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

What is the relation between pressure and air speed in isentropic rela

1.	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» 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.

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