1Groundwater Flow• Today– What causes groundwaterflow?– Mechanical Energy– Fluid Potential, !– Energy per unit mass– Hydraulic Head, h– Energy per unit weight– Composed of» Pressure head» Elevation headDatumhdzpvpopozReferencefluid parcelGroundwater BalanceChange in storage (compressibility + porosity)= Recharge – Pumping – GWDischarge – ETGW ± UnderflowWhat is the ultimate cause offluid movement?– Energy gradients, especiallygradients of mechanical energyWe quantify the mechanicalenergy of a fluid using thefluid potential,– the total mechanical energy perunit mass of fluidPumpingPumpingDatum (z = 0)hdzpvpopozReferencefluid parceld – depth below water surfacez – height above datum (a point of given total mechanical energy)h – total height of water above the datump – pressure on parcel (omni-directional)v – velocity of parcel (one direction)The reference fluid parcel is at rest at the datum, so it has a fluid potential of zeroComponents of Fluid Potential, !of a fluid ‘parcel’pppWhat makes groundwater flow?Answer: Water flows from areas of higher total energy to areas of lower total energy2What forms of energy doeswater have?Why is this water flowing?Gravity!What is the formula for gravitationalpotential energy?Gravitational PE = m g zzmass = maccel of gravity = gWhy does thewater rise?poFree surfacePistonPressure!! EE =m"( p # po)pp - poEE = elastic energy (pressure)" = water densityPiston pushing on water in a sealed tube; density ! increases.Elastic EnergySealSeal3!=ppodpm"EE! !"ppppdpdp0 011##Water is nearly incompressible; if a fluid is only slightlycompressible, So, for water, in “shallow” systems, we can say that)( EE0oppppmdpm!="#$$Elastic EnergyWhy is the waterspraying up intothe air?What is kinetic energy equal to?What drives flow is the sum ofthese types of energy, called the“fluid potential”. The fluid potentialis defined as the “total mechanicalenergy per unit mass of water”.4PumpingPumpingReview: What kinds of mechanicalenergy can a fluid (parcel) have?• Potential Energy– gravitational– reflects the work to lift mass from elevation z = 0, the datum, toelevation z:PE = mgz • Kinetic Energy– energy required to accelerate fluid from rest to observed velocity, vKE = ! mv2• Elastic Energy– compressional– work done in raising fluidpressure from referencepressure, po, to pressure, pDatum (z = 0)hdzpvpopozReferencefluid parcel•So, the components of ![total mechanical energy per unit mass] are:20201212PE EE KEmp pmgz m mvmp pgz v!!+ +" =#+ +" =#" = + +Fluid PotentialFluid Potential! " = gz +p # po$+12v25Fluid PotentialWhat are the units of fluid potential?! "g=gzg+p # po$g! h = z +p " po#"g = # = specific wt. of water= hydraulic headunits? m (i.e., height of water)Hydraulic HeadHow does it work?datumx= z = elevation head=hZ= (p-po)/# = pressure head=hPtotal head = hT = hP + hz= 2 m + 3 m= 5 m4.1 mHydraulic HeadTherefore, h, the hydraulic head, is directly related tothe fluid potential.Water flows from areas of higher head to lower head.h1 > h2, so water will flow from Well 1 toward Well 2datumland surfaceh1h2Well 1Well 2Aquifer bottomRecall that our conclusion that h is representative of !is based on three major assumptions:•Velocity is negligible•Density is essentially constant•g is constantFinally, from earlier diagrams, recall that thedimensions of h are [L], e.g., meters.-this dimensional convenience is one reason we work with head if we can.Hydraulic Head6gpgpzghghppgzoo!!!"+=#=="+=#Components of Hydraulic Head!"+=+=+=zpzhhhpzh ! p =Nm2=kg " ms2" m2=kgs2" m#=$ g =kgm3"ms2=kgs2" m2p#=kgs2" m÷kgs2" m2= mComponents of Hydraulic Head= elevation head + pressure headSI Units of Hydraulic HeadDatum12hthzhpNote: -constant head tanks at end-pressure head (constant)-elevation head (decreasing to right)-total head (decreasing to right)ExampleDatum12hthzhphLocationhphthzInterpolatebetween thepiezometersto getcontinuoushead lines:7AB CD0 m 1 m 2 m 3 m 4 m 5 m0 m1 m2 m3 m4 mAssume constant energy loss perunit length along axis. What is hz, hp,and ht at A, B, C, and D?Groundwater Flow• Review– Groundwater flow is inresponse to gradients ofmechanical energy– Three types• Potential• Kinetic– Kinetic energy is usually notimportant in groundwater• Elastic (compressional)– Fluid Potential, !– Energy per unit mass– Hydraulic Head, h– Energy per unit weight– Composed of» Pressure head» Elevation head• Next Time– Darcy’s Law– Hydraulic Conductivity– Specific DischargeNext time: Darcy’s LawHenry Darcy, a Frenchhydraulic engineerinterested in purifyingwater supplies usingsand filters, conductedexperiments to determinethe flow rate of waterthrough the filters.Published in 1856, his conclusionshave served as the basis for allmodern analysis of ground waterflowhttp://biosystems.okstate.edu/darcy/index.htmFreeze, R. Allen. "Henry Darcy and the Fountains of Dijon." Ground Water 32, no.1(1994): 23–30.Next time: Darcy’s Lawh1$lh2%%$hDatumSand-filled columnwith bulk cross-sectional area AQ - Rate ofdischarge [L3/T]Constant head tanks at each endCartoon of a Darcy experiment:What controls the discharge,