Groundwater Hydraulics: Groundwater head & flow

Question 1

True or False
Fluid potential in a fluid flow through porous media is defined as the mechanical energy per unit mass of fluid.

Answer 1

True

Question 2

Fluid potential, denoted as ɸ, is calculated as gz + u^2/2 + ∫dP/ρ, where g represents _______, u is the velocity the fluid, and P is the pressure.

Answer 2

gravitational acceleration

Question 3

What does the hydraulic head, h, represent in fluid dynamics?
A) The velocity of the fluid
B) The pressure head plus the elevation head
C) The temperature gradient of the fluid

Answer 3

B) The pressure head plus the elevation head

Question 4

What does Darcy’s Law describe?

Answer 4

Darcy’s Law describes the flow of a fluid through a porous medium, quantifying the flow rate based on the hydraulic conductivity, the area perpendicular to flow, and the hydraulic gradient.

Question 5

True or False
According to Darcy’s Law, the flow rate q is directly proportional to the hydraulic gradient Δh/Δz.

Answer 5

True

Question 6

The hydraulic head in an observation well represents the average hydraulic head over the length of the _______ section of the well.

Answer 6

open

Question 7

Which device is used to directly measure the hydraulic head at a specific point in a groundwater system?
A) Dipper
B) Piezometer
C) Thermometer

Answer 7

B) Piezometer

Question 8

True or False
The water level in a piezometer always matches the water table level in unconfined conditions.

Answer 8

False

Question 9

A dipper used to measure hydraulic head in a well has a graduated tape and makes a sound when it touches _______.

Answer 9

water

Question 10

What is the purpose of the porous tip in a piezometer?

Answer 10

The porous tip allows water from the surrounding soil to enter the piezometer, enabling accurate measurement of the hydraulic head specific to that point.

Question 11

True or False
The hydraulic head is calculated as h = z_m − d_w, where z_m is the elevation to the top of the casing and d_w is the depth of the water.

Answer 11

True

Question 12

To measure the hydraulic head accurately, one must level in the casing to ensure the correct elevation of the top of _______.

Answer 12

casings

Question 13

How many piezometers are required to determine the direction of groundwater flow?
A) 2
B) 3
C) 4

Answer 13

C) 4

Question 14

What does the equation
h (t) = z_m − d_p + [P_p(t) − P_a(t)]/ρg describe?

Answer 14

It describes how the hydraulic head varies over time, accounting for the changes in pressure and elevation.

Question 15

True or False
The gradient of the hydraulic head can be calculated without assuming constant hydraulic conductivity in the location and direction.

Answer 15

False (It assumes constant hydraulic conductivity)

Question 16

The formula dh/ds = I = √(A^2 + B^2) is used to find the ______ gradient in an aquifer.

Answer 16

hydraulic head

Question 17

In steady flow within a confined aquifer, what is significant about the product
HK?
A) It represents hydraulic conductivity.
B) It is referred to as the aquifer transmissivity.
C) It indicates hydraulic head.

Answer 17

B) It is referred to as the aquifer transmissivity.

Question 18

True or False
In an unconfined aquifer under the Dupuit-Forchheimer assumption, there is a vertical head gradient.

Answer 18

False (The assumption is that there is no vertical head gradient, and flow is purely horizontal)

Question 19

The equation h^2-h_0^2 =0 W/K(Lx - x^2) + (h_1^2 - h_0^2)x/L describes the water table profile under _______ conditions.

Answer 19

steady flow in an unconfined aquifer with recharge

Question 20

What scenario does the model of two parallel ditches with vertical recharge illustrate in groundwater studies?

Answer 20

It models an unconfined aquifer with recharge and equal boundary conditions, showing the maximum water table height at the midpoint between the ditches.

Question 21

What is A in the question for calculating hydraulic head gradient?

Answer 21

A = ∂h/∂x

Question 22

What is B in the equation?

Answer 22

B = ∂h/∂y

Question 23

How do you find direction of flow?

Answer 23

θ = arctan(A/B)

Question 24

What are the units of transmissivity?

Answer 24

L^2T^-1

Question 25

Define fluid potential in the context of groundwater flow through porous media.

Answer 25

Fluid potential is the mechanical energy per unit mass of fluid.

Question 26

Name the three forms of energy that contribute to fluid potential in groundwater.

Answer 26

Potential energy (elevation), kinetic energy (velocity), and elastic energy (pressure).

Question 27

What is the formula for the total work done w_m on a unit mass of fluid?

Answer 27

w_m = gz + u^2/2 + ∫(P0 to P) dP/ρ

Question 28

Flow always occurs from regions of lower fluid potential to higher fluid potential. (True/False)

Answer 28

False

Question 29

Hydraulic head is calculated by adding ______ head and ______ head.

