Colebrook-White

Schrick-Noah_Project-2.R

@@ -154,5 +154,38 @@ I_Planck <- function(wavelength, temp){
 
 lam.vec <- seq(100,2000,len=70) 
 plot(lam.vec, I_Planck(lam.vec,5778), type = "l", lty = 1, 
-     xlab="wavelength (nm)", ylab="Energy Density", 	   			main="Wavelength peaks for different T (K)")
+     xlab="wavelength (nm)", ylab="Energy Density", 
+     main="Wavelength peaks for different T (K)")
 grid(NULL,NULL)
+
+## Part 4: Colebrook-White
+# Solve
+implicitFF <- function(Re,ed,x.guess,tol=1e-6){
+  if (Re<2000){
+    f0 <- 16/Re
+  } else { 
+    fun.4 <- function(x) {(-16*log10((ed/3.7)+(1.255/(Re*sqrt(x)))))^-2}
+    fun.4.string <- "(-16*log10((ed/3.7)+(1.255/(Re*sqrt(x)))))^-2"
+    fun.4.estimate <- findZeroRelax(fun.4,x.guess)
+    f0 <- fun.4.estimate[1]
+  }
+  # Plot
+  func.plot <- ggplot(data.frame(x=seq(0,2,.1)), aes(x)) + 
+    stat_function(fun=fun.4, aes(col=fun.4.string)) + 
+    geom_hline(aes(yintercept=0, col = "y=0"), show.legend=TRUE)+
+    geom_vline(aes(xintercept=fun.4.estimate[1], 
+                 col = "relaxation estimate"), show.legend=TRUE)+
+    ggtitle("Zero Function") +
+    xlab("x") + ylab("Zero Function") +
+    theme(text = element_text(size=20), plot.title = element_text(hjust = 0.5))
+  print(func.plot)
+  return(f0)
+}
+
+# 4a
+fa.estimate <- implicitFF(7000, 0.0001, 0.1)
+# 4b
+fb.estimate <- implicitFF(8000, 0.0001, 0)
+# 4c
+fc.estimate <- implicitFF(9000, 0.0001, 0)
+