# 	**Problem 8.1**
# At a tropical coastal aquifer the ground water is stagnant. The density
# of fresh water is 0.998 g/cm3 and that of the underlying salt water is 
# 1.024 g/cm3. If the fresh-water head is 14.2 ft above mean sea level,
# what is the depth to the salt-water interface?
density_fresh = 0.998 g/cm^3
density_salt = 1.024 g/cm^3
h_fresh = 14.2 ft
depth = density_fresh * h_fresh /(density_salt - density_fresh); ft

# 	**Problem 8.3**
# A coastal aquifer has a mean hydraulic conductivity of 2.61 m/day. The 
# density of fresh water is 1.000 g/cm3 and the density of underlying 
# saline water is 1.024 g/cm3. The ground-water discharge per unit width 
# of the coastline is 0.00345 m2/day.
Ko = 2.61 m/day
density_fresh = 1.0 g/cm^3
density_salt = 1.024 g/cm^3
q = 0.00345 m^2/day
Go = density_fresh / (density_salt - density_fresh)

# Part A: What is the depth to the salt-water interface at a point 125 m 
# inland?
x = 125 m
depth = sqrt( (Go^2 * q^2 / Ko^2) + (2*Go*q*x/Ko) ) # Eq. 8-5

# Part B: What is the elevation of the water table above mean sea level at 
# a point 125 m inland?
h = sqrt(2*q*x/(Go*Ko))   # Eq. 8-7

# Part C: What is the depth to the salt-water interface at the shoreline?
x=0 m
depth = sqrt( (Go^2 * q^2 / Ko^2) + (2*Go*q*x/Ko) ) # Eq. 8-5

# Part D: What is the width of the outflow face?
xo = -Go*q/(2*Ko)   # Eq. 8-6

# 	**Problem 8.5**
# The aquifer beneath a circular oceanic island has a mean hydraulic 
# conductivity of 312 ft/day. The amount of recharge is 0.00831 ft/day.
# The density of fresh water is 1.000 g/cm3 and the density of underlying
# saline water is 1.024 g/cm3. If the island is 8715 ft in diameter, what
# is the depth to the salt-water interface in the center of the island?
Ko = 312 ft/day
Wo = 0.00831 ft/day
density_fresh = 1.0 g/cm^3
density_salt = 1.024 g/cm^3
diameter = 8715 ft
radius = diameter/2
r = 0 ft
Go = density_fresh / (density_salt - density_fresh)
h_center = sqrt(Wo*(radius^2 - r^2)/(2*Ko*(1+Go))); ft  # Eq. 8-9
depth = Go*h_center; ft  # Eq. 8-1