CE 374 K Hydrology. Systems and Continuity. Daene C. McKinney

Size: px

Start display at page:

Download "CE 374 K Hydrology. Systems and Continuity. Daene C. McKinney"

Harold Lane
6 years ago
Views:

1 CE 74 K Hydology Systems and Continuity Daene C. McKinney

2 Rive Basin Management Infastuctue contol, Institutional policies & incentives Wanings, Alams Pecipitation, Tempeatue, Humidity, Steamflow Wate Quality, Goundwate, Snow pack, Evapotanspiation Decision Implementation Data Measuement Decision Making Decision Suppot System Data Pocessing & Achiving Analysis MCDM Opeating ules Expet system Optimization, Wanings Risk management, Dispute Resolution Rainfall/unoff, Flooding, Hydaulics, Wate Allocation, Wate Pollution, Envionmental Flows Data base Data model Data display

3 Wate Resouces Planning and Management Identification, fomulation and analysis of poects and designs Based on scientific, legal, ethical, economic,, concepts Poblems Consideed Municipal and industial supply Iigation Flood contol Hydoelectic powe Navigation Wate quality Receation Fisheies Dainage & sediment contol Pesevation and enhancement of natual wate aeas, ecological divesity, acheology, etc

4 Wate Resouce Systems Analysis Wate esouces poblems ae Complex, inteconnected, and ovelapping Involving wate allocations, economic development, and envionmental pesevation Systems analysis Beak complex system down into components and analyze the inteactions between the components Cental method used in wate esouces planning

5 System Some Systems: Wateshed Aquife Development Aea Detention Basin Paametes, β Inputs, I Tansfomation function Q(t) Ω(α, β) * I(t) Outputs, Q Policies o contols, α

6 System Tansfomation Function Q(t) Ω(α, β) * I(t) Mathematical model Typically a set of algebaic equations Deived fom diffeential equations of Consevation of Mass (e.g., continuity) Consevation of Momentum (e.g., Manning) Consevation of Enegy (e.g., fiction loss)

7 System Chaacteistics Linea vs nonlinea Linea - supeposition is valid If I 1 Q 1 and I 2 Q 2 Then I 1 +I 2 Q 1 + Q 2 Lumped vs distibuted paamete (spatially vaying) Steady-state vs tansient (time dependent) Deteministic vs stochastic (andom)

8 Atmospheic Moistue Snow Rain Inteception Thoughfall and Stem Flow Snowpack Pevious Snowmelt Suface Infiltation Soil Moistue Pecolation Goundwate Goundwate Flow Impevious Steams and Lakes Oveland Flow Evapoation Evapotanspiation Evapoation Enegy Wateshed Bounday Channel Flow Runoff

9 Hydologic Pocesses (Pecipitation, Evapoation, Infiltation, Runoff) Tansfom the distibution of wate in the hydologic cycle Snow Atmospheic Moistue Rain Govened by fundamental consevation pinciples Reynold s Tanspot Theoem allows us to deive these fundamental pinciples Inteception Evapoation Thoughfall and Stem Flow Snowpack Snowmelt Pevious Suface Impevious Infiltation Soil Moistue Pecolation Evapotanspiation Oveland Goundwate Flow Goundwate Flow Steams and Lakes Evapoation Channel Flow Runoff Enegy Wateshed Bounday

10 Systems Laws of Mechanics Witten fo systems System abitay quantity of mass of fixed identity Fixed quantity of mass, m Consevation of Mass Mass is conseved and does not change dm 0 Momentum If suoundings exet foce on system, mass will acceleate F d ( mv ) Enegy If heat is added to system o wok is done by system, enegy will change de dq dw

11 Contol Volumes Solid Mechanics Follow the system, detemine what happens to it Fluid Mechanics Conside the behavio in a specific egion o Contol Volume Convet System appoach to CV appoach Look at specific egions, athe than specific masses Reynolds Tanspot Theoem Relates time deivative of system popeties to ate of change of popety in CV B βdm βρd CV CV mass,momentum,enegy(extensive) db β dm amountof B pe unit mass(intensive)

12 Reynolds Tanspot Theoem I II III db lim Δt 0 lim Δt 0 ( B + B ) ( B + B ) II ( B ) ( B ) ( B ) ( B ) II III t+δt Δt t+δt Δt II t + I III II t t+δt Δt I t db d βρd + CV βρv da CS

13 Continuity Equation (Consevation of Mass) B M mass of the system; β dm 1 dm db d βρd + CV βρv da CS 0 d ρd + CV ρv da CS if ρ constant d d + CV V da CS 0 ds + Q( t) I( t) 0 ds I( t) Q( t) Inflow Outflow Change in Stoage

14 Discete Time Continuity ds I( t) Q( t) Units of each tem L T m (, s ft ) s ds I( t) Q( t) S ds Δt I( t) Δt Q( t) S 1 ( 1) Δt ( 1) Δt S S 1 I Q Units of each tem L ( m, ft ) S S 1 + I Q Volume of wate in stoage at the end of the next time peiod Δt, S, equals the volume in stoage at the beginning of that peiod, S -1, plus the volume of inflow, I -1, minus the volume of outflow, Q -1

15 Shoal Ceek Flood Memoial Day 1981 Nomal flow 90 gpm Stom peak 6.5 million gpm 1 lives lost

16 Shoal Ceek Flood Memoial Day in. of ain fell unifomly ove 7.0 sq. mi. What was the equivalent volume of wate? 1ft 6.1in * 12in 770,908,921gal 2 *7.0mi * 770 million gallons in 8 hous ( 5280ft/mi) 10,055,525ft * gal/ft Pecip (in) Runoff (cfs) Time (h)

17 Example Shoal Ceek Given: Incemental pecipitation ove the wateshed, pulse Steamflow measued at the outlet, continuous Find: Stoage as function of time Convet steamflow to pulse data Aveage steamflow ove time inteval Equivalent depth ove the wateshed 1 Δt A hou ( Q Q ) Δt 1 2 i + i+1 ( Q Q ) Δt i + i+1 Continuity Eq. S S + ( I Q ) S0 0; S1 S0 + I0 Q0; S2 S1 + I1 Q1 0 i 1 i i

18 Shoal Ceek Flood Runoff (cfs) Pecip (in) Time Time Incemental Instantaneous Incemental Incemental Cumulative Inteval Pecip Steamflow Steamflow Stoage Stoage t I Q(t) Q ΔS S h in cfs in in in I Q Time (h) ΔS S S S 1 S 0 2 S1 + I1 Q1 S 0 + i 1 ( I Q ) i i

19 Shoal Ceek Flood Steamflow (in) Pecip (in) Shoal Ceek at Nothwest Pak, Austin, Texas, May 24-25, 1981 Aea 7.0 mi Time Time Incemental Instantaneous Incemental Incemental Cumulative Inteval Pecip Steamflow Steamflow Stoage Stoage t I Q(t) Q ΔS S h in cfs in in in Change in Stoage (in) Stoage (in)

Correlation between System (Lagrangian) concept Control-volume (Eulerian) concept for comprehensive understanding of fluid motion?

Correlation between System (Lagrangian) concept Control-volume (Eulerian) concept for comprehensive understanding of fluid motion? The Reynolds Tanspot Theoem Coelation between System (Lagangian) concept Contol-volume (Euleian) concept fo compehensive undestanding of fluid motion? Reynolds Tanspot Theoem Let s set a fundamental equation