Lecture 08 ground_water hydraulics

GROUNDWATER MOVEMENT AND HYDRAULICS

Well Hydraulics

• A water well is a hydraulic structure that is designed and constructed to permit economic withdrawal of water from an aquifer

• Water well construction includes:– Selection of appropriate drilling methods– Selection of appropriate completion materials– Analysis and interpretation of well and aquifer

performance

Pumping Well Terminology

• Static Water Level [SWL] (ho) is the equilibrium water level before pumping commences

• Pumping Water Level [PWL] (h) is the water level during pumping

• Drawdown (s = ho - h) is the difference between SWL and PWL

• Well Yield (Q) is the volume of water pumped per unit time

• Specific Capacity (Q/s) is the yield per unit drawdown

ho

h

s

Q

Groundwater movementSpecific discharge (v): Discharge per unit area.

(in units if velocity)

(Darcy Equation)K is the proportionality constant and has the same units as v. K is known as the hydraulic conductivity and is a property porous medium and the fluid flowing through the medium

Groundwater movement• K has higher values for

coarse sands and gravels (e.g. 10 to103 md-1)

• And lower values for compact clays and consolidated rocks (e.g. 10-5 to 1 md-1)

Hydraulic conductivity

Darcy’s law

• In terms of flow rate: Darcy’s Law may be expressed in terms of the flow rate Q through a cross-sectional area A:

• The negative means that flow is in the direction of the decreasing head.

• Darcy's law is applicable only to laminar flow i.e. non-turbulent flow.

Reynold's Number

where V is mean velocity, de is effective diameter is kinematic viscosity = 1.14 mm2 /s at 15 °C

• When Re < 2000, flow is laminar • When Re > 2000, flow is turbulent. • All groundwater flows are laminar except:

(a) Fissured rocks: limestones (b) As water approaches wall of well.

e

dVRe

Example• Example: If

A=1.5m1.5m, x = 4 m, h1=3m and h2=2.5. compute the flow rate assuming the aquifer compromises of sandstone with K = 0.08 md-1.

Transmissivity

• Transmissivity (T) is the rate of flow per unit width of the aquifer (thickness b) under unit hydraulic gradient.

b is the thickness of the saturated aquifer

Groundwater movement• In Fig. 7.5 the unconfined

aquifer is formed by porous material contained in an impermeable valley.

• If the material is homogenous and isotropic, the specific discharge through the aquifer in the direction of the arrow is given by

Where is the hydraulic gradient i. Slope of the water table

Groundwater movement• The total flow rate through the aquifer with width y and depth b is

then given by:

• Recall that • Therefore,

Example: In Fig. 7.5, the average width of the valley aquifer (y) is 0.7 km and the length of the section (x) is 2.5 km. If the average thickness of the saturated aquifer (K = 2 md-1) is 200 m, the transmissivity is 400 m2d-1 with values of z1 and z2 of 350 m and 300 m respectively, compute the flow rate through this aquifer.

Well hydraulics:Steady flow in a confined aquifer

Where Q is the pumping rate. Integrating over the radius distance rw to r1 and hw to h1 we have;

OR

Where T is the transmissivity of the aquifer!!Thiem equation

Steady flow in a confined aquifer

Example: A well in a confined aquifer was pumped at a steady rate of 0.0311 m3s-1 when the well level remained constant at 85.48 m, the observation well level at a distance of 10.4 m was 86.52 m. Calculate the transmissivity given the pumping well radius to be 30 cm.

Well hydraulics:Steady flow in an unconfined aquifer

• Groundwater flow to a well in an unconfined aquifer may be complicated by the downward movement of recharge water from ground surface infiltration.

• However, only distant sources in the aquifer are assumed to maintain the steady-state flow.

• In Fig. 7.13 water table intersects the well at hr with the water level in the well at hw.

• Between the two levels is a seepage zone.

Steady flow in an unconfined aquifer

h is the height of the water table replacing b the thickness of the confined aquifer. Integrating over the radius distance r1 and r2 with corresponding values h1 and h2 then:

Dupuit-Forschheimer equation

Steady flow in an unconfined aquifer

• If the squares term is expanded, then we have

Then K = Average transmissivity T between the observation wells (piezometers).The equation for Q becomes the same as the Thiem equation applied in confined aquifers.

NOTE: In applying this equation to unconfined aquifers, effects of seepage from the water table into the well (hw and rw) are negligible if the distance of the nearest observation well r1 is greater than 1.5 times the original water table height h0.