Question

Does the Mach number of a gas flowing at a constant velocity remain constant? Explain.

Short answer

Why or why not? Answer: It is unlikely that the Mach number of a gas flowing at a constant velocity remains constant. This is because the Mach number depends on the ratio of the gas flow velocity to the speed of sound in the medium. The speed of sound in a gas medium can be affected by several factors, such as temperature and composition. In a dynamic system, it is difficult to maintain constant temperature and gas composition, causing the speed of sound to vary and thus altering the Mach number.

Step-by-step solution

Definition of Mach Number

The Mach number is the ratio of the velocity of an object or gas flow (\(v\)) to the speed of sound in that medium (\(a\)), which is given by the formula: M = \(\frac{v}{a}\)

Factors affecting speed of sound in a gas

The speed of sound in a gas is affected by several factors, including temperature and composition. The speed of sound in a gas medium can be given by the following formula: \(a = \sqrt{γ * R * T}\) where, - \(γ\) is the adiabatic index or the ratio of specific heats (constant pressure to constant volume), - \(R\) is the specific gas constant, - \(T\) is the gas temperature.

Can the Mach number remain constant?

Since we have a gas flowing at a constant velocity (\(v\)), we need to determine if the speed of sound (\(a\)) in the gas medium will change or not. For the Mach number to remain constant, the speed of sound in the gas should also remain constant. That means, any factor affecting the speed of sound (like temperature or composition) should not change. In reality, it is difficult to maintain the constant temperature and gas composition in a dynamic system. So, even if the gas flows at a constant velocity, the speed of sound in the medium can vary, causing the Mach number to change. In conclusion, it is unlikely that the Mach number of a gas flowing at a constant velocity remains constant due to variations in speed of sound, which is affected by changing temperature and gas composition in a dynamic system.