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Question 1
ప్రశ్న 1
For one-dimensional saturated groundwater flow through a porous medium, which expression gives the magnitude of discharge according to Darcy's law?
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Explanation:
Darcy's law states that groundwater discharge is proportional to hydraulic conductivity, hydraulic gradient and cross-sectional flow area. In magnitude form, the relation is Q = K i A. Hydraulic conductivity K has dimensions of length per time, while hydraulic gradient i is dimensionless. Multiplication by area therefore gives discharge dimensions of volume per time. Hence Option A is correct.
వివరణ:
Question 2
ప్రశ్న 2
The hydraulic head decreases from 108 m to 100 m over a flow-path length of 400 m. What is the magnitude of the hydraulic gradient?
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Explanation:
The magnitude of hydraulic gradient is the head loss divided by the corresponding flow-path length. The head difference is 108 - 100 = 8 m. Therefore i = 8/400 = 0.020. Hydraulic gradient is dimensionless because both numerator and denominator have dimensions of length. Hence Option B is correct.
వివరణ:
Question 3
ప్రశ్న 3
Two points in the same groundwater-flow system have hydraulic heads of 125 m and 117 m. In the absence of other complications, what is the natural groundwater-flow tendency?
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Explanation:
Groundwater flow is driven by differences in hydraulic head. Water naturally tends to move from higher hydraulic head toward lower hydraulic head. The first location has a head of 125 m and the second has a head of 117 m. The hydraulic gradient is therefore directed toward the lower-head location. Hence Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
A saturated aquifer has hydraulic conductivity K = 12 m/day, hydraulic gradient i = 0.015 and cross-sectional flow area A = 50 m². What is the Darcy discharge?
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Explanation:
Using the magnitude form of Darcy's law, Q = K i A. Substitution gives Q = 12 × 0.015 × 50. The product is 9 m³/day. The units are consistent because m/day multiplied by m² gives m³/day. Therefore Option C is correct.
వివరణ:
Question 5
ప్రశ్న 5
Groundwater discharge through a cross-section is 24 m³/day. If the flow area is 80 m² and the hydraulic gradient is 0.020, what is the hydraulic conductivity?
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Explanation:
Darcy's law can be rearranged as K = Q/(iA). Substitution gives K = 24/(0.020 × 80). The denominator equals 1.6 m². Thus K = 15 m/day. Therefore Option C is correct.
వివరణ:
Question 6
ప్రశ్న 6
An aquifer carries 3.6 m³/day through a flow area of 30 m². If its hydraulic conductivity is 6 m/day, what hydraulic gradient is required?
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Explanation:
Rearranging Darcy's law gives i = Q/(KA). Substitution gives i = 3.6/(6 × 30). This equals 3.6/180 = 0.020. The resulting hydraulic gradient is dimensionless. Therefore Option C is correct.
వివరణ:
Question 7
ప్రశ్న 7
If the hydraulic gradient along a 500 m groundwater-flow path is 0.004, what is the corresponding hydraulic-head difference?
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Explanation:
Hydraulic gradient magnitude is defined as i = Δh/L. Therefore the head difference is Δh = iL. Substitution gives Δh = 0.004 × 500 = 2.0 m. This is the hydraulic-head loss over the stated path length. Hence Option B is correct.
వివరణ:
Question 8
ప్రశ్న 8
A porous medium has hydraulic conductivity 10 m/day and hydraulic gradient 0.03. What is the magnitude of its Darcy velocity or specific discharge?
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Explanation:
Darcy velocity, also called specific discharge or superficial velocity, is q = Q/A. Darcy's law gives q = Ki for one-dimensional flow in magnitude form. Therefore q = 10 × 0.03 = 0.30 m/day. This is not generally the actual velocity of water moving through the pore openings. Hence Option B is correct.
వివరణ:
Question 9
ప్రశ్న 9
Why is Darcy velocity generally smaller than the average seepage velocity of groundwater?
