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).
Use the following case-sensitive typed names for the various symbols.
Symbol
x
()−−√
Typed
x
sqrt( )
CONSTANT CROSS-SECTION (2 points possible)
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.
Hint: Use the average skin friction coefficient, C¯f, following section 4.13 in the book.
For case 1(i), give Vout in m/s with 3 significant digits.
laminar Vout=- unanswered
For case 1(ii), give Vout in m/s with 3 significant digits.
turbulent Vout=- unanswered
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VARIABLE CROSS-SECTION (2 points possible)
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.
h(x)=- unanswered
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.
Vout=- unanswered
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