WEE 3414 GROUNDWATER HYDRAULICS

T-1/10 (28/09/2012); (3 Questions: 2hours)

QUESTION 1.(20 pts i.e 4 marks for each sub question)

With a neat sketch,

(i) What do you understand by hydrological budget?(ii) Write and express the hydrologic budget of surface water system;(iii) Write and express the hydrologic budget of groundwater system? (iv) Deduce the system hydrologic budget of a basin;(v) The water budget terms for a lake included precipitation (P) of 48.26mm/year, evaporation

(E) of 38.1mm/year, surface water inflow (Qin)of 0 mm/year, surface out flow( Qout) of 441.96mm/year, and the change in lake volume (∆ s) of 0 mm/year. Determine the net groundwater flow.

SOLUTION

With a neat sketch,

(i) What do you understand by hydrological budget?

Components of hydrologic cycle in an open system

A hydrologic budget, water budget, or water balance is a measurement of continuity of the flow of water, which holds true for any time interval and applied to any size area ranging from local-scare areas to regional-scare areas or from any drainage area to the earth as a whole.

(ii) Write and express the hydrologic budget of surface water system;

Solution

From the figure drown in the question (1) the hydrologic budget of surface water is expressed as follow:

∆ Ss=P+Q¿−Qout+Q g−E s−T s−I

Where: P is the precipitation

Q¿ is the surface water flow into the system ,

Qout isthe surfacewater flowout of the system ,

Q gis the groundwater flow into the stream ,

E sis the surface evaporation ,

T s isthe transpiration,

I is the inflitration ,

∆ Ssis the change∈water storage of the surfacewater system.

(iii) Write and express the hydrologic budget of groundwater system?

Solution

From the figure drown in the question (1) the hydrologic budget of groundwater is expressed as follow:

∆ Sg=I+Q¿−Qout−Q g−Eg−T g

Where:

G¿ is the groundwater flow into the system ,

Gout isthe groundwater flowout of the system,

Q gis the groundwater flow into the stream ,

Egis the evaporation ,

T g isthe transpiration ,

∆ Sg isthe change∈groundwater storage .

(iv) Deduce the system hydrologic budget of a basin;

Solution

The system hydrologic budget of a basin is developed by adding the above two budget together:

P−(Qout−Q¿ )−(E s+Eg )−(T s−T g )−(G out−G¿)=∆ (Ss−Sg )

Using net mass exchanges, the above system hydrologic budget can be expressed asP−Q−G−E−T=∆ S

(v) The water budget terms for a lake included precipitation (P) of 48.26mm/year, evaporation (E) of 38.1mm/year, surface water inflow (Qin)of 0 mm/year, surface out flow( Qout) of 441.96mm/year, and the change in lake volume (∆ s) of 0 mm/year. Determine the net groundwater flow.SOLUTION Assuming T g=0 ,the water budget equation to define the net groundwater flow for the lake is:G=∆S−P+E−Q¿+Q out

¿0−48.26+38.1−0+4 41 .96¿4 31.8mm/ year

QUESTION 2.(20 pts i.e 4 marks for each sub question)

(i) Define the flowing terms relate to geological formation: a) Aquifer b) Aquicludec) Aquitardd) Phreatic aquifer

SOLUTION

Aquifer : A formation that has sufficient porosity and hydraulic conductivity to store water and transmit water in significant quantities.

Aquiclude:A saturated but relatively impervious material that does not yield appreciable quantities of water to wells; clay is an example.

Aquitard: A saturated but poorly permeable stratum that impedes groundwater movement and does not yield water freely to wells, that may transmit appreciable water to or from adjacent aquifer and, where sufficiently thick, may constitute an important groundwater storage zone; sandy clay is an example.

Phreatic or unconfined aquifer : A party filed aquifer of which the upper boundary is formed by a free groundwater table under atmospheric pressure.

(ii) With a neat sketch, differentiate between a confined and an unconfined aquifers;

SOLUTION

Unconfined aquifer: is one in which a water table varies in undulating from and in slope, depending on areas of recharge and discharge, pumpage from wells, and permeability. Rises and falls in water table correspond to changes in the volume of water in storage within an aquifer. Or

unconfined aquifer :

a party filed aquifer of which the upper boundary is formed by a free groundwater table under atmospheric pressure.

Confined aquifer: confined aquifer, also known as artesian or pressure aquifer, occur where groundwater is confined under pressure greater than atmospheric by overlying relatively impermeable strata. or

Confined aquifer

Is located between impervious layers. If the ground water head is above the ground surface it is called artesian ground water .

(iii) Define the flowing aquifer parameters:a) Transmissivityb) Storage coefficient c) Specific retention d) Specific yield

SOLUTION

a) Transmissivity

Transmissivity - is the rate at which water is transmitted through a specified thickness of aquifer that has a unit width and is under a unit hydraulic gradient.

T= K . b where: T = transmissivity, units = L

K = hydraulic conductivity,

Units = L/T, common units: ft/d, m/d, and cm/s.

b) Storage coefficient:

The volume of water an aquifer releases from or takes into storage per unit surface area of the aquifer per unit change in head. It represents the water released from or taken up into storage in confined aquifers due to the compression or expansion of water and the compression or expansion of the aquifer matrix. In unconfined aquifers the storage coefficient is usually considered to be the specific yield because the water released by gravity drainage is usually much greater than the amount of water released by expansion of water and compression of the aquifer matrix.

c) Specific retention

Specific retention of a rock or soil is the ratio of (1) the volume of water which the rock or soil, after being saturated, will retain against the pull of gravity to (2) the volume of rock or soil. The definition implies that gravity drainage is complete although this is rarely ever the case.

d) Specific yield

Specific yield: The ratio of (1) the volume of water which the rock or soil, after being saturated, will yield by gravity to (2) the volume of the rock or soil. Specific yield is only an approximate measure of the relation between storage and head in unconfined aquifers. It is equal to porosity minus specific retention.

Specific yield:

The ratio of (1) the volume of water which the rock or soil, after being saturated, will yield by gravity to (2) the volume of the rock or soil. The definition implies that gravity drainage is complete. Specific yield is only an approximate measure of the relation between storage and head in unconfined aquifers. It is equal to porosity minus specific retention.

(iv) Express the relationship between porosity, specific retention and specific yield;(6)Porosity , specific retention & specific yield

(v) With a neat sketch illustrate and differentiate between the water level of water table and the piezometric line:

a) For an unconfined aquifer ;b) For a confined aquifer.

SOLUTION

Or this figure

The piezometric line of a confined aquifer is an imaginary surface coinciding with the hydrostatic pressure level of the water in the aquifer.

The water level in a well penetrating a confined aquifer defines the elevation of the piezometric surface at that point. Should the piezometric surface lie above ground surface, a flowing well results.

QUESTION 3.(20 pts i.e 10 marks for each sub question)

(i) With neat sketches, give and describe briefly various types of Springs;

SOLUTION

(ii) Give and explain briefly the main advantages (at least 8) of groundwater compared to surface water.

SOLUTION

Various advantages of groundwater over surface water are:

(1) It is easy to store groundwater by recharge while the storage of surface water requires very expensive dams to be constructed.

(2) It is reliable in dry season or drought because of large storage;(3) It can often be accessed where it is need;(4) It is free from pollution;(turbidity, color, pathogens,etc);(5) It is cheaper to develop, since, unpolluted, it require little treatment;(6) Availability in areas where no surface water and the lakes;(7) Availability for the isolated areas and arid region where it is the potential source of

water ;(8) It is less affected by catastrophic events.