Chapter 9, Problem 51P

In the field of air pollution control, one often needs to sample the quality of a moving airstream. In such measurements a sampling probe is aligned with the flow as sketched in Fig. 9-51. A suction pump draws air through the probe at volume flow rate V as sketched. For accurate sampling, the air speed through the probe should be the same as that of the airstream (isokinetic samp ling). However if the applied suction is too large, as sketched in Fig. 9-51, the air speed through the probe is greater than that of the airstream (superisokinetic sampling). For simplicity consider a two-dimensional case in which the sampling probe height is h = 4.58 mm and its width (into the page of Fig. 9-51)is W= 39.5 mm. The values of the stream function corresponding to the lower and upper dividing streamlines are ${\psi }_1=0.093{\text{m}}^2/\text{s}$ and ${\psi }_u=0.150{\text{m}}^2/{\text{s}}_z$ , respectively. Calculate the volume flow rate through the probe (in units of ${\text{m}}^3/\text{s}$ ) and the average speed of the air sucked through the probe.

Answers: $\text{0}{\text{.00225 m}}^3/\text{s, 124}\text{.4m/s}$