Page 305 - Aerodynamics for Engineering Students

Compressible flow 287

(i) Since the maximum speed is 80 m s-l the flow may be regarded as incompressible. Then
= ~2A2
i.e.
VI x 16 = 80 x 1.25
giving
vl = 6.25ms-'
By Bernoulli's equation, and assuming standard temperature and pressure:

1
P1 +pv: =p2+;pv;
Then
1
PI -p2 =-p(4 - $) = 0.613(8d - 6.252)
2
= 0.613 x 86.25 x 73.25
= 3900 NmP2

This is the pressure across the manometer and therefore
Ap = pmgAh
where Ah is the head of liquid and pm the manometric fluid density, Le.
3900 = (1000 x 0.85) x 9.807 x Ah
This gives
Ah = 0.468 m
But
Ah = r sin B
where r is the manometer reading and B is the manometer slope. Then
1
0.468 = r sin 30" = - r
2
and therefore
r = 0.936 m
(ii) In this case the speed is well into the range where compressibility becomes important, and
it will be seen how much more complicated the solution becomes. At the smallest section,
T2 = 0°C = 273K
uz = (1.4 x 287.1 x 273$ = 334ms-'
From the equation for conservation of mass

PlAlVl = P2A2V2
i.e.

pi -42~2
-=-
P2 AlVl