水力学与桥涵水文课后习题答案.docx

'.水力学与桥涵水文课后习题答案Word文档.第一章习题1.1解：水温为30度时水的密度3995.79(kg/m)Word文档.质量M重力Gv995.7*0.001Mg0.9957*9.80.9957(kg)9.75786NWord文档.Word文档.1.2解：密度重度M6795/0.5vg13590*9.813590(kg/m3)133182(kN/m3)Word文档.1.3解：4℃时水的密度为1000(kg/m3)100℃时水的密度为958.4(kg/m3)假定1000kg的水Word文档.v(4)1000/100031(m)Word文档.v(100)1000/958.41.0434(m3)Word文档.则体积增加百分比为dvv1.043411*100%4.34%Word文档.1.4解：压缩系数v0.00155.102*1010(m2/N)Word文档.dp(5*980001*98000)Word文档.弹性系数K11.96*109(N/m2)Word文档.1.5解：运动粘滞系数为动力粘滞系数与密度的比值9.71(kN/m3)Word文档.0.599*103(Pa*s)Word文档.*g0.000599*9.89.71*1000g0.605*106(m2/s)Word文档.Word文档.1-8解：剪切力不是均匀分布dA2rdr，durdyWord文档.Word文档.dT*2r*drr*r2r3drWord文档.Word文档.d22r32Tdr0r4dd442320Word文档 .4积分后得Td32Word文档.1.9解：D12cm，d11.96cm，l14cm，0.172Pa*s，v1m/sWord文档.Word文档.接触面面积A2(d)l23.1415*11.96*102*14*1020.0526m2作Word文档.用力FAdvdyAv0.0526*0.172*y(121211.96)/2*1045.2NWord文档.第二章习题2-2解：玻璃管的自由表面为等压面，液体的质量力包括重力、一个虚构的方向向左的Word文档.惯性力，所以单位质量力的三个分量为：Xa,Y0,Zg，带入液体平衡微分Word文档.方程有：dp(adxgdz)积分得：p(axgz)CWord文档.当x30,z0时pp0，当z5,x0时pp0，从而有30a5g，得Word文档.Word文档.a9.8/61.63m/s2Word文档.Word文档.2-3解：1-1面为等压面，并且大气相通，相对压强为0，有p0h0所以得Word文档.Word文档.h44.59.84.54(m)Word文档.水下0.3m处相对压强pp00.344.50.3*9.841.56(KPa)Word文档.绝对压强pppa41.569856.44(KPa)Word文档.真空度pvPap9856.4441.56(KPa)4.24(m)Word文档 .Word文档.测压管水头zp0.341.569.84.54(m)Word文档.2-4解：2点与大气连通，相对压强p20Word文档.p1(h1h2)*p20，Word文档.Word文档.所以p1(h1h2)*(1.150.68)*9.84.606KPaWord文档.Word文档.p2(h2h3)*p3，Word文档.Word文档.所以p30(h2h3)*(0.680.44)*9.82.352KPaWord文档.3点和4点压强相等，所以有p4p32.352KPa2-8解：设水的作用力为P1，作用点距C点的斜长为e1设油的作用力为P2，作用点距B点的斜长为e2根据已知条件有：Word文档.1P1*21*h1*2*131*8*2234.62KNWord文档.Word文档.2P1(21*h1(1*h12*h2))*4*1341.107KNWord文档.Word文档.e11AC31*2330.385Word文档.Word文档.e21*h2*(21h11h12h2)1*4(2*8*1*8*19.8*2)0.943合力Word文档.331h121h11h2338*18*19.8*2Word文档 .Word文档.PP1P24.6241.10745.727KNWord文档.P1,P2对B点求距之和与合力P对B点求距相等，因而有Word文档.P1*(h2sin60e1)P2*e2P*eWord文档.得e1.12(m)算法二：压强分布图分三部分，两个三角形，一个矩形Word文档.P111h1*2e1h11h1*1sin601*21*8*1*2230.3854.62(KN)Word文档.3sin6033Word文档.Ph1222*2h2*1sin601*9.8*2*42322.632(KN)Word文档.Word文档.e1h221*40.77Word文档.3sin6033Word文档.P31h1*h2*1sin608*1*23218.475(KN)Word文档.Word文档.e1h23141.155Word文档.2sin6023Word文档.PP1P2P34.6222.63218.47545.727(KN)Word文档.Word文档.P(eh2)PePePeWord文档.11sin602233Word文档.得e1.12(m)Word文档.2-8解：设左边静水总压力为P1，作用点距水闸底距离（斜长）为e1，Word文档.