HW#1
1) For the calibration data of the Table below, determine the static sensitivity of the system at (a)
x=5; (b) x=10; (c) x=20. For which input values is the system more sensitive? Explain what this
might mean in terms of a measurement and in terms of measurement errors.
X [cm]
Y [V]
0.5
0.4
1.0
1.0
2.0
2.3
5.0
6.9
10.0
15.8
20.0
36.4
50.0
110.1
100.0
253.2
2) The following data have the form Y = aXb . Plot the data in an appropriate format to estimate
the coefficients a and b. Estimate the static sensitivity K at each value of X. How is K affected by
X?
X[cm] Y[cm]
0.5
0.14
2.0
2.51
5.0
15.30
10.0 63.71
3) The relation between the flow rate through a pipeline of area, A, and the pressure drop, p,
across an orifice-type flow meter inserted in that line is given by
Q  CA
2 p

For a pipe diameter of 1 m and a flow range of 20C water between 2 and 10 m3/min and
C=0.75, plot the expected form of the calibration curve for flow rate versus pressure drop over
the flow range. Is the static sensitivity a constant?