WATER MOVEMENT
Water is a dynamic component in soil, varies with depth and time
Water movement for a particular period depends on
1. Supply of water: Rainfall, irrigation, flood, dews
2. Demand of water: uptake, evaporation, storage/retention, percolation
Principles of water movement
Water can move in all three phases- solid, liquid, gas/vapour
In saturated soil: liquid phase
In unsaturated soil: liquid and vapour phases
Frozen soil close to clay surface: solid phase
Law of fluid flow governs water movement in liquid and vapour
phases
In saturated or flooded soils the flow velocity (due to gravity)
depends on the height of water
Type of flow
3. Laminar flow: Flow like sheet with uniform velocity throughout
Each parcel of flow is parallel to adjacent one
Streamline flow
4. Turbulent flow: movement is radially and axially i.e., erratic
forming cross currents and eddies. Whirls develop.
Reynolds number
v = velocity of water
r = radius of pore
SATURATED WATER FLOW
All pores are filled with water, i.e., volumetric water content is equal to
porosity (θ = θs with θs = f )
Non-equilibrium i.e. Water flows from points of high to points of lower
total water potential
Total water potential is sum of gravitational and soil water pressure
potential, or ΨT =Ψp + Ψz or H = h + z
Consider steady-state water flow. i.e., water flow does not cause changes
in water storage values (constant flow rate and volumetric water content
at any position (x) does not change with time). This is opposite to
transient water flow where H and θ change as a function of time.
Poured water = Discharged water Poured water > Discharged water
Water level remains to be constant Water level changes over time
Steady state Transient state
Water flow in capillary tube: Poiseuille’s equation
ΔP = ρwgh = ρwgL
Assumptions of Poiseuille’s law
The flow is steady and streamline (never cross each other).
The pressure is constant over every cross section i.e., there is no
radical flow.
The liquid in contact with the sides of the tube is stationary.
The law is applicable in cylindrical capillary tubes in soils.
Darcy’s law
Darcy’s law
Assumptions of Darcy’s law
The medium is porous
Flow is laminar/ steady state
NRe<1
No attraction between fluid and colloidal materials
Temperature remains constant
The fluid is incompressible
Flux, flow velocity, and tortuosity
Flux = flow/ unit are/ unit time = q =V/At Tortuosity
Flow velocity = pore water velocity = qp T = LT/L
Q = V/t = As × qs for soil and Q = Ap × qp for pore
The ratio of the average
roundabout path to the
apparent, or straight, flow path
Hydraulic conductivity, permeability, and fluidity
K = kf m/sec (LT−1)
fluidity (f) = ρwg/ m−1 sec−1 (L−1T−1)
intrinsic permeability (k) = K /ρwg m2 (L2)
Factors affecting K:
• Texture • Pore size
• Structure • OM
• Compaction • Temperature
• Pressure
Limitations of Darcy’s law
No attraction between pore space geometry and passage of liquid but all
soils contain some colloidal material which does interact with the fluid and
changes the pore geometry of the soil.
In coarse-textured soils (e.g., coarse sands
and gravels), hydraulic gradients above
unity may cause turbulence or non-laminar
flow conditions.
In clayey soils, low hydraulic gradients may
result in no flow or small change in flow, which
is not proportional to the applied hydraulic
gradient.
What sign for the gradients? Direction of flow + or –
Saturated flow equations:
Continuity Equation:
It describes the conservation of liquid mass of water during flow through a porous
media. The mass conservation law, expressed in the equation of continuity, states that
if the rate of inflow into the volume element exceeds the rate of outflow, then the
volume element must be storing the excess and increasing its water content.
Conversely, if outflow exceeds inflow, storage must be decreasing.
This equation is known as the continuity equation. For saturated flow, the rate of change of water content with respect
to time is zero.
Laplace equation:
Transferring Darcy’s equation into the right-hand side of the continuity equation for each
direction of flow separately results in a three-dimensional partial differential equation known
as the Laplace equation. The mathematical form of the Laplace equation is as follows:
If soil is isotropic, then the conductivity will be same in three dimensions (Ksx = Ksy = Ksz) and
the equation reduces as:
For a saturated soil, the net rate of change of soil moisture, on the left side of the equation is
zero, and after rearranging the Laplace equation reduces it to
Saturated hydraulic conductivity
Constant Head Method
Falling head method
or,
where b=b0 at t=0 and b=b1 at t=t1
Integrating the equation between the limits t1, H1 to t2, H2 and solving for Ks at time t1:
Derive the expression for Ks, if the area of the water-filled tube (a) is much smaller than the
area of the soil column (A)
Solve: A 100 cm long soil column is saturated and 10 cm of
water is ponded over the top at t = 0 in a vessel that has the
same cross sectional area as the column. At t = 1 hr the height of
overlying water has fallen to 5 cm. Calculate Ks in cm/d.
Flow system in inclined plain
Hydraulic head at point A = h1 + (-z1)
Hydraulic head at point B = h2 + (-z2)
ΔH = (h1-z1) - (h2-z2)
ΔH/L = ((h1-z1) - (h2-z2))/L
KΔH/L = q = K((h1-z1) - (h2-z2))/L
q = K((h1-h2) - (z1-z2))/L