右边静水总压力为P2，作用点距水闸底距离（斜长）为e2，Word文档.1p1*2*9.8*22227.72(KN)，e11*2230.94(m)Word文档.2p1*0.6*9.8*0.6222.49(KN)，e21*0.6230.28(m)Word文档 .由题意知，当p1，p2对o点力矩相等时，闸门将会自动打开，所以有Word文档.p1*(xe1)p2*(xe2)Word文档.Word文档.则，xp1*e1p1p2*e2p227.72*0.9427.722.49*0.282.491.008(m)Word文档.2-10解：此题只可采用解析法求解Word文档.12面积AD412*3.1415*1420.785(m)Word文档.PhcA9.8*3*0.78523.09(KN)Word文档.Word文档.Ic1r441*3.1415*0.5440.049Word文档.Word文档.ych3233.46432Word文档.Word文档.oD(yDyc)rycIcycAycr0.0493.464*0.7850.50.518Word文档.P和F对o点力矩相等时，F即为所求1Word文档.F*D2P*oDWord文档.所以F2-11解：oD*P*20.518*23.09*223.9(KN)Word文档.Word文档.Px1hc1*Ax19.8*2*4*10784(KN)（方向向右）Word文档.Word文档.Px2*hc2*Ax29.8*1*2*10196(KN)（方向向左）Word文档.Word文档.所以Px784196588(KN)（方向向右）Word文档 ..PzV9.8*3*4*22*10923(KN)（方向向上）（V为3圆柱）4.所以P角度22PxPzPzarctanPx588257.592321094(KN).2-12解：由题意画压力体图得知压力体为一个圆柱减一个半球（作用力方向向上）.PV9.8*(r2H1*4**r3)9.8*(3.1415*12*31*4*13)71.8(KN).23232-13Word文档 .2-14Word文档 .Word文档 .Word文档 .Word文档 .Word文档 .Word文档 .Word文档 .Word文档 .第三章习题内容简单回顾：水力学三大方程1.连续方程：总流各断面所通过的流量是相同的，（对理想液体和实际液体的各种流Word文档.2动状态都适用）表达式为：Q1Q2，或者v1A1v2A2Word文档.Word文档.p11.能量方程：z11v1p22z22g2v2h2gWord文档.zp表示过水断面上单位重量液体具有的势能；v2表示过水断面上单位重量液体具有的平均动能；2gh表示在1、2两过水断面之间单位重量液体的平均水头损失。注意“能量方程的适用条件及注意事项”Word文档.同一断面上任何点的zp值相等，具体选择那一点，以计算方便为宜。习题3.9Word文档.Word文档.2.动量方程：FQ(2v21v1)Word文档 .进行代数运算时，分解为三个方向的标量方程式注意应用注意事项：外力包含液体重量；流出动量减去流入动量，不可颠倒；F,v都是矢量，所以必须先明确坐标轴的正向；求出闸门对水流的作用力R后，那么，“水流对闸门的作用力与R大小相等，方向相反”，这句话不可省略，需要说明。Word文档.3-1解：QvA1d2v4Word文档.所以有2.04得d1m1*3.1415*d2*2.64Word文档.Word文档.3-4解：当管道和差压计中均为水时有u2ghWord文档.当管道中为水差压计中为水银时有Word文档.水银水u2g水h＝2g*12.6h2*9.8*12.6*0.063.85m/sWord文档.当管道中为油，差压计中为水银时有Word文档.水银油u2gh2*9.8*133.280.8*9.8*0.064.34(m/s)Word文档.油0.8*9.83-5解：（1）1-1和2-2断面列连续方程Word文档.v1d22vAvA，()，得v4(m/s)Word文档.11221v2d1假设水流从1到2，1-1和2-2断面列能量方程Word文档.z2p1v11p2v2z22h12Word文档.2g68.61602g30.211h12Word文档.9.82*9.8得h123.684m9.82*9.8Word文档.h12>0，所以假设成立，水流从1流到23-6解：（1）列连续方程Word文档 .Word文档.v1vAvA，1，v1.8vWord文档.112221v21.8Word文档.（2）列能量方程z2z2p1v1p2v2122g2g221.80v11.50v22g2g得v11.62(m/s)Word文档.PAv1.8*1*1.622.916(m3/s)Word文档.113-6解：（1）列连续方程Word文档.v1A2v2A10.0010.0021，得v222v1Word文档.