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Explanation:
Darcy velocity is calculated by dividing discharge by the total bulk cross-sectional area of the porous material. Only a fraction of that area consists of interconnected voids through which groundwater actually flows. Consequently the water must move faster within the available pore space to carry the same volumetric discharge. Average seepage velocity therefore exceeds Darcy velocity when effective porosity is less than unity. Hence Option A is correct.
వివరణ:
Question 10
ప్రశ్న 10
The Darcy velocity through an aquifer is 0.12 m/day and its effective porosity is 0.30. What is the average seepage velocity?
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Explanation:
Average seepage velocity is obtained from v_s = q/n_e. Here q = 0.12 m/day and effective porosity n_e = 0.30. Thus v_s = 0.12/0.30 = 0.40 m/day. The value exceeds the Darcy velocity because groundwater occupies only the connected pore space available for flow. Therefore Option D is correct.
వివరణ:
Question 11
ప్రశ్న 11
An aquifer has K = 8 m/day, hydraulic gradient i = 0.025 and effective porosity n_e = 0.20. What is the average seepage velocity?
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Explanation:
First calculate the Darcy velocity as q = Ki. This gives q = 8 × 0.025 = 0.20 m/day. The seepage velocity is then v_s = q/n_e = 0.20/0.20. Therefore v_s = 1.00 m/day. Hence Option C is correct.
వివరణ:
Question 12
ప్రశ్న 12
Groundwater has an average seepage velocity of 0.50 m/day along an approximately one-dimensional 500 m flow path. Ignoring dispersion and changes in velocity, what is the approximate advective travel time?
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Explanation:
Travel time is distance divided by average pore-water velocity when the stated simplifying assumptions apply. Thus t = 500/0.50. This gives 1000 days. Darcy velocity should not be substituted if the problem specifically gives the actual average seepage velocity. Therefore Option C is correct.
వివరణ:
Question 13
ప్రశ్న 13
The Darcy velocity normal to an aquifer cross-section is 0.05 m/day and the cross-sectional area is 120 m². What is the volumetric groundwater discharge?
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Explanation:
Darcy velocity is defined as q = Q/A. Rearranging gives Q = qA. Therefore Q = 0.05 × 120 = 6.0 m³/day. This calculation uses the full bulk cross-sectional flow area associated with Darcy flux. Hence Option B is correct.
వివరణ:
Question 14
ప్రశ్న 14
A confined aquifer is 10 m thick and 200 m wide perpendicular to groundwater flow. If K = 15 m/day and hydraulic gradient i = 0.002, what is the groundwater discharge across the section?
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Explanation:
The cross-sectional flow area is thickness multiplied by width. Thus A = 10 × 200 = 2000 m². Darcy's law gives Q = 15 × 0.002 × 2000. The resulting discharge is 60 m³/day. Therefore Option C is correct.
వివరణ:
Question 15
ప్రశ్న 15
A confined aquifer has transmissivity T = 300 m²/day, hydraulic gradient 0.001 and aquifer width perpendicular to flow of 500 m. What is the total discharge across that width?
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Explanation:
For a confined aquifer, transmissivity is T = Kb. Darcy discharge across width W can therefore be written Q = T i W. Substitution gives Q = 300 × 0.001 × 500. This equals 150 m³/day. Therefore Option C is correct.
వివరణ:
Question 16
ప్రశ్న 16
Which set of dimensions is correct for Darcy-flow quantities?
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Explanation:
Hydraulic conductivity has dimensions of velocity, L/T. Hydraulic gradient is head difference divided by distance and is therefore dimensionless. Darcy velocity also has dimensions L/T because it equals Ki. Volumetric discharge equals velocity times area and therefore has dimensions L³/T. Hence Option A is correct.
వివరణ:
Question 17
ప్రశ్న 17
If hydraulic conductivity doubles while hydraulic gradient and cross-sectional area remain unchanged, what happens to Darcy discharge?
