v1. 2 A2 A1. D 4Q A'. Q = U U = . 2 D 2 2 2. A V. 2. 1 V2 A'. 8 LQ 2 E 1 1 1 E 1 2 Cc =. E = 2 5 L D 5 . A2 2 Cc 2. 17 A218. D. V2.
4 (3) E = 2 g V2 . = gH V = 2 gH L >>D. 2 H. D. V. v : V2.. L L. 2 D.. d (deg ).. sin 4 = + . = sin 2 + 2. 90. o V. 2 2.. 2.. ( < < ) . d V2 L . gH = 1 + + . 2 D .. 2 gH. v =. L. 1+ + . 19 D 20. 5.