（2）列能量方程水平放置文丘里流量计，z1z20Word文档.z2p1v11p2v2z22hWord文档.2222g2g01.0v100.44v10.05v12g2g2g得v11.96(m/s)Word文档.11QAv0.002*1.960.00392(m3/s)3.92(l/s)Word文档.3-7解：列能量方程Word文档.2zp1v112zp2v22hWord文档.2g2gWord文档.250000v220.8v2Word文档.2g2g得v27.4(m/s)Word文档 .Word文档.Qv2A21d2v41*3.1415*0.12*7.440.058(m3/s)Word文档.23-6解：A-C断面列能量方程Word文档.z2pAvAAzCpCvChWord文档.22g2g230000vc12g得vc6.26(m/s)Word文档.QvcA1d2v4Word文档.c得d0.075(m)7.5(cm)B-C断面列能量方程Word文档.z2pBvBBzCpCvChWord文档.22g2gWord文档.26pBvB00vc0.5Word文档.22g2g管道直径相同，有vBvC得pB53.9(KPa)3-10解：自由表面与B断面列能量方程Word文档.pv2zz22gp2v222gWord文档.Word文档.700200v2Word文档.2g得v211.7(m/s)Word文档.Qv2A21(0.06)2*11.740.033(m3/s)33.1(l/s)Word文档.v1(d2)2v2d10.36Word文档.v10.36v24.22(m/s)Word文档 .自由表面与A断面列能量方程Word文档.pv2zz12g2p1v12gWord文档.23000pAv12g得pA20.5(KPa)3-10解：根据连续方程Word文档.v1A2v2A1H25，得v2H162.4(m/s)Word文档.QvA2*6*224(m3/s)Word文档.111H2B1*9.8*62*21212HB1*9.28*5222P12352.8(KN)Word文档.P2*2245(KN)设闸墩对水流的作用力为R(方向向左)列动量方程Word文档.P1P2RQ(2v21v1)Word文档.352.8245R1*24*(2.42)Word文档.得R98.2(KN)那么水流对闸墩的作用力R98.2(KN)（方向向右）3-11解：Word文档.AD1121*3.1415*0.2244Ad2121*3.1415*0.052440.031(m2)0.00196(m2)Word文档.vQ0.11A10.031vQ0.123.183(m/s)50.931(m/s)Word文档.A20.00196Word文档 .列能量方程Word文档.2zp1v112zp2v22Word文档.2g2gWord文档.0p13.18322*9.850.9312002*9.8Word文档.Word文档.得p11291.92(KN/m2)Word文档.Word文档.则压力P1p1*A11291.92*0.03140.586(KN)Word文档.列动量方程Word文档.P1P2RQ(v2v1)Word文档.Word文档.40.5860R1*0.1*(50.9313.183)Word文档.得R35.81(KN)（方向向左）Word文档.则每个螺栓受到的拉力RR35.81448.953(KN)（方向向右）Word文档.HB123-13解：P1121*9.8*1.52*1.2213.23(KN)Word文档.12P2H2B212*9.8*0.92*1.24.763(KN)Word文档.v1H20.9，v0.6vWord文档.v2H11.512Word文档.列能量方程z2z2p1v1p2v2122g2gWord文档.221.50v10.900.36v1Word文档.2g2gWord文档.得v12.572(m/s)，v24.287(m/s)Word文档.Word文档.QvA2.572*1.5*1.24.63(m3/s)Word文档.11列动量方程Word文档.P1P2RQ(v2v1)Word文档 .Word文档.13.234.763R1*4.63*(4.2872.572)Word文档.得R0.529(KN)（方向向左）则R0.529(KN)（方向向右）3-14解：Word文档.Ad11121*3.1415*0.22440.0314(m2)Word文档.Ad22121*3.1415*0.12440.00785(m2)Word文档.2v2(d1)2，vv1d210(m/s)，得v12.5(m/s)，Word文档.Word文档.QvA2.5*0.03140.0785(m3/s)Word文档.11列能量方程Word文档.2zp1v112zp2v22hWord文档.2g2gWord文档.0p12.522*9.80.201022*9.80.5*1022*9.8Word文档.Word文档.得p173.835(KN/m2)Word文档.Word文档.则P1p1A173.835*0.03142.319(KN)Word文档.列动量方程Word文档.P1RxQ(v2cos45v1)Word文档.Word文档.Rx2.3191*0.0785*(10*222.5)1.96(KN)（向左）Word文档.RyGQ(v2sin450)Word文档.Ry201*0.0785*10*2220.55(KN)（向上）Word文档.则Fx1.96(KN)（向右）Fy20.55(KN)（向下）Word文档 .Word文档.