Chapter 9, Oblique Shock and Expansion Waves Video Solutions, Fundamentals of Aerodynamics

Problem 1

A slender missile is flying at Mach 1.5 at low altitude. Assume the wave generated by the nose of the missile is a Mach wave. This wave intersects the ground $559 \mathrm{ft}$ behind the nose. At what altitude is the missile flying?

Penny Riley

Numerade Educator

03:07

Problem 2

Consider an oblique shock wave with a wave angle of $30^{\circ}$ in a Mach 4 flow. The upstream pressure and temperature are $2.65 \times 10^4 \mathrm{~N} / \mathrm{m}^2$ and $223.3 \mathrm{~K}$. respectivcly (corresponding to a standart altitude of $10,000 \mathrm{~m}$ ). Calculate the pressure, temperature. Mach number, total pressure, and total temperature behind the wave and the entropy increase across the wave.

Khoobchandra Agrawal

Numerade Educator

Problem 3

Equation (8.80) does not hold for an oblique shock wave, and hence the column in App. B labeled $p_{0.2} / p_{\text {, }}$ cannot he used, in conjunction with the normal component of the upstream Mach number, to obtain the total pressure behind an oblique shock wave. On the other hand. the column labeled $p_{4,2} / p_{n_2,}$ can be used for an oblique shock wave, using $M_{\text {..1. }}$. Explain why all this is so.

Check back soon!

View

Problem 4

Consider an oblique shock wave with a wave angle of $36.87^{\circ}$. The upstream flow is given by $M_1=3$ and $p_1=1 \mathrm{~atm}$. Calculate the total pressure behind the shock using
(a) $p_{0,2} / p_{0,1}$ from App. B (the correct way)
(b) $p_{0.2} / p_1$ from App. B (the incorrect way)

Compare the resulis.

Victor Salazar

Numerade Educator

04:57

Problem 5

Consider the flow over a $22.2^n$ half-angle wedge. If $M_1=2.5, p_1=1 \mathrm{~atm}$, and $T_1=300 \mathrm{~K}$, calculate the wave angle and $p_2, T_2$, and $M_2$.

Anand Jangid

Numerade Educator

01:49

Problem 6

Consider a flat plate at an angle of atlack $\alpha$ to a Mach 2.4 airflow at I atm pressure. What is the maximum pressure that can occur on the plate surface and still have an attached shock wave at the leading edge? At what value of $\alpha$ does this occur?

Chai Santi

Numerade Educator

01:35

Problem 7

A $30.2^{\circ}$ half-angle wedge is inserted into a freestream with $M_x=3.5$ and $p_x=0.5$ atm. A Pitot tube is located above the wedge surface and behind the shock wave. Calculate the magnitude of the pressure sensed by the Pitot tube.

Narayan Hari

Numerade Educator

00:22

Problem 8

Consider a Mach 4 airflow at a pressure of I atm. We wish to slow this flow to subsonic speed through a system of shock waves with as small a loss in total pressure as possible. Compare the loss in total pressure for the following three shock systems:
(a) A single normal shock wave
(b) An oblique shock with a deflection angle of $25.3^{\circ}$. followed by a normal shock
(c) An oblique shock with a deflection angle of $25.3^{\circ}$, followed by a second oblique shock of deflection angle of $20^{\circ}$. followed by a normal shock

From the results of $(a),(b)$, and $(c)$. what can you induce about the efficiency of the various shock systems.

Dading Chen

Numerade Educator

02:17

Problem 9

Consider an oblique shock generated at a compression corner with a defiection angle $\theta=18.2^{\circ}$. A straight horizontal wall is present above the corner, as shown in Fig. 9.14. If the upstream flow has the properties $M_1=3.2, p_1=1$ atm and $T_1=520^{\circ} \mathrm{R}$, calculate $M_1, p_3$, and $T_1$ behind the reflected shock from the upper wall. Also obtain the angle $\Phi$ which the reflected shock makes with the upper wall.

Chai Santi

Numerade Educator

08:40

Problem 10

Consider the supersonic flow over an expansion comer, such as given in Fig. 9.20. The deflection angle $\theta=23.38^{\circ}$. If the flow upstream of the comer is given by $M_1=2, p_1=0.7 \mathrm{~atm}, T_1=630^{\circ} \mathrm{R}$, calculate $M_2, p_2, T_2, P_2, p_{0.7}$, and $T_{n, 2}$ downstream of the comer. Also, obtain the angles the forward and rearward Mach lines make with respect to the upstream direction.

Ankit Pandey

Numerade Educator

Problem 11

A supersonic flow at $M_1=1.58$ and $p_1=1 \mathrm{~atm}$ expands around a sharp comer. If the pressure downstream of the comer is $0.1306 \mathrm{~atm}$, calculate the deflection angle of the corner.

Check back soon!

01:55

Problem 12

A supersonic flow at $M_1=3, T_1=285 \mathrm{~K}$, and $p_1=1 \mathrm{~atm}$ is deflected upward through a compression comer with $\theta=30.6^{\circ}$ and then is subsequently expanded around a comer of the same angle such that the flow direction is the same as its original direction. Calculate $M_3, p_3$. and $T_3$ downstream of the expansion corner. Since the resulting flow is in the same direction as the original flow, would you expect $M_3=M_1$, $p_3=p_1$, and $T_3=T_1$ ? Explain.

James Kiss

Numerade Educator

Problem 13

Consider an infinitely thin flat plate at an angle of attack $\alpha$ in a Mach 2.6 flow. Calculate the lift and wave-drag coefficients for
(a) $\alpha=5^{\circ}$
(b) $\alpha=15^{\circ}$
(c) $\alpha=30^{\circ}$
(Note: Save the results of this problem for use in Chap. 12.)

Check back soon!

Problem 14

Consider a diamond-wedge airfoil such as shown in Fig. 9.24, with a half-angle $\varepsilon=10^{\circ}$. The airfoil it at an angle of atlack $\alpha=15^{\circ}$ to a Mach 3 freestream. Calculate the lift and wave-drag coefficients for the airfoil.

Check back soon!

05:54

Problem 15

Consider sonic flow. Calculate the maximum deflection angle through which this flow can be expanded via a centered expansion wave.

Satpal Satpal

Numerade Educator