library(deSolve)
library(ggplot2)

# Load the outflow data from a CSV file
outflow_data <- read.csv("outflow_data.csv", header = TRUE)

# Extract the times and outflow rates
times <- outflow_data$Time
outflow <- outflow_data$Outflow

# Define the differential equation
tank_eqn <- function(time, state, parameters) {
  with(as.list(c(state, parameters)), {
    inflow_rate <- 2  # Inflow rate in liters per hour
    outflow_rate <- outflow[which(times == time)]  # Outflow rate in liters per hour
    dV_dt <- (inflow_rate - outflow_rate)  # Rate of change of volume in liters per second
    return(list(dV_dt))
  })
}

# Set initial conditions
V0 <- 1000  # Initial volume of the tank in liters

# Set parameters
params <- NULL

# Set time interval
times <- seq(0, max(times), by = 1)  # Time interval from 0 to the maximum time in the outflow data

# Solve the differential equation
out <- ode(y = V0, times = times, func = tank_eqn, parms = params)

# Plot the results
plot <- ggplot(data = data.frame(time = out[, 1], volume = out[, 2]), aes(x = time, y = volume)) +
  geom_line() +
  xlab("Time (s)") +
  ylab("Volume (L)") +
  ggtitle("Volume of Tank Over Time") +
  theme_minimal()

# Save the plot as a PDF file
ggsave("tank_volume.pdf", plot, width = 8, height = 6, dpi = 300)