A = 1.94.hmax = 0.559.R = 206 1. Filling the tank (30%) a) If the tap on the output pipe is closed (i.e. R = ∞) determine how long it will take the tank to fill up assuming qi = 0.001 m3/s. b) If the tap on the output is open liquid will be coming out at the same time as liquid is going in. If the flow rate in is bigger than flow rate out the height of the liquid in the tank will rise. Using the R value given on the Results Sheet, determine the steady state height of liquid in the tank assuming qi = 0.001 m3/s. c) In theory it will take an infinite amount of time to achieve steady state so in practice we define the time to respond as the 95% settling time (i.e. the time taken to get to within 5% of the steady state output.) Measure the 95% settling time from your simulation in Q1b)

 

2. Emptying the tank (10%)
a) Assuming the tank is initially full (i.e. h(0) = hmax) and the input is turned off (i.e. qi = 0) the tank will
start to empty. Assuming the R value in Q1b), determine the time taken to get to half empty, t1/2. (Hint:
if you double click the integrator, you change the initial value of the output of the integrator.)

 

3. Theory (30%)
a) The gain of a system is defined as the Steady State Output divided by the input. Determine K assuming
the value of R given in Q1b).
b) In theory it takes one Time Constant to reach 63% of the steady state output. Using the time
response in Q1b), measure the time constant.
c) Hence write down the Transfer Function for the system in standard form.
4. Manual Control (30%)
a) Whilst you cannot physically change the dimensions of the tank you can change the speed of response
by turning the tap to adjust the flow rate out. i.e. adjust the R value. If the desired 95% settling time
is to be the value given on the result sheet, use your simulation to determine the R value required to
achieve this.
b) Using the new R value in Q4a), determine the new Time Constant.
c) Using the new R value in Q4a), determine the new Gain of the system