Consider the flow over a circular cylinder; the incompressible flow over such a cylinder is discussed in Section 3.13. Consider also the flow over a sphere; the incompressible flow over a sphere is described in Section 6.4. The subsonic compressible flow over both the cylinder and the sphere is qualitatively similar but quantitatively different from their incompressible counterparts. Indeed, because of the “bluntness” of these bodies, their critical Mach numbers are relatively low. In particular:
For a cylinder:
For a sphere:
Explain on a physical basis why the sphere has a higher
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- Please show all work of a,b,&c. A supersonic converging-diverging nozzle is near the exit of a turbojet engine. Its cross-section is circular. The gas has the properties of air, and the flow is isentropic. At the throat location (the minimum area) the air flow is choked (is Mach one) and the throat has diameter of 20 cm.arrow_forwardAssume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2(2116 lb/ft2), respectively. Consider the flow field over a circular cylinder mounted perpendicular tothe flow in the test section of a low-speed subsonic wind tunnel. Atstandard sea level conditions, if the flow velocity at some region of theflow field exceeds about 250 mi/h, compressibility begins to have an effectin that region. Calculate the velocity of the flow in the test section of thewind tunnel above which compressibility effects begin to become important, i.e., above which we cannot accurately assume totallyincompressible flow over the cylinder for the wind tunnel tests.arrow_forward1. Consider a low-speed subsonic wind tunnel designed with a reservoir cross-sectional area A, = 2 m2 and a test-section cross-sectional area A2 = 0.5 m2. The pressure in the test section is P2 = 1 atm. Assume constant density equal to standard sea level density, calculate the pressure (in kPa) required in the reservoir, P1, necessary to achieve a flow velocity V2: 40 m/s in the test section. a. From item no. 1, calculate the mass flow rate (in kg/s) through the wind tunnel. b. Calculate the Mach number of the vehicle in air. c. Calculate the Mach number of the vehicle in hydrogen.arrow_forward
- Consider the flow over a circular cylinder; the incompressible flow oversuch a cylinder . Consider also the flow over a sphere; the incompressible flow over a sphere .The subsonic compressible flow over both the cylinder and the sphere isqualitatively similar but quantitatively different from their incompressiblecounterparts. Indeed, because of the “bluntness” of these bodies, theircritical Mach numbers are relatively low. In particular: For a cylinder: Mcr = 0.404 For a sphere: Mcr = 0.57Explain on a physical basis why the sphere has a higher Mcr than thecylinder.arrow_forward3. The NASA X-43 flies at a Mach number of 9.4 at an altitude of 30,000 m, where thepressure is 1171.8 Pa and the temperature is 226 K. If a supersonic wind tunnel isdesigned to reproduce these conditions, calculate the following:(a) The velocity (m/s), total/stagnation temperature (K), and total/stagnation pres-sure (kPa) in the test section.(b) The velocity (m/s), total temperature (K), and total pressure (kPa) behind thenormal shock formed in front of a blunt surface in the test section.(c) The change in entropy across this normal shock.arrow_forwardConsider a low-speed subsonic wind tunnel designed with a reservoir cross-sectional area of 2 m2 and a test-section cross-sectional area of 0.5 m2. The pressure in the test section is 1 atm. Assume constant density equal to standard sea level density, calculate the pressure (in Pa) required in the reservoir necessary to achieve a flow velocity of 40 m/s in the test section.arrow_forward
- Please answer fastarrow_forward1. a. Consider a low-speed subsonic wind tunnel designed with a reservoir cross-sectional area A1 = 2 m2 and a test-section cross-sectional area A2 = 0.5 m2. The pressure in the test section is P2 = 1 atm. Assume constant density equal to standard sea level density, calculate the pressure (in kPa) required in the reservoir, P1, necessary to achieve a flow velocity V2 = 40 m/s in the test section. b. calculate the mass flow rate (in kg/s) through the wind tunnel.arrow_forwardIn your own words, write a summary of the differences between incompressible flow, subsonic flow, and supersonic flow.arrow_forward
- Handwritten answer pls.arrow_forwardAssume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2(2116 lb/ft2), respectively. Prove that the flow field specified is not incompressible;i.e., it is a compressible flow as stated without proof .arrow_forwardA supersonic wind tunnel is in the design stage. It is to be driven by a large upstream reservoir of compressed air and discharges to atmospheric conditions downstream. The test section has a constant cross-sectional area and lies downstream of a throat, which is a converging-diverging section that serves to accelerate the flow to supersonic conditions. For the duration of any given experiment, the reservoir can be considered to have constant stagnation conditions that are To = 313K and po = 6x105 Pa. The specific gas constant R = 287 J kg-¹ K-1 and the specific heat ratio is y = 1.4. The wind tunnel test section is designed to run with a cross-sectional area A (test section ) = 1.2 m² and Mach number M (test section ) = 4. Find the area of the throat that lies between the reservoir and the test section. Give your answer in m² to two decimal places.arrow_forward
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