所以F22FxFy1.96220.55220.65(KN)Word文档.Word文档.FyarctanFxarctan20.551.9684.6Word文档.如果G＝20Kg时RyGQ(v2sin450)Word文档.Ry20*9.8/100021*0.0785*10*20.75(KN)（向上）Word文档.Fy0.75(KN)（向下）Word文档.所以F22FxFy1.9620.7522.1(KN)Word文档.Word文档.Fyarctanarctan0.7520.1Word文档.Fx1.96第四章习题内容简单回顾：1.湿周、水力半径R概念及计算湿周：断面上液体与固体边界所接触的周线长，水力半径R：过水断面面积A与湿周的比值，即RA以梯形为例：梯形底宽b，高h，底坡m，面积A(bmh)h，Word文档.湿周b水力半径R2h1m2AWord文档.1.满宁公式、谢才公式121Word文档.C1R6，Qn1AR3i2nWord文档 .1.沿程水头损失计算Word文档.计算公式：hflv2Word文档.4R2gWord文档.对于圆管，R1r1d，hflv2Word文档.24d2g2.局部水头损失计算产生局部水头损失的情况有：（1）流动断面改变；（2）流动方向改变；（3）流道中有障碍物（如闸、阀、栅、网等）；（4）流动中有流量的汇入或分出。v2计算公式：hj2gWord文档.一般需要记住进口水头损失系数的0.5，出口的水头损失系数1.0Word文档.4-1解：雷诺数Revd，随管径的加大，雷诺数会减小Word文档.A1d2，vQ4A4Q2，Redvd4Qd，所以随管径增加，雷诺数会减小。Word文档.4-2解：沿程水头损失hflv2，64，RevdWord文档.（1）油d2g水，当流速v相等时，ReRe油Re水，油水，所以hf油hf水Word文档.Word文档.（2）如果两管中的雷诺数相等，则v油v水，所以hf油hf水Word文档.4-3解：水温为10℃时，运动粘滞系数1.306*106Word文档.Revd1*0.11.306*106v*0.176569.7>2300,流动为紊流Word文档.23001.306*1026，则临界流速vz220.03(m/s)Word文档.4-12解：z1p1v12gp2v2h2gWord文档.Word文档.10000020.03*25v(0.52*(0.1310.163*13.5)2.0621)vWord文档.0.0252g2g2得v0.574，流速v0.758(m/s)Word文档 .Word文档.流量Q1d2v41*3.1415*0.0252*0.75840.372(l/s)Word文档.4-12解：hf121.51.25lv21*9，得0.027Word文档.d2g0.052*9.8Word文档.Word文档.h231.250.4lv2v22323220.027**Word文档.d2g2g0.052*9.82*9.8Word文档.得0.762Word文档.或者hf121.51.250.25(m)Word文档.l232l12，那么hf232hf120.5(m)Word文档.0.850.5322*9.8Word文档.得0.7624-14解：1-1和2-2列能量方程Word文档.HP11H2hfhjWord文档.1196.29.85(0.025*100.0250.54.03*0.31)v22gWord文档.得流速v流量Q4.376(m/s)12*3.1415*0.0254*4.3762.15(l/s)Word文档.4-15解：列能量方程Word文档.2200000(l1l2l3)v(102*1.521.0)vWord文档.d2g2g得v1.587(m/s)Word文档.流量Q1d2v41*3.1415*0.22*1.587449.8(l/s)Word文档.解第二个弯头处压强最低Word文档.列能量方程000hpv22g(l1l2)v2d2g(101.5)v22gWord文档 .得p2.74(m水柱)26.85(KPa)4-15解：列能量方程Word文档.10z3(6)vlv2(90.3)vWord文档.222gd12g2g得v1.52(m/s)Word文档.12Qdv412*3.1415*0.154*1.5230.027(m/s)Word文档.蓄水池自由表面与吸水井自由表面列能量方程Word文档.z00000hfhjWord文档.Word文档.lv2zv2(2.01)20(0.03*3.0)1.5220.825(m)Word文档.d2g2g0.152*9.8Word文档.第五章习题内容简单回顾：1.底坡i：单位长度渠底高程减小值Word文档.iz1z2LsinWord文档.顺坡，i0底坡平坡，i0逆坡，i01.水力最佳断面：在底坡i、糙率n和过水断面面积A一定的条件下，能使渠道的输水能力最大的断面形状称为水力最佳断面。工程中最常用的是梯形断面形状，经推导梯形断面水力最佳断面的宽深比Word文档.b2(1hm2m)，水力最佳断面的宽深比仅是m的函数，当m0时，断面为矩Word文档.形，此时2，说明矩形水力最佳断面底宽b为水深h的2倍。1.梯形断面渠道水力计算Word文档 .(1)已知K,i求Q,QKi(2)已知b,h,m,n,Q或者v求i(3)已知Q,i,n,m求b和h（2）种情况，已知b,h,m,n,Q可求得面积A(bmh)hWord文档.