# Water Budget Equation

The quantity of water going through various individual paths of the hydrological cycle in a given system can be described by the continuity principle known as Water Budget equation or Hydrologic Equations.

The conservation of Mass is the most useful physical principle in hydrologic analysis and is required in almost all applied problem.

For a given catchment area in an interval of time Δt, the continuity equation for water is

Mass of water inflow – mass of water outflow = change in mass of water storage

If the density of water inflow, outflow and storage water are same, then

Volume of inflow water – Volume of outflow water = Change in storage volume of water

i.e.                                                          Vi – V0 = ΔS

For solving the problem of water budget equation we should be clear in mind, what factor recharges the water discharged in the water body.

Water Budget Equation for a Catchment

For a particular time Δt

P – R – G – E – T = ΔS

Water Budget Equation for Water Bodies

I + P – G – E – O = ΔS

Water Budget Equation for Surface Flow

P + I + IG – O – E – T – In = ΔS

Water Budget Equation for Underground Flow

IG + In – OG – OS – T = ΔS

Where,

P = Precipitation

R = Surface Runoff

G = Net ground water flow out of the catchment

E = Evaporation

T = Transpiration

ΔS = Change in storage = SS + SSM + SG

SS = Surface water storage

SSM = Water storage as soil moisture

SG = Water in storage as ground water

I = Inflow

O = Outflow

IG = Ground water come to the surface

In = Infiltration

OG = Ground water outflow

OS = Ground water come to the surface

Water Budget Equation in terms of rainfall runoff relationship can be represented as

R = P – L,              where, R = Runoff

P = Precipitation

L = Losses (infiltration, evaporation, transpiration and surface storage)

• For large catchment area, ground water inflow and outflow are almost equal.
• In general, after a long period the storage in catchment be same as prior.