Movement of Soil Water (With Equation)

1. Torricelli’s Equation:

When the water level falls through a distance Z, the velocity of its flow (v) at depth z, as described by Torricelli’s equation, is equal to the velocity acquired by water due to the fall of water level.

2. Bernoulli’s Equation:

In flooded or saturated soil when water moves under hydrostatic pressure difference through a uniform horizontal pore, the energy state of water at any point is characterised by (a) velocity (v), (b) mass density (p), pressure (P), and height above the reference level (z).

The pressure of water decreases with an increase in distance due to friction and the loss in pressure head due to friction is called friction head (h_f) which is proportional to the square of the velocity, as follows:

h_f = Kv²

The drop in the potential energy due to fall in water level is converted to kinetic energy and such fall in water level is known as velocity head (h_v), as given below:

h_v = v²/2g

The final pressure head (h_p) along the length of the pore will be initial maximum hydrostatic pressure minus the loss in pressure head due to friction and velocity, which expressed as,

hp = h – (h_v +h_f)

At any point on the flow path, the energy state of water, either potential or kinetic remains constant. The sum of the pressure head (h_p = P/P_wg), potential head (mgz/mg = z) and velocity head (v²/2g) remains constant and such relation is known as Bernoulli’s equation as represented by,

Z + v²/2g + P/P_wg = C

3. Poiseuille’s Law:

Poiseuille’s law states that flow of water through a narrow tube is directly proportional to the fourth power of its radius and pressure difference, and inversely proportional to the viscosity and length of the tube, which is given by,

q = Ï€r⁴/8Æž (∆P/L)

where, ∆P = pressure difference (dynes/cm²)

r = radius of the tube (cm)

L = length of the tube (cm)

Æž = co-efficient of viscosity of the liquid (dyne-sec-cm², poise).