Consider the air sampling probe of Prob. 9–52. If the upper and lower streamlines are 6.24 mm apart in the airstream far upstream of the probe, estimate the free stream speed V_{free stream}.

Data from Problem 52.

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. P9–52. A suction pump draws air through the probe at volume flow rate V̇ as sketched. For accurate sampling, the air speed through the probe should be the same as that of the airstream (isokinetic sampling). However, if the applied suction is too large, as sketched in Fig. P9–52, the air speed through the probe is greater than that of the airstream (superiso kinetic 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. P9–52) is W = 39.5 mm. The values of the stream function corresponding to the lower and upper dividing streamlines are ψ₁ = 0.093 m²/s and ψ_u = 0.150 m²/s, respectively. Calculate the volume flow rate through the probe (in units of m³/s) and the average speed of the air sucked through the probe.

FIGURE P9–52

Transcribed Image Text:

V = Vu Vfree stream Dividing streamlines V = V₁ Sampling probe Vavg