消力井、陡槽水力计算

,,陡槽水力计算———参考《中小型水库设计》中册,,,,,,

一已知条件,,,,,,,,

设计流量(m3/s),,Q=,60,"沟槽后接以渐变段,其底坡为",,,0.050,

沟槽内水深(m),,H=,1.5,"渐变段后为陡槽,首末端落差P=",,,12.000,

沟槽宽度(m),,B=,16,陡槽底坡为,,i=,0.125,

"混凝土衬砌,糙率",,n=,0.017,初选陡槽底宽(m)b=,,,8.000,

,,,,初选陡槽边坡系数m=,,,1.000,

,以下进行水面曲线计算:,,,,,,,

(一)渐变槽计算,,,,,,,,

1渐变槽长度,,,,,,,,

取渐变收缩角θ0=,,30,由公式L=B-b/2tgθ/2(m)求得L=,,,,15,

2渐变段的临界坡度ik及首端水深h1,,,,,,,,

单宽流量q=,,3.75,m3/s/m,临界水深hk=,,1.16,(m),

,其相应水力要素为,,,,,,,

,ωk=,18.62,,,χk=,18.33,,

,Rk=,1.016,,,Ck=,59.0,,

,ik=,0.0029,＜,0.050,故属陡坡，,则渐变段首端水深取,,

,,,,为临界水深，h1=hk=,,1.16,(m),

3渐变槽末端水深h2,,,,,,,,

,由公式Э1+iL=Э2+hf,,,,,,,

,首端断面能量Э1求之如下：,,,,,,,

,Э1=,1.746,,首末两端的落差为il=,,0.75,(m),

为求Э2和沿途损失能量hf，先假定h2=,,,,1.652,(m),末端断面为梯形则,,

,ω2=,15.945104,(m),,V2=,3.76,(m/s),

,Э2=,2.446,(m),,,,,

,χ2=,12.67,(m),,,,,

,计算两断面的平均水力要素如下：,,,,,,,

,ω=,17.28,,,C=,59.9,,

,χ=,15.50,沿途损失能量hf=,,,0.045,(m),

,R=,1.12,,,Э1+iL=,2.492,(m),

,V=,3.47,,,Э2+hf=,2.491,(m),

,因Э1+iL与Э2+hf很相近，说明假设的h2=,,,,1.652,米是合适的。,,

(二)陡槽计算,,,,,,,,

1求临界坡降,,,,,,,,

,由A=,0.231,查图14-19曲线得f(A)=,,0.928,故hk=,1.71,

,其相应水力要素为,,,,,,,

,Bk=,11.43,,,Ck=,61.4,,

,ωk=,16.66,,,ik=,0.0027,,

,χk=,12.85,陡槽底坡I=,0.125,＞ik，属于陡坡。水面线为bⅡ型,,,

,Rk=,1.296,,降水曲线。,,,,

2陡槽长度,,,,,,,,

Ls=,96.75,≈,97,米,,,,

3陡槽水深及水面曲线的绘制,,,,,,,,

假设h0=,0.543,则相应的水力要素为：,,,,,,

,ω0=,4.64,,,C0=,52.2,,

,χ0=,9.54,,,Q0=,60,(m3/s),

,R0=,0.486,求出的Q0与实际流量相等，说明假设的h0合适。,,,,,

因陡槽前的渐变槽亦为陡坡，故陡槽首端断面水深hH取为渐变槽末端断面水深，即,,,,,,,,

hH=,1.652,米。假设陡槽末端断面水深接近于正常水深h，故可求出全陡槽,,,,,,

的平均水力要素，即：,,,,,,,,

,h=,1.10,米,,C=,57.8,,

,B=,10.20,米。陡槽段的平均动能变化值j=,,,43.0,,

,ω=,9.98,相应于平均水深的流量模数K=,,,547,,

,χ=,11.10,相应于正常水深的流量模数K0=,,,169,,

,R=,0.899,故水力指数X=,,,3.34,,

假设若干水深，按公式（14-2）计算相应于这些水深的各断面之间的距离L：,,,,,,,,

,L=h0/I｛η2-η1-(1-j)〔φ(η2)-φ(η1)〕｝,,,,,,,

h1(m),h2(m),η1,η2,φ(η1),φ(η2),iL/h0,L(m),∑L(m)

1.60,1.200,2.95,2.21,0.035,0.070,0.73,3.16,3.16

1.20,0.900,2.21,1.66,0.070,0.143,2.51,10.91,14.08

0.90,0.700,1.66,1.29,0.143,0.295,6.02,26.17,40.25

0.70,0.585,1.29,1.08,0.295,0.616,13.26,57.62,97.86

,,"计算结果与陡槽长度L=97米很相近,故陡槽末端水深为0.585米。",,,,,,

4陡槽流速及掺气水深,,,,,,,,

,,,水面曲线计算成果表,,,,,

断面,,水深,过水断面积,,流速,掺气高度,掺气水深,断面距离

编号,,h(m),ω(m2),,V(m/s),hB(m),h+hB(m),∑L(m)

1,,1.600,15.36,,3.91,0.063,1.663,0.00

2,,1.200,11.04,,5.43,0.065,1.265,3.16

3,,0.900,8.01,,7.49,0.067,0.967,14.08

4,,0.700,6.09,,9.85,0.069,0.769,40.25

5,,0.585,5.02,,11.95,0.070,0.655,97.86

,当陡槽中流速大于允许不冲流速时陡槽应采取以下措施：,,,,,,,

（1）采用较高的混凝土衬砌；,,,,,,,,

（2）减缓陡槽坡度；,,,,,,,,

（3）当流量较小时，可采用人工加糙的措施。,,,,,,,,

(三)消能计算,,,,,,,,

1求第一共轭水深h、和第二共轭水深h＂,,,,,,,,

,取陡槽末端水深为第一共轭水深h、=,,,,0.585,则ξ、=h、/hk=,,0.34

,由公式计算出第二共轭水深,,,h＂=,3.78,h＂/hk=,2.21,≤5故适用

,当h＂＞hb(为下游渠道水深)说明在陡槽末端不会立即产生水跃，需要设置消力池。,,,,,,,

2消力池深度d的计算,,,,,,,,

,下游渠道水深(m)hb=,,,2.00,,,,

,消力池深度(m),,d=σh＂-hb=,2.16,,,,

3消力池长度Lk的计算,,,,,,,,

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因陡槽末端与消力池连接，故可取消力池长度等于水跃长度。,,,,,,,,

,水跃长度的计算：,,,,,,,

,对于梯形断面渠床，单宽流量可按渠底及水面的平均宽度计算，即,,,,,,,

,q=Q/b+mh=,,,,,,,

,B1、B2为水跃前后两断面的水面宽度。,,,,,,,

,,B1=b+2mh、=,,9.17,,,,

,,B2=b+2mh＂=,,15.57,,,,

,水跃长度Ln=5h＂(1+4((B2-B1)/B1)^0.5)=,,,,82.11,米,,

,,故消力池长度取为Lk=,,,82,米