Question

The point of maximum entropy on a Fanno-curve in a Temperature–Entropy (T–s) diagram represents the

• A. maximum flow Mach number
• B. minimum flow Mach number
• C. sonic Mach number
• D. normal shock in the flow

Hint:

In Fanno flow, friction pushes any flow (subsonic or supersonic) toward Mach 1. Maximum entropy always occurs at the sonic condition.

Answer 1

The Correct Option is C

In Fanno flow (adiabatic flow with friction through a constant-area duct), the T–s diagram shows the variation of entropy with temperature as Mach number changes. As friction increases, the entropy rises until a maximum point is reached. In Fanno flow theory:
- Subsonic flow accelerates due to friction.
- Supersonic flow decelerates due to friction.
- Both regimes tend toward $M=1$.
The point where entropy reaches its maximum corresponds to the choked condition, where the Mach number is exactly 1. Therefore, the maximum entropy point on the Fanno curve denotes the sonic Mach number, $M=1$.