湿周b水力半径R2h1m2AWord文档.521211A31Word文档.QAR3i2ni2，一个未知数i，即可求得in3Word文档.（3）种情况两个未知数，一般要加附加条件，下面按附加条件为“水力最佳断面”Word文档.来讲水力最佳断面宽深比b2(1hm2m)，bh建立b,h关系，然后Word文档.面积A(bmh)hWord文档.湿周b水力半径R2h1m2AWord文档.55105Q1n21AR3i21nA3231i21n((m)3h32221m2)3h31i21n1i2((2m)321m2)38h3Word文档.h(Qn(2821m2)3351)Word文档.(m)3i22.水面线的定性分析NN正常水深线；Word文档 .KK临界水深线；Word文档.NN与KK线一般不重合，在临界坡时NN与KK线重合Word文档.Word文档.a位于NN与KK之上；Word文档.Word文档.b介于NN与KK之间；Word文档.Word文档.c－－位于NN与KK之下。Word文档.Word文档.下标1――i0,iik，缓坡；Word文档.Word文档.下标2――i0,iik，急坡；Word文档.Word文档.下标3――i0,iik，临界坡；Word文档.下标0――i0，平坡；上标――i<0,逆坡。Word文档.顺坡,i缓坡，iik0急坡，iik临界坡,iikWord文档.底坡按i跟0的比较关系可以分为平坡,i0逆坡,i0Word文档.Word文档.Q5-4解：Av2.280.6523.508(m)Word文档.A(bmh)hWord文档.2h2.5h3.5080Word文档.解得h1.0(m)Word文档.2h1m2b2*1*1122.55.328(m)Word文档.Word文档.A(bmh)h(2.51.0*1.0)*1.03.5(m2)Word文档.512111*A3i2QAR3i2n2n3Word文档 .Word文档.解得i=0.373‰5-6解：宽深比bh2(112mm)Word文档.矩形时m0，，b8,h42Word文档.面积Abh8*432(m2)Word文档.Word文档.湿周b2h82*416(m)Word文档.Word文档.水力半径RA32162(m)Word文档.2121Word文档.流量QA1R3i2n32*10.028*23*0.00025228.68(m3/s)Word文档.5-7解：宽深比b2(1hm2m)Word文档.m1.0，b0.828hWord文档.根据下列公式：Word文档.A(bmh)h,b2h12m,RA,Q21A1R3i2nWord文档.Word文档.22/31/23h(m)x(m)A(m)RRiiQ(m/s)Word文档.1.0003.656431.828000.499940.629910.00040.021.151480.9803.583301.755610.489940.621480.00040.021.091080.9603.510171.684680.479940.613000.00040.021.032710.9553.491891.667180.477440.610870.00040.021.018430.9453.455321.632450.472440.606600.00040.020.990240.9503.473611.649770.474940.608740.00040.021.00427Word文档.根据试算得h0.95(m),b0.787(m)Word文档.Word文档.5-8解：n0.03,m1.0,b2.0(m),h1.2(m),i0.0008Word文档.Word文档.面积A(mhb)h(1*1.22)*1.23.84(m2)Word文档 .Word文档.湿周b2h1m222*1.2115.39(m)Word文档.Word文档.水力半径RA3.845.390.71(m)Word文档.2121Word文档.流速v1R3i2n10.03*0.713*0.000820.75(m/s)Word文档.Word文档.流量QAv3.84*0.752.88(m3/s)Word文档.Word文档.5-7解：Q3.0(m3/s),i0.0022,m1.0,n0.03,vmax0.8(m/s)Word文档.Word文档.AQvmax3.00.83.75(m2)Word文档.Word文档.根据v211A3i2Word文档.n23解得10.245Word文档.A(bmh)hbhh23.75Word文档.2b2h1mb2.828h10.245Word文档.联立求解，得h0.394(m),b9.132(m)Word文档.5-8解：Q23(m3/s),h1.5(m),b10(m),m1.5(m),i0.0005Word文档.A(bmh)h(101.5*1.5)*1.518.375(m2)Word文档.b2h1m2102*1.5*11.5215.408(m)Word文档.A18.375R15.408Q23vA18.3751.193(m)1.252(m/s)Word文档.21v1R3i2n2121Word文档.R3i2nv1.1933*0.000521.2520.02Word文档 .5-12解：按水力最佳断面，Word文档.