环工原理答案

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2.2 pdp+ RTgMdz=0 T=288.15-5Z pdp= - 5Z)-R(288.15gMdz

两边分别积分, pdp= - 5Z)-R(288.15

gMdz + c

即:lnp = 5RgMln(288.15- 5z)+ c 当z=0时, p=760mmHg

c= ln760 - 5RgMln288.15 当p=380mmHg 代入,得z=5.56103 m 2.4(a)设高度为h, 由题意知:1=1109 kg/m3 2=1020 kg/m3 Z1=0.6m Z2=0.4m 1 Z1+ 2 Z2 = 1 h 解得h=0.968m (b)若h有50mm误差, 设有误差后,界面高度为Z0,

1 Z0 + 2(1- Z0)= 1 (h0.05)

解得 Z0 = 1.22m 或 -0.022m 均无意义。

3.1 Re=vD 查得各数据,算的: (1) Re = 1.53105 > 4000 湍流 (2) Re = 4.51105 > 4000 湍流 (3) Re = 3019 2100<3019<4000 过渡流 (4) Re = 2.7 < 2100 层流 3.4(1)查

算出Re = vD = 57.2 属于层流 故 xt = 0.05 Re D = 44mm

(2) Re = vD > 4000 属于湍流 xt为直径得40到50倍 故xt  (120-150)in 4.1 S= 1/4*D2 = 4415.625 mm2 将整个管道分为11个同心圆环,iius.为同心圆环得面积,

为同心圆环中流体的平均

流速,为同心圆环中两圆上的速度。 (a) v = S1 sdsu. = S1 111.iiius= 0.801 m/s

(b) α = sdsu.3/ v3.S = SV 13 111.iiius3 = 1.184 (C) β = S1 sdsvu.)(2= S

1

111.iis

2)(

v

ui = 1.071

(计算结果仅供参考) 4.4 设水面上一点为a, 出水处为b 由伯努利方程

η wp + aP + g Za + 22aav = bP + g Zb +

2

2bbv

+ hf

其中aP=bP,Zb = 5m,av=0 hf = 2.5 J/kg bv= 24Dq = 1.27m/s

m= q = 2.5kg/s wp= w/m = 40 J/kg 代入以上数据得 Za= 1.26m 5.1 证明:取a、b两点,能量守恒得:

aP = bP+ hfs

又hfs = 4 f DL 22V 间距为b的平行面的等效直径D=2b, 对层流来讲,f = Re16 Фa

对于平行面Фa = 1.5 将以上数据代入,整理变形后得证

Pa – Pb = 212bLv 5.2 由题意知:D= 60mm = 0.06m Re = 5  104 Re = vD 查水 = 1  103 kg/m3  = 1.0050  10-3 Pa S 解出v = 0.8375 m/s

①在层流层中y+ = u+ 设厚度为y 当厚度为y时,y = 5

y = yu = 

y

v

2

f = 5

f = 0.046 Re-0.2 将各数据代入得: y = 0.117mm ② 设截面积得比例为η 截面积为一圆环,

η = 1- 2

2

)2()2(DyD

= 0.778%

③Q总 = v S总 = 0.8375  2)2(D = 2.368  10-3 m3/s 设层流层流量为Q,

Q = su ds = su u+ ds = su y+ ds = s(v2f)2 y d(y2)

= (v2f)2 -410 17.102y2 dy = 6.18  10-9 m3/s

总QQ= 0.00026%

5.4 由题意知,v = Q/S = Q/2)2(D = 4.63 m/s Re = vD = 1956< 2100 属于层流 由5.1中公式

Pa – Pb = 212bLv 代入数据得 Pa – Pb = 115750Pa 功率P = F v = (Pa – Pb)S v = 3215.5W

7.1 由题意及查表得: = 3 10-5 Pa s Фs = 1 = RTpM= 1.133kg/m3 Dp = 3mm =0.4 Deq = 32Фs Dp 1 Re = vDeq = 49.85 1< 49.85<1000 故Lp= 3222)1(150psoDV + 32175.1psoDV = 9009Pa/m 同理,当Dp = 4mm 时,算出Lp=6229 Pa/m 7.5 进行单位换算得

Lp = 1.9  106 Pa/m v = 4.57  10-3 m/s

=0.47 Фs =0.7

查表得 = 1.8 10-5 Pa s = 1.205kg/m3 设Re≤1

Lp= 3222)1(150psoDV

代入数据解得 Dp =6  10-6 m 校核 Re = vDeq= 7.6  10-6 < 1 符合题意。 1g 固体体积为V V= 1/固 = 2.44  10-7 m3

V

S

psD6

得S = 0.349 m2 8.2 查表得甲苯蒸汽压Pv= 111414 Pa

由公式NPSH = g1(vaPP'- hfs)- Za

其中= 866kg/m3 'aP= 1.1101325 Pa hfs = 7000/866 NPSH = 2.5m 代入算出Za = -3.32m 故容器中叶面应高于水泵3.32m 8.3 在第一个蒸馏器的再沸器液面上一点为a, 第二个单元出口处一点为b 由伯努利方程

η wp + aP + g Za + 22aav = bP + g Zb +

2

2bbv

+ hf

其中,av可忽略为0,设Za= 0'aP= 1.1101325 Pa bP = 101325 Pa Zb = 10m bv

= 2m/s hf = (35+7)

1000/ 866 a= b = 1

代入以上数据算出η wp = 136.8J/kg PB= m η wp= 10000/3600 136.8W = 380.1W

10.11 A表示钢管,B表示玻璃纤维,C表示空气 (a)kA=25.9×1.73073=44.8W·m/m2·℃ kB=0.019×1.73073=0.032 W·m/m2·℃

RA=WCmkBAA/1046.48.441020243

RB=WCmkBBB/56.1032.0105023 RC=WCm/05.0u12 令A=1m2 05.056.11046.4501504CBARRRTAq q =80.7W (b) RB’=WCmkBBB/12.3032.010100223

WRRRTAqCBA4105.012.31046.420150''4

Wqqq7.39417.80' 11.1 (a) D0=3/4in=19.0mm Di=0.620in=15.7mm XW=0.065in=1.65mm

mmDDDDDiOiOL31.177.1519ln7.1519ln

CmWhkXDDhDDUomWiOiiOO2/8.533611

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(b) D0=25mm Di=18mm XW=3.5mm mmDDDDDiOiOL3.211825ln1825ln CmWhkXDDhDDUomWiOiiOO2/2.1411

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CmWUi23/5.191200118253.21245105.3201

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