A shock wave is best described thermodynamically as
Answer: A
No heat crosses the shock, so it is adiabatic, but the steep gradients inside it dissipate energy and raise entropy, so it is irreversible. That combination is why stagnation temperature survives a shock while stagnation pressure does not, a distinction worth keeping firmly in mind.
Please log in or register to report this question.
The Rankine-Hugoniot relations express, across a shock,
Answer: B
The three conservation laws applied across the discontinuity, together with the equation of state, give the complete jump conditions. They are not isentropic relations and must not be confused with them: entropy is an output of the Rankine-Hugoniot analysis, not an assumed constant.
Please log in or register to report this question.
The sonic line on a blunt body with a detached bow shock is where
Answer: C
Immediately behind the nearly normal portion of the bow shock the flow is subsonic. As it expands round the shoulder of the body it accelerates again, and the locus where it passes back through Mach one is the sonic line. Downstream of it the flow is supersonic once more.
Please log in or register to report this question.
For a fixed upstream Mach number, increasing the wedge half-angle in supersonic flow
Answer: D
A larger deflection needs a stronger shock, and on the weak branch that means a larger shock angle. The angle grows until the maximum deflection for that Mach number is reached, and any further increase in wedge angle detaches the shock, which then stands off ahead of the leading edge.
Please log in or register to report this question.
For a fixed wedge angle, raising the upstream Mach number causes the attached oblique shock to
Answer: A
Higher Mach number means a smaller Mach angle and, on the weak branch, a smaller shock angle for the same deflection, so the shock wraps in closer to the surface. At hypersonic speeds the shock lies very close indeed, producing the thin shock layer characteristic of that regime.
Please log in or register to report this question.
A normal shock stands in a stream at \( M_1 = 2 \). The downstream Mach number is nearest to
Answer: B
The relation is \( M_2^2 = (1 + 0.2 M_1^2)/(1.4 M_1^2 - 0.2) \). Substituting, the numerator is \( 1 + 0.8 = 1.8 \) and the denominator \( 5.6 - 0.2 = 5.4 \), so \( M_2^2 = 0.3333 \) and \( M_2 = 0.577 \). Every normal shock leaves the flow subsonic, so any answer above one would be wrong on principle.
Please log in or register to report this question.
For a normal shock at \( M_1 = 2 \), the static pressure ratio \( p_2/p_1 \) is
Answer: C
The relation is \( p_2/p_1 = 1 + \frac{2\gamma}{\gamma+1}(M_1^2 - 1) \). With \( \gamma = 1.4 \) the coefficient is \( 2.8/2.4 = 1.1667 \), and \( M_1^2 - 1 = 3 \), so the ratio is \( 1 + 3.5 = 4.5 \). The pressure has more than quadrupled across a discontinuity a fraction of a micron thick.
Please log in or register to report this question.
For a normal shock at \( M_1 = 2 \), the density ratio \( \rho_2/\rho_1 \) is nearest to
Answer: D
The relation is \( \rho_2/\rho_1 = (\gamma+1)M_1^2 / ((\gamma-1)M_1^2 + 2) \), which gives \( 9.6 / 3.6 = 2.667 \). Compare this with the limiting value of six as the Mach number grows without bound: even at Mach 2 the shock has already achieved nearly half the compression that is available at any speed.
Please log in or register to report this question.
For a normal shock at \( M_1 = 2 \), the static temperature ratio \( T_2/T_1 \) is nearest to
Answer: A
The equation of state gives the temperature ratio as the pressure ratio divided by the density ratio, so \( 4.5 / 2.667 = 1.688 \). A stream at 250 K would emerge at about 422 K, which is why shock heating matters structurally even at modest supersonic speeds.
Please log in or register to report this question.
Air approaching an obstacle at \( M = 1.5 \) crosses a normal shock. The Mach number with which it emerges is nearest to
Answer: B
Substituting into \( M_2^2 = (1 + 0.2 M_1^2)/(1.4 M_1^2 - 0.2) \), the numerator is \( 1 + 0.45 = 1.45 \) and the denominator \( 3.15 - 0.2 = 2.95 \), giving \( M_2^2 = 0.4915 \) and \( M_2 = 0.701 \). The weaker shock leaves the flow closer to sonic than the Mach 2 case did.
Please log in or register to report this question.
