Question
Match the parameters listed in Group I with the units listed in Group II.Group I Group II P. Hydraulic conductivity 1. Newton sec./m$^2$ Q. Permeability 2. m/sec. R. Viscosity 3. m S. Hydraulic head 4. m$^2$
The correct answer is
P-2; Q-4; R-1; S-3
Parameter Unit Matching Solution
This solution explains the matching between physical parameters and their standard units as presented in Group I and Group II.
Matching Parameters and Units
The correct matching is derived by understanding the definition and units of each parameter:
- P. Hydraulic conductivity: Represents the flow rate of a fluid under a unit hydraulic gradient. Its unit is a velocity, matching 2. m/sec.
- Q. Permeability: An intrinsic property of the porous medium, indicating its ability to transmit fluids. Its unit is length squared, matching 4. m$^2$.
- R. Viscosity: A measure of a fluid's resistance to flow. Dynamic viscosity has units of force per area per velocity gradient, matching 1. Newton sec./m$^2$.
- S. Hydraulic head: The measure of mechanical energy per unit weight of fluid, often expressed as a height of fluid, matching 3. m.
Final Match Summary
The confirmed pairings are:
- P - 2 (m/sec)
- Q - 4 (m$^2$)
- R - 1 (Newton sec./m$^2$)
- S - 3 (m)
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Important Questions from Hydrogeology (Darcy Flow/Flow Rate)
- A soil mass comprises two horizontal layers (of equal thickness and equal width) stacked one above the other. The hydraulic conductivities of the two layers are $5 \times 10^{-2}$ cm/s and $3 \times 10^{-2}$ cm/s. Considering Darcian flow of water and same hydraulic gradient for both the layers, the effective hydraulic conductivity of the soil mass in cm/s is ________ (rounded off to two decimal places).
- A cylindrical soil sample of 10 cm diameter is tested in a constant-head permeameter. A volume of 250 cm$^3$ of water is collected in 5 minutes when the constant-head difference between tapping points 15 cm apart is 5 cm. Considering Darcy flow, the absolute value of coefficient of permeability in cm/s is _________ ($\pi = 3.14$) [round off to 3 decimal places]
- For a productive alluvial aquifer with hydraulic conductivity = 105 m/day and hydraulic gradient = 0.01, the flow rate is _______ m/day. [round off to 2 decimal places]
- The cross section of a river channel is approximated by a trapezium. The river has an average channel width of 40 m and average depth of 3 m. If the average flow speed is 2 m/s, the discharge rate is __________ m³/s. [in integer]
- A constant-head permeability test was performed on a vertical sand column of height 40 cm and cross-sectional area of 25 cm². During the test, when the loss of head was 50 cm, the volume of water collected in 2 minutes was 300 cm³. Applying Darcy's law, the calculated coefficient of permeability of the sand column is __________ cm/sec. [round off to 2 decimal places]
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