GATE 2026 AE – Question 65
A Mach 1.5 air flow enters a round duct of length 20 cm and diameter 3 cm. If the flow exits with Mach number 1.1, the average Fanning friction factor $f$ of the duct is ________ $\times 10^{-3}$ (rounded off to 1 decimal place).
An excerpt from the Fanno flow table for air is given below.
| M | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 |
|---|---|---|---|---|---|---|
| $\frac{4fL^*}{D} \times 10^4$ | 99.35 | 336.4 | 648.3 | 997.4 | 1361 | 1724 |
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Correct answer: 4.68 to 4.72
Explanation
The length of duct between two Mach numbers uses the difference of $\frac{4fL^*}{D}$: $\frac{4fL}{D} = (0.1361) - (0.009935) = 0.12617$. With $L = 0.2$ m and $D = 0.03$ m, $f = 0.12617 \times \frac{0.03}{4 \times 0.2} = 4.73 \times 10^{-3}$, so 4.7.