In ToonVanDaele/hydranalytic: A Collection of Some Analytic Hydrological Equations

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List of formulas

Theis (1935)

$$ u^2 = \frac{S r^2}{4 Kh D t} $$

$$ s(r, t) = \frac{Q}{4 \pi Kh D} * W(u) $$

Dupuit

$$ s(r) = D - \sqrt{D^2 - (\frac{Q}{\pi Kh}) log(\frac{r0}{r})} $$

Edelman

$$ s(r,t) = h_0 (1 - erf(r \sqrt{\frac{S}{4 Kh D t}}) $$

peilverlaging

r <- c(1, 10, 50, 100)
edelman_s(r = r, S = 0.25, Kh = 7, D = 50, t = 1, h0 = -1)

Peilverhoging grafiek

library(tidyverse)
library(hydranalytic)

t <- c(1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121)
r <- seq(from = 0, to = 700, by = 10)
Kh <- 7
D <- 100
S <- 0.25

df <- expand.grid(t = t, r = r, Kh = Kh, D = D, S = S)
df <- df %>%
  rowwise() %>%
  mutate(s = edelman_s(r = r, S = S, Kh = Kh, D = D, t = t, 1))

ggplot(data = df, aes(x = r, y = s, group = t, colour = t)) + geom_line() +
  scale_y_continuous(breaks=seq(from = 0, to = 1, by = 0.2)) +
  scale_x_continuous(breaks=seq(from = 0, to = 700, by = 100))

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ToonVanDaele/hydranalytic documentation built on Dec. 25, 2021, 7:55 p.m.