SI and English Units

1
SI and English Units

• SI
• - Mass kilogram
• - Length meter
• - time second
• English
• - Mass slug
• - Length foot
• - time second

2
(No Transcript)
3
Transmissivity

• The amount of water that can be transmitted
  horizontally through a unit width by the full
  saturated thickness of the aquifer under a
  hydraulic gradient of 1.
• T bK
• T transmissivity.
• b saturated thickness.
• K hydraulic conductivity.
• Multilayer gt T1 T2 Tn

4
Specific Storage

• Specific storage Ss amount of water per unit
  volume stored or expelled owing to
  compressibility of mineral skeleton and pore
  water per unit change in head (1/L).
• Ss ?wg(anß)
• a compressibiliy of aquifer skeleton.
• n porosity.
• ß compressibility of water.

5
Storativity of confined Unit

• S b Ss
• Ss specific storage.
• b aquifer thickness.
• All water released in confined, saturated aquifer
  comes from compressibility of mineral skeleton
  and pore water.

6
Storativity in Unconfined Unit

• Changes in saturation associated with changes in
  storage.
• Storage or release depends on specific yield Sy
  and specific storage Ss.
• S Sy b Ss

7
Volume of water drained from aquifer

• Vw SAdh
• Vw volume of water drained.
• S storativity (dimensionless).
• A area overlying drained aquifer.
• dh average decline in head.

8
Average horizontal conductivity Kh avg
?m1,n (Khmbm/b)
Kv avg
Kh avg
Average vertical conductivity Kv avg b /
?m1,n (bm /Kvm)
9
(No Transcript)
10
Grad h (dh/dx)2 (dh/dy)20.5
Y
? arctan ((dh/dy)/(dh/dx))
dh/dy
?
O
dh/dx
X
11
(No Transcript)
12
Forces

• Gravity pulls water downward.
• External pressure
• - Vadose zone atmospheric pressure
• - Saturation zone atmospheric water
• Molecular attraction.

13
Resisting Forces

• Shear stresses - shear resistance viscosity.
• Normal stresses.
• Friction Shear stresses Normal stresses.

14
Mechanical Energy

• Kinetic energy
• Ek ½ m v2 ML2/T2 slug-ft2/s2 or kg-m2/s2
• m mass M slug or kg
• v velocity L/T ft/s or m/s

15
Mechanical Energy

• Gravitational potential energy
• W Eg mgz. ML2/T2 slug-ft2/s2 or kg-m2/s2.
• z elevation L ft or m.
• g gravitational acceleration L/T2 ft/s2 or
  m/s2.

16
Pressure

• Pressure P F/A.
• P pressure M/LT2 slug/ft/s2 or (kg-m/s2)/m2.
• A is cross-sectional area perpendicular to the
  direction of the force (L2 ft2 or m2).
• F is force (ML/T2 slug-ft/s2 or kg-m/s2).
• P unit is Pascal (N/m2).
• P gt potential energy per unit volume.

17
Energy per unit mass

• Etm v2/2 gz P/?. (L/T)2

18
Hydraulic head, h

• Hydraulic head is energy per unit weight.
• h v2/2g z P/g?. L.
• Unit (L ft or m).
• v 10-6 m/s or 30 m/y for ground water flows.
• v2/2g 10-12 m2/s2 / (2 x 9.8 m/s2) 10-13 m.
• h z P/g?. L.

19
Hydraulic head, h

• h z P/g? z hp.
• z elevation.
• hp P/g? - pressure head height of water
  column.

20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
Head in water with variable density

• P2 ?fghf
• P1 ?pghp
• P2 P1
• ?fghf ?pghp
• hf (?p/?f )hp

24
(No Transcript)
25
Force potential and hydraulic head

• Force potential
• ? gz P/? gz ? ghp/ ? g(zhp)
• h z hp
• ? gh.
• g can be considered a constant head can be used
  to represent the force potential.
• Head controls the movement of ground water.

26
(No Transcript)
27
Darcys Law

• Q -KA(dh/dl).
• dh/dl Hydraulic gradient.
• dh change in head between two points separated
  by small distance dl.

28
Reynolds number

• R ?qd/µ.
• R - the Reynolds number (dimensionless).
• ? fluid density (M/L3 kg/m3).
• µ fluid viscosity (M/T-L kg/s-m).
• q discharge velocity (L/T m/s).
• d diameter of the passageway through which the
  fluid moves (L m).

29
Laminar flow (Small R lt 10)
Darcys Law Yes
Flow lines
Darcys Law No
Flow lines
Turbulent flow (Large R)
30
Specific discharge

• Q vA
• v Q/A -K dh/dl
• Specific discharge is also called Darcy flux.

31
Seepage (average linear) velocity

• vx Q/(neA) -K/ne dh/dl
• vx average linear velocity (L/T ft/s m/s).
• ne the effective porosity (dimensionless)

32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
Dupuit assumptions

• Hydraulic gradient is equal to the slope of the
  water table.
• For small water-table gradients, the streamlines
  are horizontal and equipotential lines are
  vertical.

36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40
Flow lines and flow nets

• A flow line is an imaginary line that traces the
  path that a particle of ground water would flow
  as it flows through an aquifer.
• A flow net is a network of equipotential lines
  and associated flow lines.

41
(No Transcript)
42
Boundary conditions

• No-flow boundary
• flow line parallel to the boundary.
• Equipotential line - intersect at right
  angle.
• Constant-head boundary
• flow line intersect at right angle.
• Equipotential line - parallel to the
  boundary.
• Water-table boundary
• flow line depends.
• Equipotential line - depends.

43
Constant head
h 40 feet
44
Estimate the quantity of water from flow net

• q Kph/f.
• q total volume discharge per unit width of
  aquifer (L3/T ft3/d or m3/d).
• K hydraulic conductivity (L/T ft/d or m/d).
• p number of flowtubes bounded by adjacent pairs
  of flow lines.
• h total head loss over the length of flow lines
  (L ft or m).
• f - number of squares bounded by any two
  adjacent flow lines and covering the entire
  length of flow.

45
(No Transcript)
46
(No Transcript)
47
(No Transcript)
48
(No Transcript)
49
(No Transcript)
50
(No Transcript)
51
(No Transcript)
52
(No Transcript)
53
(No Transcript)
54
(No Transcript)