Chapter 5, Problem 75P

A tank contains water (20°C) at an initial depth y₀ = 1 m. The tank diameter is D = 250 mm and a tube of diameter d = 3 mm and length L = 4 m is attached to the bottom of the tank. For laminar flow a reasonable model for the water level over time is

$\begin{array}{cc}\frac{dy}{dt}=-\frac{d^4\rho g}{32D^2\mu L}y& y(0)=y_0\end{array}$

Using Euler methods with time steps of 12 min and 6 min:

1. (a) Estimate the water depth after 120 min, and compute the errors compared to the exact solution

$y_{\text{exact}}\left(t\right)=y_0{e}^{-\frac{d^4\rho g}{32D^2\mu L}}$

1. (b) Plot the Euler and exact results.

P5.75