Answer 29

Elevation head and pressure head.

Question 30

Why can we assume pressure to be atmospheric in groundwater flow problems?

Answer 30

Because the reference pressure is set to atmospheric pressure.

Question 31

Provide the formula for hydraulic head h assuming incompressible fluid and negligible velocity.

Answer 31

h = z + P/ρg

Question 32

Velocities in porous media are generally large, justifying the inclusion of kinetic energy in groundwater calculations. (True/False)

Answer 32

False

Question 33

Who empirically established the law governing groundwater flow in porous media?

Answer 33

Henri Darcy.

Question 34

In Darcy's Law, the quantity q represents the _______ flux or specific discharge.

Answer 34

Darcy

Question 35

Write Darcy’s Law for volumetric flow rate Q in terms of cross-sectional area A and head loss Δh.

Answer 35

Q = -KA Δh/L

Question 36

In Darcy’s law, which of the following is NOT a correct unit for hydraulic conductivity? (m/s, L/T, m²/s, ft/day)

Answer 36

m²/s

Question 37

Define hydraulic gradient in groundwater flow.

Answer 37

Hydraulic gradient is the change in hydraulic head per unit distance, ∇h.

Question 38

Which material has the lowest hydraulic conductivity? (Gravel, Sand, Clay, Weathered granite)

Answer 38

Clay

Question 39

What is the typical porosity range for sand?

Answer 39

26% to 53%

Question 40

Hydraulic conductivity of sandstone is generally higher than that of siltstone. (True/False)

Answer 40

True

Question 41

What does the water level in an observation well represent in an unconfined aquifer?

Answer 41

The level of the prevailing water table.

Question 42

Define a piezometer in groundwater studies.

Answer 42

A piezometer measures hydraulic head at a specific point or small depth in the ground.

Question 43

What instrument is commonly used to measure water levels in boreholes?

Answer 43

Electric water level meter (Dipper).

Question 44

What is water level dipping?

Answer 44

The process of manually measuring the depth to water using a dipper.

Question 45

What surveying method is used to determine the elevation of the borehole top?

Answer 45

Levelling.

Question 46

Pressure head ψp is given by ψp = (Pp - Pa)/____.

Answer 46

ρg

Question 47

A level logger records both groundwater pressure and air pressure. (True/False)

Answer 47

False

Question 48

What must be subtracted from total pressure recorded in a groundwater logger to get the true pressure head?

Answer 48

Atmospheric pressure.

Question 49

What is the minimum number of piezometers needed to determine groundwater flow direction?

Answer 49

Four.

Question 50

Write Darcy’s Law in vector form.

Answer 50

q = -K ∇h

Question 51

In Darcy's vector form, K is best described as: (Constant scalar, Tensor, Vector, Energy term)

Answer 51

Tensor

Question 52

Locally assuming constant hydraulic conductivity means that ∂²h/∂x² = ____ and ∂²h/∂y² = ____.

Answer 52

0, 0.

Question 53

How many (x, y, h) measurements are needed to uniquely solve for hydraulic head gradient?

Answer 53

Three.

Question 54

What mathematical method is used when more than three measurements of head are available?

Answer 54

Least squares fit.

Question 55

Give the formula for magnitude of the hydraulic head gradient i.

Answer 55

i = √(A² + B²)

Question 56

Write the formula for the direction θ of the head gradient in degrees.

Answer 56

θ = arctan(A/B) × 180/π

Question 57

Groundwater flow is in the same direction as the head gradient. (True/False)

Answer 57

False

Question 58

Write the solution for steady confined flow discharge Q'.

Answer 58

Q' = HK(h1 - h0)/L

Question 59

What is the term for the product of hydraulic conductivity K and saturated thickness H?

Answer 59

Transmissivity T.

Question 60

The Dupuit-Forchheimer assumption assumes ______ head gradient and purely ______ flow.

Answer 60

No vertical head gradient, purely horizontal flow.

Question 61

Provide the final integrated expression for discharge in unconfined steady flow.

Answer 61

Q' = (K/L)(h1² - h0²)

Question 62

In the case of an unconfined aquifer with no recharge and almost equal boundary conditions, what approximation can you make about head difference?

Answer 62

h1 - h0 ≈ 0, thus Q' ≈ (T*/L)(h1 - h0)

Question 63

In agricultural drainage design, h_max must be: (Higher than the crop height, Lower than the critical crop depth, Equal to the recharge rate, Independent of soil properties)

Answer 63

Lower than the critical crop depth

Question 64

Write the expression to estimate spacing L for two drains with vertical recharge.

Answer 64

h_max² = h0² + (WL²)/(8K)

Question 65

In representing an alluvial aquifer, what does the 'groundwater divide' signify?

Answer 65

A boundary across which there is no flow.