第九章渗流

1、1 Fluid Mechanics23Chapter 9 Seepage Flow9-1 Introduction92 Section 1 Basic law of seepage flow9-3 Uniform and non-uniform flow of groundwater9-4 Well and catchment passage4第九章第九章 渗渗 流流9-1 引引 言言92 渗流基本定律渗流基本定律 9-3 地下水均匀流和非均匀流地下水均匀流和非均匀流9-4 井和集水廊道井和集水廊道5Chapter 9 Chapter 9 Seepage Flow Flow Seepage f

2、low occurs during fluid flows through porous medium ,Mechanics of seepage flow is the study of fluids movement law in porous media. It is one of offsets of Mechanics of fluids, a subject developed by mechanics of fluids, medium theory, physics and chemistry, biology. Seepage phenomenon is common in

3、nature and artificial materials. Such as seepage of groundwater, hot water and brine ;seepage of oil, natural gas and coal seam gas;seepage of blood micro-circulation and micro-bronchia in animals; transportation of water,gas and sugar in plant; seepage of pottery, tile and so on artificial porous m

4、aterials.9-1 9-1 Introduction6第九章第九章 渗渗 流流 渗流是流体通过多孔介质的流动，渗流力学就是研究流体在多孔介质中运动规律的科学。渗流力学是流体力学的一个分支，是流体力学与介质理论、表面物理、物理化学以及生物学交叉渗透而发展起来的一门边缘学科。 渗流现象普遍存在于自然界和人造材料中。如地下水、热水和盐水的渗流；石油、天然气和煤层气的渗流；动物体内的血液微循环和微细支气管的渗流；植物体内水分、气体和糖分的输送；陶瓷、砖石、砂模、填充床等人造多孔材料中的渗流等。9-1 9-1 引引 言言7 Mechanics of seepage is widely applie

5、d in application science and project technology.Such as mechanics of soil,subterranean hydrology ,oil engineering, terrestrial heat engineering and micro-mechanism and so on. Furthermore, it is also involved in national defense industry,such as study of gas mask . Characteristic of seepage flow:firs

6、t, the area of unit volume space is very large in porous medium, surface action is distinct, viscous action is considered to any body and anytime ; second, the pressure is large in subterranean seepage flow, so,the compressibility is usual considered; third, the complexity of hole,large resistance,

7、capillary effect and force of molecular ; fourth, complicated process of physics and chemistry 。8 渗流力学在很多应用科学和工程技术领域有着广泛的应用。如土壤力学、地下水文学、石油工程、地热工程、给水工程、环境工程、化工和微机械等等。此外，在国防工业中，如航空航天工业中的发热冷却，核废料的处理以及诸如防毒面罩的研制等都涉及渗流力学问题。 渗流的特点在于：第一，多孔介质单位体积空隙的表面积较大，表面作用明显，任何人和时候都必须考虑粘性作用；第二，在地下渗流中往往压力较大，因而通常要考虑流体的压缩性；第

8、三，孔道形状复杂、阻力大、毛细管作用较普遍，有时还要考虑分子力；第四，往往伴随有复杂的物理化学过程。9 Mechanics of seepage flow is not only long historical but also young science. It has been past one and half centuries since Darcy law The grow up of oil industry in 20th promoted the develop of seepage flow. Along with correlative science develops,

9、 it is promote seepage flow again. Recently mechanics of seepage flow developed into a new stage along with develop of nonlinear mechanics; the establishment of bifurcate theory and other theory.10 渗流力学是一门既有较长历史又年轻活跃的科学。从达西定律的出现到现在已过去一个半世纪。20世纪石油工业的崛起极大地推动了渗流力学的发展。随着相关科学技术的发展，如高性能计算机的出现，核磁共振、CT 扫描成像

10、以及其他先进实验方法用于渗流，又将渗流力学大大推进了一步。近年来，随着非线性力学的发展，将分叉、混沌理论以及分形理论用于渗流，其他诸如格气模型的建立等等，更使渗流力学的发展进入一个全新的阶段。11 9-2 Basic law of seepage flow1. Model Figure 9 1 is experiment set, cylinder is full of sand, interface area is A , sand layer thick is l , thin net in the sand bottom。Water flow through A to C determi

11、ne。Neglecting kinetic energy ，difference of measure hydraulic headH1H2 is water head loss。 2. Darcys law for seepage flow French engineer - Henri Darcy, did many experiment utilize sandy soil in 1852-1855, achieved Darcys lawAQlBC1H2HFig.91 experiment set12 9-2 渗流基本定律渗流基本定律 一、渗流模型 图 9 1 为 渗流实验装置，圆筒内

12、充填沙粒，界面积为 A , 沙 层厚为 l , 沙底部有细网支撑。水由稳压箱经阀 A 进入圆筒 C 测定。忽略动能，测压管水头差H1H2为渗流的水头损失。 二、达西渗流定律 法国工程师达西（Henri Darcy)在1852至1855年利用沙质土壤进行了大量实验，得到线性渗流定律。即达西定律：AQlBC1H2H图91 渗流实验装置133. coefficient of seepage flow metrical method for coefficient： （1）empirical formula method:estimating according as soil diameter ,

