Question 6.0:
Figure 6 shows a system for measuring the pressure of exploding gases inside a steel chamber. A computer is used to measure the
pressure. The pressure sensor has a transfer function of $V_r = 0.05p + 500$ and a first-order time constant of '$\tau$'. When an
explosion occurs, the pressure rises virtually instantaneously from 0 psi to some maximum, $P_{max}$ (psi). At $t = 0$, the explosion occurs,
and the computer must take a reading at 't' in seconds and determine the pressure, $P_{max}$. This is before the sensor signal has stabilized.
(i)Explain how $P_{max}$ can be determined from a measurement taken at 't' sec.
(ii)Suppose the sensor signal at 't' sec is 1.45 volts. What is the value of $P_{max}$?
(iii) Suppose $P_{max}$ is equal to 2500 psi, what value will the sensor voltage have at 1.0 sec?
(iv) What equations will the computer be programmed to use in order to find $P_{max}$
from the sensor voltage taken at 't'?
[3]
[4]
[4]
[4]
[Total 15 marks]
Table 6
$\tau$ (sec)
t (sec)
4
24
Valve
Valve
Pressure
chamber
Figure 6
