Hooghoudt's Drainage Rate Equation and Calculator

Related Resources: calculators

Hooghoudt's Drainage Rate Equation and Calculator

Civil Engineering Application & Design Resources
Fluids Flow Design and Engineering

A drainage equation is an equation describing the relation between depth and spacing of parallel subsurface drains, depth of the water table, depth and hydraulic conductivity of the soils. It is used in drainage design. A well known steady-state drainage equation is the Hooghoudt drain spacing equation. Its original publication is in Dutch. The equation was introduced in the USA by van Schilfgaarde. In steady state, the level of the water table remains constant and the discharge rate (Q) equals the rate of groundwater recharge®, i.e. the amount of water entering the groundwater through the watertable per unit of time. By considering a long-term (e.g. seasonal) average depth of the water table (D_w) in combination with the long-term average recharge rate, the net storage of water in that period of time is negligibly small and the steady state condition is satisfied: one obtains a dynamic equilibrium.

Geometry subsurface drainage system
Hooghoudt Drain Spacing Equation

Eq. 1
Hooghoudt Drain Spacing Equation
Q = ( 8 · K_b · d · (D_d - D_w) + 4 · K_a · (D_d - D_w)² ) / L²

Eq. 2
Equivalent Depth
d = πL / 8 { ln(L/πr) + F(x) }

Eq. 3
x = 2π (D_i − D_d) / L

Eq. 4
F(x) = Σ 4e −2nx / n (1 − e −2nx ), with n = 1, 3, 5,

Where:

Q = steady state drainage discharge rate (m/day)
K_a = hydraulic conductivity of the soil above drain level (m/day)
K_b = hydraulic conductivity of the soil below drain level (m/day)
D_i = depth of the impermeable layer below drain level (m)
D_d = depth of the drains (m)
D_w = steady state depth of the watertable midway between the drains (m)
L = spacing between the drains (m)
d = equivalent depth, a function of L, (D_i-D_d), and r
r = drain radius (m)

Reference:

S.B.Hooghoudt, 1940 (in Dutch). Algemene beschouwing van het probleem van de detailontwatering en de infiltratie door middel van parallel loopende drains, greppels, slooten en kanalen . No. 7 in de serie: Bijdragen tot de kennis van eenige natuurkundige grootheden van den grond. Bodemkundig Instituut te Groningen. Rijksuitgeverij Dienst van de Nderlandse Staatscourant. 's-Gravenhage, Algemeene Landsdrukkerij.

Storm Drain Pipe Size Requirement Formula and Calculator
Rainfall Runoff Rate On Minor Size Land Formulas and Calculator
Storm Drains Junction Losses Calculation For adjoining pipes to be considered a pipe junction, the node and only two inflow pipes (a lateral and a trunk) may enter the junction.
Pipe Exit Loss Equation The exit loss, ho, is a function of the change in velocity at the outlet of the pipe as
Rainfall Intensity and Peak Storm Water Runoff Rate Equations and Calculator Rainfall Intensity and Peak Storm Water Runoff Rate for proper design of drainage requirements.
Pressure on Submerged Curved Surfaces Equation Hydrostatic pressure on a submerged curved surface
Fluid Flow Open Channel Calculator calculator uses Chezy and Manning's equation to determine the wetted perimeter, hydraulic radius, flow area, Chezy coefficient and flow velocity.
Hydrostatic Pressure Force of a Fluid On Vessel Planes Equations The hydrostatic force of pressure F is that force which is exerted on the wall by the fluid only - i.e. without consideration of pressure p 0 .
Hydrostatic Discharge of Liquid From Vessel Bottom Equations and Calculator