What is the relationship for the density ratio (rho_y/rho_x) across a normal shock as a function of the upstream Mach number (Mx) and specific heat ratio (k)?
Explanation
Similar to pressure and temperature ratios, the density ratio across a normal shock can be expressed solely as a function of the upstream Mach number (Mx) and the specific heat ratio (k). Equation (5.24) provides this important relationship.
Other questions
What are the four primary equations used to describe the conditions across a normal shock for a perfect gas?
What fundamental principle dictates that a normal shock wave can only proceed from a supersonic flow (Mx > 1) to a subsonic flow (My < 1)?
How does the total temperature (T0) of a perfect gas change across a stationary normal shock?
According to the Rankine-Hugoniot relation for a normal shock, what is the downstream Mach number (My) squared, as a function of the upstream Mach number (Mx) squared and the specific heat ratio (k)?
For a normal shock in a perfect gas with k=1.4, if the upstream Mach number (Mx) is 3.0, what is the approximate ratio of downstream pressure to upstream pressure (Py/Px)?
What is Prandtl's condition for a normal shock, relating the upstream velocity (U1), downstream velocity (U2), and the critical speed of sound (c*)?
As the upstream Mach number (Mx) of a normal shock becomes very large (approaches infinity), what is the limiting value of the downstream Mach number (My)?
How is the analysis of a moving shock wave, such as one created by a suddenly closed valve, typically simplified?
In the analysis of a moving shock created by a valve suddenly stopping a flow, what is the 'upstream' Mach number in the moving coordinate system (Mx') if the original flow Mach number was Mx and the shock Mach number is Msx?
What happens to the total pressure (P0) of a gas as it passes through a normal shock?
The strength of a weak normal shock is defined by the dimensionless pressure rise, P-hat = (Py - Px) / Px. How is P-hat related to the upstream Mach number (Mx) for small perturbations?
A gas flowing at a Mach number of 0.4 is brought to a partial stop by closing a valve, such that the Mach number behind the shock is 0.2. What type of problem does this scenario represent?
In a shock tube, what are the conditions in zone 2, the region immediately behind the moving shock front?
What is the relationship between the density ratio (rho_y/rho_x) and the velocity ratio (Ux/Uy) across a normal shock?
In a reflective shock from a suddenly closed valve, a gas flow at a prime Mach number Mx' of 1.2961 is brought to a complete stop (My' = 0). For k=1.4, what is the resulting pressure ratio (Py/Px) of the shock?
Why are two solutions (intersections) obtained when plotting Fanno flow and Rayleigh flow curves on a T-s diagram?
When a piston moves into a still gas, it creates a moving shock. The analysis involves a 'strange' Mach number, Myx', which is defined as what?
What is the primary reason for the total pressure loss across a normal shock?
In the analysis of a moving shock in a stationary medium (suddenly open valve), the stagnation temperature in stationary coordinates rises. Why does this occur?
For a shock moving at 450 m/sec into stagnant air at 300 K (k=1.3, R=287 J/kgK), the calculated prime Mach number My' is approximately 1.296. What is the corresponding stationary upstream Mach number (Mx) for this shock?
What is the relationship between the temperature ratio (Ty/Tx) and the pressure ratio (Py/Px) across a normal shock?
In the shock tube diagram (Figure 5.16), what separates zone 2 (shocked gas) from zone 3 (expanded driver gas)?
A shock is moving into a stationary medium. If the specific heat ratio is k=1.4, what is the theoretical maximum possible Mach number of the gas behind the shock (My') in the stationary frame?
For a gas with k=1.4, what is the minimum upstream Mach number (Mx) required to create a normal shock?
What physical assumption allows the thickness of a normal shock to be considered very small or negligible in the governing equations?
In the analysis of a moving shock into stationary medium from a suddenly opened valve, how is the shock Mach number ahead of the shock (Msx) defined?
For a normal shock with an upstream Mach number of 2.0 and k=1.4, what is the total pressure ratio P0y/P0x?
What is assumed about chemical reactions, such as condensation, within the very narrow width of a normal shock in the simplified model?
What does the star Mach number, M*, represent?
A gas is flowing in a pipe with a Mach number of 0.4. A valve is closed such that the Mach number is reduced by half to 0.2. What is the approximate stationary Mach number (Mx) of the shock wave generated, assuming k=1.4?
In the momentum equation for a normal shock, Px - Py = rho_y * Uy^2 - rho_x * Ux^2, what physical principle does this equation represent?
For a shock moving into still air (Mx'=0), how is the downstream Mach number in the moving frame (My') related to the shock Mach number (Msy)?
What is the primary characteristic of the 'contact surface' in a shock tube?
If a piston accelerates very rapidly in a tube of air at 300 C with M=0.4, and the air next to the piston reaches M=0.8, what is the approximate speed of the shock wave created? The speed of sound in the undisturbed air is 347.2 m/s and k=1.4.
What does the dimensionless group M*1 * M*2 equal, according to Prandtl's condition?
In the industrial problem presented in Example 5.10, a valve is opened between a 30 Bar reservoir and a pipe leading to a 1 Bar ambient condition. What phenomenon limits the initial flow characteristics?
If a normal shock occurs with an upstream Mach number of 4.0 in a gas with k=1.4, what is the approximate downstream Mach number (My)?
What is the primary difference in the stagnation temperature change between a stationary shock and a moving shock (viewed from a stationary frame)?
In order to double the temperature across a reflective shock from a suddenly closed valve (Ty/Tx = 2.0), what must be the stationary Mach number (Mx) of the shock, assuming k=1.4?
What does a value of P0y/P0x = 1.0 signify for a flow process?
If two pistons in a 1-meter long tube move toward each other, one creating a shock with Us=1.0715*c and the other Us=1.1283*c, where c=347 m/s, approximately how long will it take for the shocks to collide?
Which statement accurately describes the change in static properties across a normal shock?
What is the key simplification that allows the Fanno flow and Rayleigh flow models to be used in analyzing a normal shock?
For a shock moving into a stationary medium with k=1.3, what is the maximum possible Mach number of the gas behind the shock (My')?
According to Figure 5.3, how does the total pressure ratio (P0y/P0x) change as the upstream Mach number (Mx) increases from 1 to 10?
If a shock has a static pressure ratio (Py/Px) of 6.317 and a temperature ratio (Ty/Tx) of 2.0, what was the approximate upstream prime Mach number (Mx') of the flow before it was stopped by a valve, for a gas with k=1.4?
The relationship My^2 = (Mx^2 + 2/(k-1)) / ( (2k/(k-1))Mx^2 - 1 ) is described as a 'symmetrical equation'. What does this symmetry imply?
In the general case of a moving shock where a gas flows into another gas with a different velocity (partially open valve), what additional parameter must be supplied to solve the problem, compared to a shock in a stationary medium?
What is the physical interpretation of the 'shock-choking' phenomenon?