A small wind tunnel is being built for studying insect flight. The first test section built has a uniform height h=0.1m and length ℓ=1m. During operation its walls are found to have boundary layers which effectively start at the inlet at x=0 (the BL growth is negligible in the rapid contraction).
1) During operation it is found that there's a slight but undesirable centerline velocity increase from the inlet to the outlet of the test section. For an inlet velocity of Vin=5m/s at sea level where ν=1.45×10−5m2/s, estimate the centerline outlet velocity Vout for the case of
(i) laminar boundary layers, assuming H=2.59
(ii) fully turbulent boundary layers, assuming H=1.5.
For both cases, for the purpose of estimating the boundary layer development you may assume a ue(x) distribution obtained via the simple inviscid model of Section 3.1. Then determine Vout using a more accurate model.
2) A new test section is designed to obtain a constant ue(x)=Vin=5m/s along the entire test section with laminar boundary layers. Determine the height function h(x), in meters, required to achieve this, with h(0)=0.1m and ℓ=1m. Enter numerical values with 3 significant digits.
3)What Vout will result when the tunnel inlet speed is reduced to Vin=3m/s on the new test section, still with laminar flow? Round your answer to three significant digits.
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