§AERE 261 Homework 10

Sep 25, 2025

§1.

Asingle inlet=0.16m2 A_\text{single inlet}=0.16m^2
Aturbofan=0.29m2 A_\text{turbofan}=0.29m^2
V∞=68m/s V_\infty=68m/s

§1. (a)

Qsingle inlet=V∞Asingle inlet=68m/s∗0.16m2=10.9m3/s Q_\text{single inlet}=V_\infty A_\text{single inlet}=68m/s * 0.16m^2=\boxed{10.9m^3/s}

§1. (b)

Qturbofan=Q=2Qsingle inlet=2∗10.9m3/s=21.8m3/s Q_\text{turbofan}=Q=2Q_\text{single inlet}=2 * 10.9m^3/s=\boxed{21.8m^3/s}

§1. (c)

Q=VA Q=VA
V=QA V=\frac{Q}{A}
Vturbofan=QAturbofan=21.8m3/s0.29m2=75.2m/s V_\text{turbofan}=\frac{Q}{A_\text{turbofan}}=\frac{21.8m^3/s}{0.29m^2}=\boxed{75.2m/s}

§1. (d)

Vturbofan=75.2m/s>V∞=68m/s  ⟹  the air accelerated V_\text{turbofan}=75.2m/s>V_\infty=68m/s\implies\boxed{\text{the air accelerated}}

§2.

h=2000m h=2000m
W0=16481N W_0=16481N
S=22.9m2 S=22.9m^2
CL,max=1.37 C_{L,max}=1.37

§2. (a)

Point A measures the static pressure.

§2. (b)

Point B measures the total pressure.

§2. (c)

V∞=89.5m/s V_\infty=89.5m/s
From appendix A for h=2000mh=2000m:
ρ∞=1.0066kg/m3 \rho_\infty=1.0066kg/m^3
pstatic=p∞=7.9501∗104Pa=79501Pa p_\text{static}=p_\infty=7.9501*10^4Pa=\boxed{79501Pa}

§2. (d)

12ρ∞V∞2=Ptotal−P∞ \frac{1}{2} \rho_\infty V_\infty^2 = P_\text{total} - P_\infty
Ptotal=12ρ∞V∞2+P∞=12∗1.0066kg/m3∗(89.5m/s)2+79501Pa=83530Pa P_\text{total} = \frac{1}{2} \rho_\infty V_\infty^2 + P_\infty = \frac{1}{2} * 1.0066kg/m^3 * (89.5m/s)^2 + 79501Pa = \boxed{83530Pa}

§2. (e)

Vstall=2Wρ∞SCL,max=2∗16481N1.0066kg/m3∗22.9m2∗1.37=32.31m/s V_{stall}=\sqrt{\frac{2 W}{\rho_\infty S C_{L,max}}}=\sqrt{\frac{2 * 16481N}{1.0066kg/m^3 * 22.9m^2 * 1.37}}=\boxed{32.31m/s}

§2. (f)

The static pressure remains the same.
pstatic=79501Pa p_\text{static}=\boxed{79501Pa}

§2. (g)

Ptotal=12ρ∞V∞2+P∞=12∗1.0066kg/m3∗(32.31m/s)2+79501Pa=80026Pa P_\text{total} = \frac{1}{2} \rho_\infty V_\infty^2 + P_\infty = \frac{1}{2} * 1.0066kg/m^3 * (32.31m/s)^2 + 79501Pa = \boxed{80026Pa}