Page 298 - Aerodynamics for Engineering Students

280 Aerodynamics for Engineering Students

Example 6.1 In streamline airflow near the upper surface of an aeroplane wing the velocity
just outside the boundary layer changes from 257 km h-’ at a point A near the leading edge to
466 kmh-’ at a point B to the rear of A. If the temperature at A is 281 K calculate the
temperature at B. Take 7 = 1.4. Find also the value of the local Mach number at the point B.
(LU)
Assume that the flow outside the boundary layer approximates closely to quasi-one-dimen-
sional, isentropic flow.
Then

UA = 72.4fi and TA = 8 + 273 = 281 K
UA = 1215kmh-’

1
-_ - 1 + - [0.2122 - 0.385’1 = 0.979 = 1 - 0.021
TB
TA 5
Therefore
TB = 0.979 x 281 = 275K = temperature at B
UB = 72.4&% = 1200 km h-’
MB=-- 466 -0.386
1200

Example 6.2 An aerofoil is tested in a high-speed wind tunnel at a Mach number of 0.7 and at
a point on the upper surface the pressure drop is found to be numerically equal to twice the
stagnation pressure of the undisturbed stream. Calculate from first principles the Mach
number found just outside the boundary layer at the point concerned. Take y = 1.4. (LU)
Let suffix 30 refer to the undisturbed stream. Then, from above,

with = 1.4, this becomes
5a2, + 2, = 52 + 3
Dividing by 2,

but