Question

For a given airfoil, the critical Mach number is 0.8. Calculate the value of p/p[infinity]. at the minimum pressure point when M[infinity] = 0.8.

Answer 1

At the point of minimum pressure,
`(P)/(P_(\infty)) = 0.7095`

Solution:

As per the question;

Critical Mach no. for the air foil,
`M_(critical) = 0.8`

`M_(\infty)` = 0.8

Now, for the value of the minimum pressure point:

Pressure of the air foil is critical,
`P_(critical)` when
`M_(critical) = M_(\infty)`

Now,

`(P_(critical))/(P_(\infty)) = (P_(critical))/(P)* (P)/(P_(\infty))` (1)

When M = 1:

`(P_(critical))/(P) = ((5 - 1)/(2)M^(2) + 1)^{- (5)/(5 - 1)})`

`(P_(critical))/(P) = ((5 - 1)/(2)1^(2) + 1)^{- (5)/(5 - 1)} = 0.2532` (2)

When
`M_(\infty) = 0.8`:

`(P_(critical))/(P) = ((5 - 1)/(2)M_(\infty)^(2) + 1)^{- (5)/(5 - 1)})`

`(P_(critical))/(P) = ((5 - 1)/(2)* 0.8^(2) + 1)^{(5)/(5 - 1)} = 2.8016` (3)

Now, from the eqns (1), (2) and (3):

`(P)/(P_(\infty)) = 0.2532* 2.8016 = 0.7095`