HYDROLOGY Lecture 6 GROUNDWATER 2 Assoc.Prof. dr.tarkan erdik

Groundwater flow 1-Groundwater moves with the effect of the gravity within the pores of the aquifer which are small, irregular and related with each other. 2- The flow is from the points where energy of the water is higher to the points where it is lower. 3- Energy losses are large therefore flow is very slow ( few m/year). Therefore, groundwater flow is laminar, turbılent flow occurs in soils with very large pores or near wells Macroscopic scale: Laboratory scale, say 1 to 2m Microscopic scale: The flow between the grains of gravel, sand, silt, and clay. Darcy Law Vf=KI (1) I:Piezometric slope Vf=Q/A (2) The empirical formula states that velocity and head loss are linearly related as is the case in laminar flows. Q=AKI (3) Re=Vf D/µ <1-10

Entire cross section, A, without any grains. Actual cross section, Aa, with grains. Flow actually takes place only through interconnected pore channels Darcy velocity is a fictitious velocity. It assumes flow across the entire cross-section of the soil sample Vf is not the actual velocity of the flow. It is the fictive (filter) velocity as Vf=Q/A.

Actual velocity is greater than the fictive velocity Va>Vf Va=Q/Aa=Q/(pA)=Vf/p Here p shows the porosity I=hL/L=dh/dL=slope of piozemetric line. I=Slope of water for unconfined aquifer. Why? is neglected. Why?

In the Darch Law, the proportionality coefficient between velocity and the piezometric sslope is K, hydraulic conductivity (permeability) coefficient. It is unit is in velocity form (Why?) The coefficient K depends on both the properties of the soil and fluid. The unit of k is in [L2] very very small. Generally Darch unit is used. 1 Darcy=0.987×10-8 cm2 Specific permeability, dependent on soil properties. The ratio of specific weight and dynamic viscosity

Transmissivity is used to determine hydraulic properties of aquifers. Aquifer cross section Aquifer thickness Area= mB Q=AKI= mBKI Aquifer width Transmissivity=discharge per unit width and unit gradient The unit of Transmissivity= L2/T

Groundwater flow is potential flow Groundwater flow is potential flow. Therefore potential flow equations should be adapted. Isn’t it a contradiction that we described groundwater as a laminar flow of a viscous fluid? However, we know Potential flow (no vorticity) can only be applied for nonviscous internal flows. Vorticities in small pores cancel each other as a result, average velocity can be considered as potential flow.

What is safe (secure) yield? It is the maximum amount of water that can be withdrawn from an aquifer without harming it. What would happen if we extract too much water from the well? If too much water is extracted water table drops and salty water will enter the aquifer near the coast.

Safe yield might be bounded by the following factors 1-In arid regions, by the amount of feeding. P-R-E-G Water table 2-Transmissivity of the soil. Even if the recharge is sufficient the soil may not transmit required water. 3-By the danger that aquifer gets polluted. How? (The drop of water table may cause sea water and polluted water to enter to the aquifer).

Artificial feeding of the groundwater 1-By seepage: digging wells near the stream can increase recharge to an aquifer from stream. 2-Spreading: Spreading of water on a wide area will increase seepage in flat and pervious regions. 3-Recharge wells.

Well Hydraulics Dupuit Hypothesis 1-Velocity is horizontal at all points along a vertical line 2-Velocity is uniform along a vertical 3-The length dL in the expression for the hydraulic gradient can be measured horizontally instead of along the piezometric line

Unconfined Aquifer Plan view Side view

Dupuit hypothesis 1 and 2 Dupuit hypothesis 3

Confined Aquifer

Measurement of Hydraulic Conductivity 1.Measurement in the lab a) Constant head permeameter b)Variable head permeameter

2.Measurement in the field Velocity method Time measured for a tracer given to the aquifer to reach the observation well. Va is calculated. Porosity is known and slope of the water table is measured then K can be calculated. b) Potential method Thiem method Theis method Tracer is introduced into aquifer x,t Va