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Explanation:
Darcy's law is Q = K i A. With hydraulic gradient and area fixed, discharge is directly proportional to hydraulic conductivity. Doubling K therefore doubles Q. This proportionality is part of the linear Darcy-flow model. Therefore Option C is correct.
వివరణ:
Question 18
ప్రశ్న 18
If the hydraulic gradient is reduced from 0.04 to 0.02 while K and A remain unchanged, how does Darcy discharge change?
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Explanation:
Darcy discharge is directly proportional to hydraulic gradient when K and A are constant. The gradient decreases from 0.04 to 0.02, which is a factor of one-half. Consequently the discharge is also reduced to one-half of its original value. This result follows from the linearity of Darcy's law within its applicable regime. Therefore Option B is correct.
వివరణ:
Question 19
ప్రశ్న 19
In an ideal homogeneous saturated aquifer governed by Darcy's law, what is the Darcy discharge if two points along the considered flow direction have equal hydraulic head?
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Explanation:
Equal hydraulic heads over a finite distance give zero hydraulic gradient. Darcy's law gives q = Ki, so q is zero when i is zero. The corresponding volumetric discharge in that direction is also zero. This conclusion assumes no other driving gradient or transient effect has been introduced. Therefore Option A is correct.
వివరణ:
Question 20
ప్రశ్న 20
Under which condition is the classical linear form of Darcy's law most appropriately applicable?
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Explanation:
Darcy's law was established for flow through porous media where velocities are relatively small. In its classical linear regime, viscous resistance dominates and specific discharge is proportional to hydraulic gradient. At sufficiently high pore-flow Reynolds numbers, inertial effects can become important and the relationship may become nonlinear. Ordinary groundwater flow through many soils and aquifers commonly lies within the Darcy regime. Therefore Option A is correct.
వివరణ:
Question 21
ప్రశ్న 21
What is the principal implication if inertial effects become significant at very high groundwater velocities in a coarse porous medium?
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Explanation:
Classical Darcy flow assumes a linear relation between specific discharge and hydraulic gradient. At sufficiently high flow velocities, inertial effects can become significant relative to viscous effects. The flow-resistance relation can then depart from the simple Darcy form. Non-Darcy formulations may be needed in such circumstances. Therefore Option A is correct.
వివరణ:
Question 22
ప్రశ్న 22
Which statement about hydraulic conductivity in Darcy's law is correct?
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Explanation:
Hydraulic conductivity measures the ease with which a particular fluid can move through a porous medium. It depends on the pore geometry of the medium as well as fluid properties such as density and viscosity. It therefore differs conceptually from intrinsic permeability, which describes the porous medium independently of the fluid. Hydraulic conductivity has dimensions of length per time. Therefore Option A is correct.
వివరణ:
Question 23
ప్రశ్న 23
Two aquifers have the same Darcy velocity, but Aquifer X has effective porosity 0.20 and Aquifer Y has effective porosity 0.40. How do their average seepage velocities compare?
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Explanation:
Average seepage velocity is v_s = q/n_e. At the same Darcy velocity, seepage velocity is inversely proportional to effective porosity. For Aquifer X the denominator is 0.20, whereas for Aquifer Y it is 0.40. Thus the seepage velocity in X is twice that in Y. Therefore Option B is correct.
వివరణ:
Question 24
ప్రశ్న 24
Why is effective porosity generally more appropriate than total porosity when converting Darcy velocity to average groundwater seepage velocity?
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Explanation:
Total porosity includes all void space, including pores that may be isolated or poorly connected. Such voids do not necessarily participate effectively in advective groundwater flow. Effective porosity represents the connected void fraction through which groundwater can move. Dividing Darcy flux by this effective flow fraction gives a better estimate of average linear pore-water velocity. Therefore Option A is correct.
