A bomb blast sends a shock wave through the 20 $$20 ^ { \circ } \mathrm { C }$$ C atmosphere. At a certain location, the shock wave is travelling at M = 3. The induced velocity behind the wave is nearest:
A) 760 m/s
B) 620 m/s
C) 540 m/s
D) 410 m/s

Question

Quizplus · Accepted Answer

A
 $760 \mathrm {~m} / \mathrm { s }$
$\text {At $\mathrm { M } = 3$ the normal-shock flow Table D.2 gives $\mathrm { M } _ { 2 } = 0.4752$ and $T _ { 2 } = 293 \times 2.679$}$ $\text {$= 785 \mathrm {~K}$. Hence,}$
$$V _ { 2 } = M _ { 2 } \sqrt { k R T _ { 2 } } = 0.4752 \sqrt { 1.4 \times 287 \times 785 } = 267 \mathrm {~m} / \mathrm { s }$$
$\text {This is the velocity behind a stationary shock wave. Superpose the velocity}$ $\text {$V _ { 1 } = 3 \sqrt { 1.4 \times 287 \times 293 } = 1029 \mathrm {~m} / \mathrm { s }$ and find}$
$$V = 1029 - 267 = \underline { 762 \mathrm {~m} / \mathrm { s } }$$
$\text {Such high induced velocities obviously cause severe damage.}$

A Bomb Blast Sends a Shock Wave Through the 20 20∘C20 ^ { \circ } \mathrm { C }20∘C

A Bomb Blast Sends a Shock Wave Through the 20 $20 ^ { \circ } \mathrm { C }$