The level in a tank responds as a first-order system with changes in the inlet flow. Given
the following level versus time data that were gathered (Fig. P4–16) after the inlet flow was increased quickly from 1.5 to 4.8 gal/min, determine
the transfer function that relates the height
in the tank to the inlet flow. Be sure to use deviation
variables and include units on the steady-state
gain and the time constant.

Time (min) Level (ft)
0 4.8
0.138 5.3673
0.2761 5.9041
0.4141 6.412
0.5521 6.8927
0.6902 7.3475
0.8282 7.7779
0.9663 8.1852
1.1043 8.5706
1.2423 8.9354
1.3804 9.2805
1.5184 9.6071
1.6564 9.9161
1.7945 10.2085
1.9325 10.4853
2.0705 10.7471
2.2086 10.9949
2.3466 11.2294
2.4847 11.4513
2.6227 11.6612
2.7607 11.8599
............ ............
14.3558 15.3261
14.4938 15.328
14.6319 15.3297
14.7699 15.3313