水深h，面积Abh，湿周b2h，水力半径RAbhb2hWord文档.Word文档.流量Q21A1R3i2nWord文档.hARQ1.000460.6666666675.3868905531.1004.46.20.7096774196.1777785221.2004.86.40.756.9923165271.3005.26.60.7878787887.8279603231.4005.66.80.8235294128.6825328791.3405.366.680.802395218.1676291011.3205.286.640.7951807237.997424546经试算求得正常水深h1.32(m)Word文档.所以A湿周bh4*1.3242*1.325.28(m2)6.64(m)Word文档.Word文档.水力半径RA5.286.640.795(m)Word文档.Word文档.临界水深hkQ232gBk38*89.8*4*40.74(m)1.32(m),所以水流为缓流Word文档.Word文档.Akbhk4*0.742.96(m2)Word文档.Word文档.kb2hk42*0.745.48(m)Word文档.Word文档.RAk2.96kk5.480.54(m)Word文档 .1Ck1n1R60.5460.017Q253.1临界底坡ikAkCkRk228*82.96*2.96*53.1*53.1*0.540.00480.0009,所以水流为缓流佛汝德数FrQ2gA38*89.8*5.28430.1771，所以水流为缓流B微波流速Cgh9.8*1.323.597(m/s)Q流速vA85.281.515vC，所以水流为缓流5-18KNKNa3iN1>ikc3KNKi2=iki3ikNKi20i2<0Word文档 .KNNWord文档.Kb1Ni1NKNb2Word文档.Ki2Ni3第七章习题Word文档.7-11解：已知流域面积F468000(km2)，多年平均流量Q6300(m3/s)，多年平均降Word文档.（m0）雨量X0990(mm)。Word文档.多年平均年径流总量W0Q0T6300*365*24*36001.9868*10113Word文档.Word文档.年径流深y0W1000F1.98*10111000*468000424.52(mm)Word文档.Word文档.x0年径流系数0y0424.529900.429Word文档.Word文档.年径流模数M01000Q0F1000*630046800013.46(l/km2s)Word文档.Word文档.7-12解：ih1h0lWord文档.Word文档.全河流平均比降iWord文档 .(h0h1)l1(h1h2)l2L2(hn1hn)ln2h0LWord文档 .关于平均比降的推导：根据各梯形面积之和与整个梯形面积相等Word文档.01(h2h1)l11(h12h2)l21(hn12hn)ln1(h02h)LWord文档.ihh0，那么hiLLh0，代入上式得Word文档.Word文档.(h0h1)l1(h1h2)l2(hn1hn)ln2h0LiL2Word文档.Word文档.所以得i(h0h1)l1(h1h2)l2L2(hn1hn)ln2h0LWord文档.特征点ABCDEF河口河底高程(m)2411411069176665651起点距(km)01025436590120140i1i2i3i4i5i6i70.010.002330.000830.000680.00040.000330.00025千分之i102.333330.833330.681820.40.333330.25(h0+h1)l1(h1+h2)l2(h2+h3)l3(h3+h4)l4(h4+h5)l5(h5+h6)l6(h6+h7)l7382000037050003546000367400035500003660000214000024095000平均比降i0.00050077平均水深86.0535714第九章习题9.11Word文档.2序号年份流量x-xi(x-xi)(x-xi)3流量（大-p小）Word文档.119752270625.7391500.524496185730250.045455219761750105.711172.491180932.228050.09090931977480-1164.31355594-1.578E+0925700.13636441978720-924.3854330.5-78965767222700.18181851979840-804.3646898.5-52030045619600.227273Word文档 .6198028051160.713472241.564E+0918400.272727719811960315.799666.493146471117500.318182819821840195.738298.497495014.517100.363636919831460-184.333966.49-6260024.116800.4090911019841550-94.38892.49-838561.8116000.4545451119852570925.7856920.579325129815800.5121986171065.74316.49283593.3915500.5454551319871600-44.31962.49-86938.30715100.5909091419881490-154.323808.49-367365014900.6363641519891280-364.3132714.5-4834788914600.6818181619901510-134.318036.49-2422300.613100.72727317199130251380.719063322.632E+0912800.7727271819921100-544.3296262.5-16125567311000.8181821919931310-334.3111756.5-373601958400.863636201994168035.71274.4945499.2937200.9090912119951580-64.34134.49-265847.714800.954545均值1644.2981450642.126E+09均方差638.1639Cv0.38811Cs0.4543923?(p=1)2.65Word文档 .Qp3335.4cs?(p=1)0.42.620.52.680.452.659.12根据A与B站的11对同期观测资料建立A与B直线方程，（以B为y，以A为x）Word文档.y0.7407x2.5634，根据方程延长B站资料Word文档.年份1982A127B1301985198136198615454198744321989242619902721199118418219923018199354461994715619959876Word文档 .Word文档.B200180160140120100806040200y=0.7407x+2.5634R2=0.7611050100150200250Word文档.B与A直线相关A延长后数据年份AB197912292.928819805442.56121981109.9704198212713019833629.228619846752.190319851981361986154541987443219886953.671719892426199027211991184182Word文档 .19923018199354461994715619959876nWord文档.也可以按yy(xii1nx)(yiy)(xix)Word文档.(xii1x)2Word文档.序号1y130x127y-yi59.4x-xi35.12(y-yi)3528.362(x-xi)1232.01（y-yi）（x-xi）2084.94213619865.4106.14277.1611257.216938.94354154-16.662.1275.563856.41-1030.8643244-38.6-47.91489.962294.411848.9452624-44.6-67.91989.164610.413028.3462127-49.6-64.92460.164212.013219.047182184111.492.112409.968482.4110259.9481830-52.6-61.92766.763831.613255.9494654-24.6-37.9605.161436.41932.34105671-14.6-20.9213.16436.81305.141176985.46.129.1637.2132.94均值和70.636491.90930044.5641686.9130875.64相关系数r0.87244Word文档 .a0.74066b2.56339y=0.7407x+2.5634求得线性方程，即可延长数据。第十一章习题11.7数据与9.11相同序号1年份1975流量2270x-xi625.7(x-xi)2391500.5流量（大-小）3025频率p0.045455219761750105.711172.4928050.09090931977480-1164.3135559425700.13636441978720-924.3854330.522700.18181851979840-804.3646898.519600.2272736198028051160.7134722418400.272727719811960315.799666.4917500.318182819821840195.738298.4917100.363636919831460-184.333966.4916800.4090911019841550-94.38892.4916000.4545451119852570925.7856920.515800.5121986171065.74316.4915500.5454551319871600-44.31962.4915100.590909Word文档 .Cv0.388111419881490-154.323808.4914900.6363641519891280-364.3132714.514600.6818181619901510-134.318036.4913100.72727317199130251380.7190633212800.7727271819921100-544.3296262.511000.8181821919931310-334.3111756.58400.863636201994168035.71274.497200.9090912119951580-64.34134.494800.954545均值1644.2868145064均方差638.1639Word文档 .