Step 1: Meaning of isentropic flow.
In gas dynamics, an isentropic flow is one in which the process is both adiabatic (no heat exchange with surroundings) and reversible. Because of this, the entropy remains constant and the stagnation (total) temperature does not change along the flow.
Step 2: Temperature–Mach number relation.
For an ideal (calorically perfect) gas, the relation between stagnation temperature \(T_0\), static temperature \(T\), and Mach number \(M\) is:
\[ \frac{T_0}{T} = 1 + \frac{\gamma - 1}{2} M^2 \]
Step 3: Effect of increasing Mach number.
Rewriting the equation for static temperature:
\[ T = \frac{T_0}{1 + \frac{\gamma - 1}{2} M^2} \]
Here, \(T_0\) remains constant in isentropic flow. As the Mach number \(M\) increases, the term \(\frac{\gamma - 1}{2} M^2\) becomes larger (since \(\gamma > 1\)). This increases the denominator, which causes the static temperature \(T\) to decrease.
Physically, this happens because part of the internal (thermal) energy of the gas is converted into kinetic energy as the flow accelerates.
Step 4: Final conclusion.
When the Mach number increases in an isentropic flow, the static temperature decreases.