Question

What is the relation between pressure and air speed in isentropic relations?

(a) \(\frac{p_1}{p_2}\)=\(\Big\{1+\frac{\gamma-1}{2}(\frac{V1}{a1})^2\Big\}^\frac{\gamma}{\gamma-1}\)

(b) \(\frac{p_1}{p_2}\)=\(\Big\{1+\frac{\gamma+1}{2}(\frac{V1}{a1})^2\Big\}^\frac{\gamma}{\gamma+1}\)

(c) \(\frac{p_1}{p_2}\)=\(\Big\{1+\frac{\gamma+1}{2}(\frac{V1}{a1})^2\Big\}^\frac{\gamma}{\gamma-1}\)

(d) \(\frac{p_1}{p_2}\)=\(\Big\{1+\frac{\gamma-1}{2}(\frac{V1}{a1})^2\Big\}^\frac{\gamma}{\gamma+1}\)

I got this question in examination.

My question is based upon Measurement of Airspeed topic in division Atmosphere and Air Data Measurement of Aircraft Performance

Answer 1

Correct option is (a) \(\frac{p_1}{p_2}\)=\(\Big\{1+\frac{\gamma-1}{2}(\frac{V1}{a1})^2\Big\}^\frac{\gamma}{\gamma-1}\)

The explanation: The relation between pressure and air speed in isentropic relations is

\(\frac{p_1}{p_2}\)=\(\Big\{1+\frac{\gamma-1}{2}(\frac{V1}{a1})^2\Big\}^\frac{\gamma}{\gamma-1}\) where p1, p2 are pressures at two points, V1=velocity at one point, a1=speed of sound at point one and γ is the ratio of specific heat at constant pressure to that of specific heat at constant volume.