The rate of discharge of percolating water per unit cross-sectional area of voids perpendicular to the direction of flow is called:

This question was previously asked in

PGCIL DT Civil 2018 Official Paper

Option 4 : seepage velocity

__Concept:__

Apparent velocity (V):

- It is called apparent velocity because the actual flow is through pores in the cross-section and not through the entire cross-sectional area.
- It is also called discharge velocity (V)

Seepage velocity (Vs):

- The
**rate of discharge of percolating water per unit cross-sectional area of voids**perpendicular to the direction of flow is called Seepage velocity. - The velocity of water through pores is called seepage velocity (VS). As the flow is continuous, discharge Q must be the same throughout the system

Q = A × V = AV × Vs

Where,

A = total cross-sectional area,

AV = area of voids in the total cross-sectional area

\({\rm{V}} = \frac{{{{\rm{A}}_{\rm{V}}}}}{{\rm{A}}} \times {{\rm{V}}_{\rm{s}}}\)

The porosity of soil is given by,

\({\rm{n}} = \frac{{{\rm{volume\;of\;void}}}}{{{\rm{total\;volume}}}} = \frac{{{{\rm{A}}_{\rm{V}}} \times {\rm{L}}}}{{{\rm{A}} \times {\rm{L}}}} = \frac{{{{\rm{A}}_{\rm{V}}}}}{{\rm{A}}}{\rm{\;}}\)

V = n × Vs

\(\therefore {{\bf{V}}_{\bf{s}}} = \frac{{\bf{V}}}{{\bf{n}}}\)

As porosity (n) ranges between 0 < n < 1

\( \frac{V}{V_S} <1 \)

Hence, \(V_s>V\)

Seepage velocity (Vs) is always greater than or equal to discharge velocity.