Hydrogeology Part – 2
Darcy’s law and hydraulic conductivity
Water contained within the interconnected voids of soils and rocks is capable of moving, and the ability of a rock to store and transmit water constitutes its hydraulic properties.
The laws that govern the behaviour of groundwater flow in saturated material is that formulated empirically by the French municipal engineer for Dijon, Henry Darcy, in 1856.
Darcy studied the flow of water through porous material contained in a column and found that the
Total flow - Q, is proportional - difference in water level, h1 − h2, the cross-sectional area of flow, A, and inversely proportional to the column length, L. proportionality constant - K
where dh/dl represents the hydraulic gradient, with the negative sign indicating flow in the direction of decreasing hydraulic head.
Limitations:
Darcy’s law is valid for laminar flow, i.e., the Reynolds number (Re) varies from 1 to 10,
ρ = density of water µ = dynamic viscosity of water d = mean grain size of the aquifer; v - velocity
Other terms and relations:
Hydraulic conductivity is a measure of a material’s ability to transmit water through its pore spaces or fractures. It depends on both the properties of the material and the properties of the fluid, such as viscosity and density.
Transmissibility, the transmissibility is the flow capacity of an aquifer per unit width under unit hydraulic gradient and is equal to the product of permeability times the saturated thickness of the aquifer.
- In a confined aquifer, T = Kb and is independent of the piezometric surface.
- In a water table aquifer, T = KH, where H is the saturated thickness. As the water table drops, H decreases, and the transmissibility is reduced. Thus, the transmissibility of an unconfined aquifer depends upon the depth of GWT.
Calculating volume of voids from Mass, Density & Volume
Calculate the Volume of Solids (Vol. solid) = Mass of the solid / Density of the solid (or) Average density of the particles
Calculate the Volume of Voids (Vol. voids) = total volume −Volume of solids
Calculate Specific Yield (Sy): Sy= Porosity (ϕ) − Specific retention (Sr)
Calculate change in storage = Area X drop in water table X Specific yield
Relation between porosity (n) and void ratio (e) ; n = e / 1 + e [or] e = Vol. of voids / Vol. of solid
Calculate cross section area of a cylindrical sample; Area =π r2
Calculate the Flow Rate (Q) : Q = v / t; v – volume of water collected, t – time.
Coefficient of Permeability
discharge per unit area(q),
hydraulic gradient (i)
JAM Question from (2005 2024)
Q.48 An aquifer has a cross-sectional area of 10 m2 and a hydraulic conductivity of 0.25 cm/s. The volume of water that will flow per second through the aquifer for a hydraulic gradient of 0.04 is ___ cm3. (Round off to three decimal places) (2024)
Q.56 A partially saturated soil sample has a volume of 1200 cc. The volume of water present in the sample is 300 cc. The mass of solid in the sample is 1908 g and the particle density is 2.65 g/cc. The porosity (n) of the soil sample is ___ %. (In integer) (2024)
Q.50 The water table over an area of 1 km2 was lowered by 4 m. If the porosity of rock is 30% and the specific retention is 10%, the change in the groundwater storage is ____ × 103 m3 (In integer) (2023)
Q.43 A soil has a void ratio of 0.5. The total porosity of the soil is ____. (Round off to two decimal places) (2022)
Q.53 A cylindrical soil sample is encased in an open-ended inclined tube with a diameter of 100 mm. There is a constant supply of water from the upper end of the sample and the outflow from the other end is collected in a beaker. The average amount of water collected is 1000 mm3 every 10 sec. The average outflow velocity is____ mm/sec. (π = 3.14) (Round off to three decimal places) (2022)
Q.53 In a laboratory experiment, water discharge through a porous rock sample in 2 hours was 10 cm3 The cylindrical rock sample is 10 cm long and has a diameter of 50 mm. If the discharge occurred at a constant head of 300 cm, the coefficient of permeability of the rock sample is ___ x 10−6cm/s.(Round off to two decimal places). (2021)
Q.48 An aquifer has a cross sectional area of 1000 m2 and a hydraulic gradient of 0.01. If water is flowing from the aquifer at a rate of 10 m3/sec, the hydraulic conductivity (in m/sec) of the aquifer is __ (2020)
Q.53 Mass and volume of a fully dried soil sample are 500 g and 250 cm3 respectively. The average density of the particles in the soil sample is 2.5 g/cm3. The void ratio of the soil sample is ____%. (2019)
Q.58 Two vertical wells penetrating a confined aquifer are 200 m apart. The water surface elevations in these wells are 35 m and 40 m above a common reference datum. The discharge per unit area through the aquifer is 0.05 m/day. Using Darcy’s law, the coefficient of permeability is _____m/day. (2019)
Q.59 A confined sandstone aquifer with a uniform cross-sectional area of 7 m2 and a hydraulic conductivity of 2 m/s, transmits water across a hydraulic gradient of 3.2. Assuming steady state Darcian flow, the volumetric flow rate through the aquifer is ___ m3/s (answer in one decimal place). (2018)
Q.44 Weight of a10 cm3 medium grained sandstone block with 20% (v/v) porosity, in dry state is 26g. The density of the block when fully saturated with water is _____g/cm3 (2016)
Q.37 (b) A sandstone core of 15 cm length and cross-sectional area of 25 cm2 was evaluated for permeability, using a constant head permeameter. For a hydraulic head of 5 cm, a total of 100 ml of water was collected in 10 minutes. Estimate hydraulic conductivity (cm/min) using the Darcy’s equation, Q = K.A.(dh/dl), where Q = discharge (cm3/min), K = hydraulic conductivity (cm/min), A = cross-sectional area (cm2) and (dh/dl) = hydraulic head. (2012)
KEY 👍
2024. 48. 1000
56. 40
2023. 50. 800
2022. 43. 0.33 - 0.34
53. 0.012 - 0.013
2021. 53. 2.3 - 2.34
2020. 48. 1
2019. 53. 25
58. 2
2018. 59. 44.8
2016. 44. 2.8
2012. 37. 1.2
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