Consider a subsonic compressible flow in cartesian coordinates where the velocity potential is given by
If the freestream properties are given by
The Mach number of the subsonic compressible flow.
The temperature of the subsonic compressible flow.
The pressure of the subsonic compressible flow.
Answer to Problem 11.1P
The Mach number for the fluid at the given point is
The pressure for the fluid at the given point is
The temperature for the fluid at the given point is
Explanation of Solution
Given:
The freestream velocity of the compressible flow is
The pressure of the compressible flow is
The temperature of the compressible flow is
Formula used:
The velocity component in the x-direction is given as,
The velocity component in the y-direction is given as,
The expression for the Mach number is given as,
Here,
The velocity of the flow is given as,
The expression for the temperature for the given point is given as,
The expression for the pressure is given as,
Calculation:
The “Properties of air” is given as,
The velocity component of the fluid in x-direction can be calculated as,
The velocity component of the fluid in the y-direction can be calculated as,
The resultant velocity of the flow can be calculated as,
The Mach number of the supersonic flow can be calculated as,
For
The pressure at starts can be calculated as,
The required temperature can be calculated by the energy equation as,
The required Mach number can be calculated as,
The required pressure for the flow can be calculated as,
Conclusion:
Therefore, the Mach number for the fluid at the given point is
Therefore, the pressure for the fluid at the given point is
Therefore, the temperature for the fluid at the given point is
Want to see more full solutions like this?
Chapter 11 Solutions
FUND. OF AERODYNAMICS-W/ACCESS
Additional Engineering Textbook Solutions
Thermodynamics: An Engineering Approach
Fluid Mechanics Fundamentals And Applications
Mechanics of Materials
Vector Mechanics for Engineers: Statics and Dynamics
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Vector Mechanics for Engineers: Statics, 11th Edition
- An aircraft is flying at supersonic speed. At a component of an aircraft where the flow is perpendicular (normalshock), the density ratio is 5. Solve for: a.Mach Number Downstream b. Pressure Ratio c. Temperature Ratio d. Mach Number upstreamarrow_forwardAn aircraft is flying at a speed less than 100 meters per second in sea level. Which of the following statement is true? A. density changes are small and the flow can be regarded as incompressible B. the flow should be regarded as compressible since Mach number is less than 0.3 C. the flow should be regarded as compressible since Mach number is greater than 0.3 D. density changes are small and the flow can be regarded as compressiblearrow_forwardA uniform supersonic flow of air at Mach 3.8, with a stagnation pressure of 5.0 MPa and stagnationtemperature of 1100 K, expands around a 23o convex corner. Determine the downstream Macharrow_forward
- The flow just upstream of a normal shock wave is given by p1 = 1 atm,T1 = 288 K, and M1 = 2.6. Calculate the following properties justdownstream of the shock: p2, T2, ρ2, M2, p0,2, T0,2, and the change inentropy across the shock.arrow_forwardConsider the Eulerian velocity u=(4y−16x)i+(16y−60x)j, where (x,y)are Cartesian coordinates. Determine the stream functionarrow_forwardThe velocity ratio (v1/v2) of an isentropic flow through a supersonic wind tunnel is 0.615. if the mach number at the tunnels entry section is 0.95 find the value of mach number at the exitarrow_forward
- Consider a cone at zero angle of attack in a hypersonic flow. (Hypersonic flow is very high-speed flow, generally defined as any flow above a Mach number of 5.) The half-angle of the cone is θc, as shown inthe figure. An approximate expression for the pressure coefficient on the surface of ahypersonic body is given by the newtonian sine-squared law : Cp = 2 sin2 θcNote that Cp, hence, p, is constant along the inclined surface of the cone. Along the base of the body, we assume that p = p∞. Neglecting the effect of friction, obtain an expression for the drag coefficient of the cone, where CD is based on the area of the base Sb.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_forward5. At 30000ft, estimate the magnitude of transonic drag rise. Using this estimate, calculate the maximum velocity of the airplane at this altitude. Assume drag-divergence Mach number of 0.82 and d(D/D₁)/dM = 14.3 where D₁=1750lb is drag at Mach number 0.9 and D₂ = 4250lb at Mach number 1. 6 Estimate maximum range at 30000€ Also calculate the flight speed to obtain thisarrow_forward
- For a converging-diverging nozzle that is choked what is the ratio of nozzle area divided by the throat area for a Mach number of 2.1? (Assume isentropic flow for an ideal gas and k = 1.4.) Enter your answer to the fourth decimal place.arrow_forwardIn your own words, write a summary of the differences between incompressible flow, subsonic flow, and supersonic flow.arrow_forwardAERODYNAMICS 1. A uniform supersonic air flow at Mach 2.0 passes over a wedge. An oblique shock, making an angle of 40° with the flow direction, is attached to the wedge. If the static pressure and temperature in the freestream are 0.5 Pa and 0°C, determine: a. the deflection angle in degrees b. the pressure ratio c. the Mach number in the downstream regionarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY