Step 1: State the Fanno flow relation between two stations.
The Fanno flow function $4fL^*/D$ measures, in a dimensionless way, how far a given Mach number is from the sonic point $M=1$. Between any two stations 1 (inlet) and 2 (exit) of an actual duct of length $L$, the physical length traveled equals the difference between the two "distance-to-sonic" values:
\[ \frac{4fL}{D} = \left(\frac{4fL^*}{D}\right)_{M_1} - \left(\frac{4fL^*}{D}\right)_{M_2} \]
Step 2: Pull the two table entries.
$M_1 = 1.5 \Rightarrow 1361\times10^{-4}$; $M_2 = 1.1 \Rightarrow 99.35\times10^{-4}$. Difference: $(1361-99.35)\times10^{-4} = 1261.65\times10^{-4}$.
Step 3: Keep L and D in centimeters, since only their ratio matters.
$L/D$ is dimensionless, so unit conversion to meters is not actually needed; working directly in cm gives the same ratio:
\[ \frac{L}{D} = \frac{20 \text{ cm}}{3 \text{ cm}} = 6.667 \]
Step 4: Solve for f.
\[ f = \frac{1}{4}\left(\frac{D}{L}\right)\left[\left(\frac{4fL^*}{D}\right)_{M_1} - \left(\frac{4fL^*}{D}\right)_{M_2}\right] = \frac{1}{4}\left(\frac{3}{20}\right)(1261.65\times10^{-4}) \]
\[ f = (0.0375)(0.126165) = 0.0047312 \]
Final Answer:
\[ \boxed{f \approx 4.7\times10^{-3}} \]