10.1. Modified Newtonian theory
Modification to the above mentioned Newtonian theory has been proposed by Laster Lees where,
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10.1 |
Since 
Since Rayleigh Pitot tube formula is
But we know that,
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10.2 |
For high Mach numbers the above expression reduces to,
Coefficient of sin2θ is 1.839 for γ = 1.4 and 2 for γ = 1. However in practical situations as well when M∞ becomes very large γ tends to 1 which in turn results in the expected Newtonian theory arrangement.Results of modified Newtonian theory holds good for blunt body configuration, since this theory predicts exact pressure at stagnation point.
10.2. Newtonian-Busemann theory
This theory modifies basic Newtonian theory with implementation of centrifugal correction. The force or pressure predicted by Newtonian theory is appropriate for hypersonic situations if we have slender configuration like wedge or cone. The force balance for a fluid particle in the presence of centrifugal force is shown in Fig. 10.1. However, if we have blunt nosed configuration then the pressure on the wall should be lower than that of predicted by Newtonian theory by the virtue of centrifugal force applied on the fluid particle as shown in Fig. 10.1.