వివరణ:
Question 25
ప్రశ్న 25
In the coordinate form q_x = -K dh/dx for an isotropic aquifer, what is the physical meaning of the negative sign?
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Explanation:
The hydraulic-head gradient points mathematically toward increasing head. Natural groundwater flow proceeds from higher head toward lower head. The negative sign in Darcy's law therefore makes the flow vector oppose the direction of increasing hydraulic head. Hydraulic conductivity itself remains a positive material coefficient. Therefore Option A is correct.
వివరణ:
Question 26
ప్రశ్న 26
Consider the following statements about Darcy's law: I. Hydraulic gradient is head change per unit flow-path length. II. Darcy velocity is discharge divided by the total bulk flow area. III. Average seepage velocity can be estimated as Darcy velocity divided by effective porosity. IV. Classical Darcy's law assumes an approximately linear relation between specific discharge and hydraulic gradient within the laminar porous-media regime. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I correctly defines hydraulic gradient. Statement II correctly identifies Darcy velocity or specific discharge as Q divided by the bulk cross-sectional area. Statement III correctly accounts for the smaller interconnected pore area through effective porosity. Statement IV correctly states the principal flow-regime condition for the classical linear Darcy relationship. Therefore all four statements are correct and Option D is the valid answer.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: A. Q = K i A సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: B. 0.020 సమాధానం: B.
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Question 3 ప్రశ్న 3Answer: A. From the 125 m head location toward the 117 m head location సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: C. 9 m³/day సమాధానం: C.
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Question 5 ప్రశ్న 5Answer: C. 15 m/day సమాధానం: C.
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Question 6 ప్రశ్న 6Answer: C. 0.020 సమాధానం: C.
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Question 7 ప్రశ్న 7Answer: B. 2.0 m సమాధానం: B.
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Question 8 ప్రశ్న 8Answer: B. 0.30 m/day సమాధానం: B.
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Question 9 ప్రశ్న 9Answer: A. Darcy velocity is based on the entire bulk cross-sectional area, whereas groundwater actually moves through only the interconnected pore area సమాధానం: A.
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Question 10 ప్రశ్న 10Answer: D. 0.40 m/day సమాధానం: D.
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Question 11 ప్రశ్న 11Answer: C. 1.00 m/day సమాధానం: C.
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Question 12 ప్రశ్న 12Answer: C. 1000 days సమాధానం: C.
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Question 13 ప్రశ్న 13Answer: B. 6.0 m³/day సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: C. 60 m³/day సమాధానం: C.
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Question 15 ప్రశ్న 15Answer: C. 150 m³/day సమాధానం: C.
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Question 16 ప్రశ్న 16Answer: A. Hydraulic conductivity: L/T; hydraulic gradient: dimensionless; Darcy velocity: L/T; discharge: L³/T సమాధానం: A.
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Question 17 ప్రశ్న 17Answer: C. It doubles సమాధానం: C.
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Question 18 ప్రశ్న 18Answer: B. It is reduced to one-half సమాధానం: B.
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Question 19 ప్రశ్న 19Answer: A. Zero, because the hydraulic gradient is zero సమాధానం: A.
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Question 20 ప్రశ్న 20Answer: A. Steady laminar flow through a saturated porous medium where viscous effects dominate సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: A. The linear proportionality between specific discharge and hydraulic gradient may no longer be adequate సమాధానం: A.
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Question 22 ప్రశ్న 22Answer: A. It reflects both characteristics of the porous medium and properties of the flowing fluid సమాధానం: A.
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Question 23 ప్రశ్న 23Answer: B. Aquifer X has twice the seepage velocity of Aquifer Y సమాధానం: B.
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Question 24 ప్రశ్న 24Answer: A. Because effective porosity represents interconnected void space available for groundwater flow సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: A. Groundwater flows in the direction of decreasing hydraulic head సమాధానం: A.
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Question 26 ప్రశ్న 26Answer: D. I, II, III and IV సమాధానం: D.