13、shape, structure , porosity, temperature . （2）experimental method，utilizing the setting like Fig.91 and formula( 91). （3）spot method:do experiment by pumping water from well, calculate k according as well formula. 91 wwhhQkAVkkJllkJor（ ）Coefficient of seepage flow Hydraulic gradient14坡度，即水力坡度。流程范围内平

14、均测压管具有流速的量纲；流的一个系数，和流体性质综合影响渗渗流系数，是土壤性质式中：）（或JkkJlhkVlhkAQww 19 三、渗流系数 渗流系数测定方法： （1）经验公式法，根据土壤粒径、形状、结构、孔隙率，影响流体粘性的温度等参数所组成的经验公式估算。 （2）实验室方法，在实验室利用类似图91的装置及公式（91）计算，方法简易，但不易取得未扰动土样。 （3）现场方法，在现场利用钻井或原有井作抽水或灌水实验，根据水井的计算公式求 k 值。15 9-3 Uniform and non-uniform flow of groundwater 1. invariable uniform and

15、 non-uniform flow1.1 invariable uniform seepage flow, hydraulic gradient is uniform in any section,according to Darcys law u is equal in any point. 1.2 invariable non-uniform seepage flowas Fig. 92hydraulic pipe gradient of point in any section 12dHJds1200HFig. 92 hydraulic pipe gradient formulaDupu

16、it29 constant ）（dSdHkkJUdSdHJ-16 9-3 地下水均匀流和非均匀流地下水均匀流和非均匀流 一、恒定均匀流和非均匀流（1）恒定均匀渗流，任一断面水力坡相同，由达西定律，任意点流速 u 都相等。（2）恒定非均匀渗流，如图 92 所示任意过水断面上各点测压管坡度）。此式称为裘皮幼公式（）（常数Dupuit29 dSdHkkJUdSdHJ- 图 92 测压管坡度 12dHJds1200H172. Gradual change basic differential equation and soakage curve In non-hydraulic seepage flo

17、w, surface of G-water is called soakage surface,in plane is soakage curve. As in 93,due to Dupuit formula () 93where hydraulic gradient 0,smooth gradient 0,up-gradient 0,down-gradient94 is soakage curve equation dHdhVkJk idSdSiiiiwhe -（ ）；。22122212 0 2 2 or 94 where , n iQlhhkbqlhhkQqb-（ ） Fig. 94 J

18、00H Fig. 93 hsl 002h 1h18二、渐变渗流基本微分方程和浸润曲线 在无压渗流中，重力水自由表面称浸润表面，平面问题中为浸润曲线。如图93所示，由裘皮幼公式即单宽流量。式中：）（或。的浸润曲线方程，见图下面仅给出称为逆坡。称为顺坡；称为平坡；渗流底坡；式中）（ , 49 2 2 490, 0 , 0 , 0 39 )( 22212221bQqhhlkqhhlkbQiiiiidSdhikdSdHkJV- J00H 图 93 hs 图 94 002h 1h19 9-4 Well and catchment passage 1. Catchment corridor A catch

19、ment corridor, section is rectangle,the bottom is impermeability , i = 0,due to（93）get:)0(dsdhbhkQ）（），（，）（69 2)( obtaining59 formula into , Takingcorridor. attachment of scope effected ,affectt isn levelter ungroundwa equation. curve soakage is 59 2 obtaining and gintegratinafter 2222LhHkqHzLxisLLxT

20、hisxkbQhz- Fig. 95 Catchment corridor LxoxHhzN20 9-4 井和集水廊道井和集水廊道 一、集水廊道 某集水廊道，横断面为矩形，底为不透水层，见图108，底坡 i = 0,由式（93）得)0(dsdhbhkQ积分得）（）式，可得单侧渗流量代入（。将为集水廊道的影响范围，称后，地下水位不受影响此式为浸润曲线方程。）（69 2)( 59, 59 2 2222LhHkqHzLxLLxxkbQhz- 图 95 集水廊道 LxoxHhzN212. Diving well（non-hydraulic well） Diving water has free sur

21、face，the well constructed in it called diving well. The bottom of well is impermeability, as 96220220Due to Dupuit formula2ln 97when R,H, is called well effected diameter() 98lnthe max descent of underground water calleddzQAUrz kdrQrzhkrrzRkHhQRrSHh is-（ ）（ ） water level depthFig. 96 Diving well rHh

22、N0r22二、潜水井（无压井） 具有自由水面的地下水称无压水或潜水，在其中建的井称潜水井。井底打到不透水层称完全井，如图96称水位降深地下水面的最大降落）（为井的影响半径称时，在）（应用裘皮幼公式hHSrRhHkQRHzRrrrkQhzdrdzkrzAUQ-89 ln)(,79 ln2022022 图 96 潜水井 rHhN0r233. Artesian well Aquifer is between two impermeable layer, pressure is larger than air pressure, called artesian, the well is served

23、by it called artesian well，as in fig.97，for entirety well002 , is hydraulic head for corresponding pointafter integrating and getting hydraulic conduit head curve equationln 99take into , () lndzQAVrt kzdrrQrzhktrzH rR getHh ktQRr-（ ） 910910formula is try to deduce equation when htht（ ）（ ），。 Fig. 97 Artesian entire well rHhN0rxs24三、自流井 含水层位于两不透水层之间，压强大于大气压，称为自流层，由其供水的井称自流井，见图97，对完全井的情况。时公式，试推导）式是（）（得流量公式代入）（方