Due: 01-30-06

1. Find the response in height in the tank H(s) to a step change of 0.1 m³/s in inflow Q₁(s) for the tank shown in the following schematic when the steady state level in the tank is at 1.5 meters. Determine the time constant for the system and plot the response using MATLAB™. The pump removes water at a rate of 0.1 m³/s independent of head. The valve resistance R is 0.05 s/m₂. The cross-sectional area of the tank is 2.4 m².

2. Determine the equation for the time constant for the liquid level system shown in the following schematic. Assume a linear valve resistance, R and a steady state inflow rate of 0.2 m³/s. The tank walls not shown are vertical.

3. Consider the following pond where a model of the fate of phosphorous is being modeled. An approach might be to model phosphorous incorporation by biological organisms in the pond as a simple first order reaction where:

P ----> P_biologically_incorporated at a rate of r = kC₂. Where: C₂ is the concentration of Phosphorous in the pond in moles of P/ m³, and r is the moles of P reacting/ m³-s. k is the reaction velocity constant. C₁ is the concentration of Phosphorous entering the pond in moles of P/ m³at a flowrate of q₁ m³/s. Find the transfer function relating P concentration in the pond to the inlet P concentration. Assume the pond is well mixed.