第一次适线Word文档.x1650,Cv0.4,Cs2CvWord文档 .第一次适线Word文档 .Word文档.x1650,Cv0.4,Cs2.5CvWord文档 .第三次适线Word文档.x1650,Cv0.4,Cs3CvWord文档.最终选用第三次适线结果Word文档.x1650,Cv0.2,Cs3Cv，Qp(p1%)Kp*Q1650*2.263729(m3/s)Word文档 .11.8Word文档.由题意可知N19951925171，特大洪水项数a4，实测系列中特大洪水项Word文档.数l2，实测系列从1964年开始，但是是个不连续系列，因而实测期为实测数据实有项数，本题目实测期n27N71,a4,l2,n27序号年份流量（大-小）序号PM=M/(N+1)（m-l）/(n-l+1)Pm=PMa+(1-PMa)((m-l)/(n-l+1))频率1192583010.01391.38892195475620.02782.77783196472030.04174.16674196570040.05565.55565196965030.03850.09199.18806197064540.07690.128212.82057197163550.11540.164516.45308197263060.15380.200920.08559197362670.19230.237223.717910197461880.23080.273527.350411197561690.26920.309830.9829121977610100.30770.346234.6154Word文档 .131978600110.34620.382538.2479141979580120.38460.418841.8803151980572130.42310.455145.5128161982568140.46150.491549.1453171983530150.50000.527852.7778181984522160.53850.564156.4103191985500170.57690.600460.0427201986492180.61540.636863.6752211987483190.65380.673167.3077221988480200.69230.709470.9402231989470210.73080.745774.5726241990450220.76920.782178.2051251991440230.80770.818481.8376261992420240.84620.854785.4701271993405250.88460.891089.1026281994382260.92310.927492.7350291995370270.96150.963796.3675Word文档.4j均值1[Q71427Qi]1(3006714*13294)544.14(m3/s)Word文档.Nj1272i2171272Word文档 .序号1流量830xi-x285.9(xi-x)281738.812756211.944901.613720175.930940.814700155.924304.811818865650105.911214.816645100.910180.81763590.98262.81863085.97378.81962681.96707.611061873.95461.211161671.95169.611261065.94342.811360055.93124.811458035.91288.811557227.9778.411656823.9571.2117530-14.1198.8118522-22.1488.4119500-44.11944.8120492-52.12714.4121483-61.13733.21Word文档 .22480-64.14108.8123470-74.15490.8124450-94.18854.8125440-104.110836.8126420-124.115400.8127405-139.119348.8128382-162.126276.4129370-174.130310.81194189.5Word文档.Cv114[(QjQ)2Na27(QiQ)2]Word文档.QN1j1nli3Word文档.15440.1841(1818867067*194489.5)25Word文档.经适线Word文档 .Word文档.选定Q540,Cv0.2,Cs3Cv，作为最终结果Word文档.Word文档.那么Qp(p1%)Kp*Q1.55*540837(m3/s)Word文档 .Word文档'