The formula to calculate the Mach number in an isentropic flow is:
\[ M = \sqrt{\left(\frac{2}{\gamma - 1}\right) \left(\left(\frac{P_t}{P}\right)^{\frac{\gamma - 1}{\gamma}} - 1\right)} \]
Where:
Isentropic flow is a concept in fluid dynamics that describes a fluid flow in which the entropy, a measure of disorder or randomness, remains constant. This condition is typically associated with idealized, reversible processes and is often used in thermodynamic analysis. In an isentropic flow, there is no heat transfer or friction, meaning that no energy is added or removed from the fluid, and no energy is lost due to friction. This results in the total energy of the fluid remaining constant. Isentropic flows are often used to model ideal gas behavior, and they are particularly useful in the study of supersonic and hypersonic flows, as well as in the design of nozzles and diffusers.
Let's assume the following values:
Using the formula:
\[ M = \sqrt{\left(\frac{2}{1.4 - 1}\right) \left(\left(\frac{200000}{100000}\right)^{\frac{1.4 - 1}{1.4}} - 1\right)} \approx 1.05 \]
The Mach number would be approximately 1.05.
Let's assume the following values:
Using the formula:
\[ M = \sqrt{\left(\frac{2}{1.4 - 1}\right) \left(\left(\frac{300000}{150000}\right)^{\frac{1.4 - 1}{1.4}} - 1\right)} \approx 1.05 \]
The Mach number would be approximately 1.05.