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Chapter 17: Problem 102

What is the characteristic aspect of Rayleigh flow? What are the main assumptions associated with Rayleigh flow?

Short Answer

Expert verified
Answer: The characteristic aspect of Rayleigh flow is that it is a frictionless flow with no external body forces and any change in the flow properties, such as Mach number, temperature, and pressure, is due to the transfer of heat along the flow direction. The main assumptions associated with Rayleigh flow include steady flow, one-dimensional flow, ideal gas, calorically perfect gas, frictionless flow, no external body forces, and change in flow properties being solely due to heat transfer along the flow direction.

Step by step solution

01

(Step 1: Define Rayleigh flow)

(Rayleigh flow is a steady, one-dimensional flow of an ideal, calorically perfect, and compressible gas where the only mechanism responsible for the change in the gas properties is the heat addition or removal.)
02

(Step 2: Characteristic aspect of Rayleigh flow)

(The characteristic aspect of Rayleigh flow is that there is frictionless flow with no external body forces, and any change in the flow properties, such as Mach number, temperature, and pressure, is due to the transfer of heat along the flow direction. This means that if heat is added to the flow, the temperature and pressure will increase, while the Mach number will decrease, and vice versa for heat removal.)
03

(Step 3: Main assumptions associated with Rayleigh flow)

(The main assumptions associated with Rayleigh flow include the following: 1. The flow is steady, meaning that flow properties do not change with time. 2. The flow is one-dimensional, indicating that the flow properties vary only along the flow direction and not in the perpendicular directions. 3. The gas is ideal, which means that the gas follows the equation of state p = ρRT, where p is pressure, ρ is density, R is the specific gas constant, and T is temperature. 4. The gas is calorically perfect, implying that the specific heat at constant pressure (Cp) and specific heat at constant volume (Cv) do not change with temperature. 5. The flow is frictionless, so there is no energy loss due to viscous effects. 6. There are no external body forces acting on the flow. 7. The change in flow properties is solely due to the transfer of heat along the flow direction.)

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Most popular questions from this chapter

Explain why the maximum flow rate per unit area for a given ideal gas depends only on \(P_{0} / \sqrt{T_{0}} .\) For an ideal gas with \(k=1.4\) and \(R=0.287 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K},\) find the constant \(a\) such that \(\dot{m} / A^{*}=a P_{0} / \sqrt{T_{0}}\).

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Consider subsonic flow in a converging nozzle with specified conditions at the nozzle inlet and critical pressure at the nozzle exit. What is the effect of dropping the back pressure well below the critical pressure on \((a)\) the exit velocity, \((b)\) the exit pressure, and \((c)\) the mass flow rate through the nozzle?

Derive an expression for the speed of sound based on van der Waals' equation of state \(P=R T(v-b)-a / v^{2}\) Using this relation, determine the speed of sound in carbon dioxide at \(80^{\circ} \mathrm{C}\) and \(320 \mathrm{kPa}\), and compare your result to that obtained by assuming ideal-gas behavior. The van der Waals constants for carbon dioxide are \(a=364.3 \mathrm{kPa} \cdot \mathrm{m}^{6} / \mathrm{kmol}^{2}\) and \(b=0.0427 \mathrm{m}^{3} / \mathrm{kmol}\)
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