Page 306 - Aerodynamics for Engineering Students

288 Aerodynamics for Engineering Students

Also, from the isentropic flow relation Eqn (6.19) for compressible flow:

Equating these expressions for PI/&, and putting in the known values for AI, A2, v2 and a2
16vl [ 5 (334)2 1
1.25 x 240 1 v: - (240)2 2'5
= 1--
or

v1
A first approximation to v1 can be obtained by assuming incompressible flow, for which
v1 = 240 x 1.25/16 = 18.75m s-l

With this value, v:/557 780 = 0.0008. Therefore the second term within the brackets on the
right-hand side can be ignored, and
18.75/v1 = (1.1035)2'5 = 1.278

Therefore
v1 = 14.7ms-'
which value makes the ignored term even smaller.
Further
p1/p2 = 18.75/~1 = 1.278

and therefore
7
E = (2) = (1.278)'.4 = 1.410

Therefore
t)
PI -p2 =pz -- 1

= 101 325 x 0.410
= 41 500Nm-2

Then the reading of the manometer is given by
AP 41 500 x 2
r=--
hgsint9 - 1000 x 0.85 x 9.807
= 9.95 m

This result for the manometer reading shows that for speeds of this order a manometer using
a low-density liquid is unsuitable. In practice it is probable that mercury would be used, when
the reading would be reduced to 9.95 x 0.85113.6 = 0.62m, a far more manageable figure. The
use of a suitable transducer that converts the pressure into an electrical signal is even more
probable in a modem laboratory.