# flow2 - 53:030 Class Notes C.C Swan University of Iowa...

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Period #8: Fluid Flow in Soils (II) A. Measuring Permeabilities in Soils 1. The Constant Head Test (For Coarse-Grained Soils): Upstream and downstream head elevations are maintained at constant levels. The head difference across the soil is a constant value h. The hydraulic gradient i across the sample is also constant. i = hydraulic gradient in the soil ( h/L) Q = vAT = volumetric flow through the soil over an elapsed time T . q = Q/T = vA = rate of volume flow v = q/A = the so-called discharge velocity A = the cross-sectional area of the soil sample Recall from Darcy’s Law that : v = ki From a constant head test, soil permeability k can be computed as: k = Q/(AiT) where 1 L h Soil 53:030 Class Notes; C.C. Swan, University of Iowa

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2. The Falling Head Test (relatively impermeable soils). The total head difference h(t) across the sample changes with time. -> The flow rate through the soil is not constant. q in = Flow rate into the soil = - a dh(t)/dt q out = Flow rate out of the soil = kA * i(t) = kA * h(t)/L Conservation of fluid mass gives: q in = q out - a dh(t)/dt = kA * h(t)/L This represents a first order ODE to be solved for h(t) : Solution: ln(h(t)) - ln(h o ) = -kAt/ (aL) The permeability k of the soil can thus be determined from this test as follows: k = - ln(h(t)/h o ) aL/[At] 2 h(t) L a Soil 53:030 Class Notes; C.C. Swan, University of Iowa
3. The well-drawdown test: used to measure in-situ permeabilities of soils Procedure: a) drill a test well and two observation wells; b) continuously pump water out of the test well until water levels in all three wells achieve equilibrium levels; c) once steady state flow is achieved, the radial flow rate q(r) is constant; q = ki(r)A(r) = constant as function of r where: k = soil permeability i = local gradient = dh/dr A = cross-sectional area of flow = 2 π rh(r) Assumptions: |dh/dr| <<1 (i.e. the gradient is small)

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