
Concept explainers
Note: The purpose of the following problem is to provide an exercise in carrying out a unit process for the method of characteristics. A more extensive application to a complete flow field is left to your specific desires. Also, an extensive practical problem utilizing the finite-difference method requires a large number of arithmetic operations and is practical only on a digital computer. You are encouraged to set up such a problem at your leisure. The main purpose of the present chapter is to present the essence of several numerical methods, not to burden the reader with a lot of calculations or the requirement to write an extensive computer program.
Consider two points in a supersonic flow. These points are located in a cartesian coordinate system at

The numerical value of
The numerical value of
The numerical value of
The numerical value of
The location of point 3.
Answer to Problem 13.1P
The value of
The value of
The value of
The value of
The location of point 3 is
Explanation of Solution
Given:
The Cartesian coordinate system at
The Cartesian coordinate system at
The numerical value of
The numerical value of
The numerical value of
The numerical value of
The numerical value of
The numerical value of
The numerical value of
The numerical value of
Formula used:
The expression for the Mach number is given as,
Here,
The expression for speed of object is given as,
The expression for speed of sound is given as,
The expression for angle of object is given as,
Calculation:
The speed of sound at point 1 can be calculated,
The speed of object at point 1 can be calculated as,
The Mach number at point 1 can be calculated as,
The angle of object at point 1 can be calculated as,
The constant at point 1 can be calculated as,
The flow constant at point 1 can be calculated as,
The speed of sound at point 2 can be calculated as,
The speed of object at point 2 can be calculated as,
The Mach number at point 2 can be calculated as,
The angle of object at point 2 can be calculated as,
The constant at point 2 can be calculated as,
The flow constant at point 2 can be calculated as,
The angle of object at point 3 can be calculated as given bellow,
The constant at point 3 can be calculated as,
The Mach number at point 3 can be calculated as,
To obtain the other flow variables at point 3, expression is given as,
The pressure at point 2 can be calculated as,
The temperature at point 3 is given as below,
Expression for the temperature,
The speed of sound at point 3 can be calculated as,
The speed of object at point 3 can be calculated as,
The initial velocity of object at point 3 can be calculated as,
The final velocity of object at point 3 can be calculated as,
To locate point 3 expression is,
The average angle at point 2 and 3 along the
The average angle at point 2 and 3 along the
The final angle at point 2 and 3 is given as,
The equation for the point on they-axis is given as,
The average angle at point 1 and 3 along the
The average angle at point 1 and 3 along the
The final angle at point 1 and 3 is given as below,
The equation for the point on the x-axis is given as below,
On solving equation (1) and (2), we will get the point 3 as,
Thus,
Conclusion:
Therefore, the value of
Therefore, the value of
Therefore, the value of
Therefore, the value of
Therefore, the location of point 3 is
Want to see more full solutions like this?
Chapter 13 Solutions
Fundamentals of Aerodynamics
- Consider a very long, slender rod. One end of the rod is attached to a base surface maintained at Tb, while the surface of the rod is exposed to an air temperature of 400°C. Thermocouples imbedded in the rod at locations 25 mm and 120 mm from the base surface register temperatures of 325°C and 375°C, respectively. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. . x1 32 x Calculate the rod base temperature (°C). The rod base temperature is °C. Air T∞arrow_forward(read image)arrow_forwardThis is a tilt and rotation question. Here are notes attached for reference. ONLY UPLOAD A SOLUTION IF YOU ARE SURE ABOUT THE ANSWER PLEASE.arrow_forward
- What is the difference between true stress/strain and engineering stess/strain? And how do I calculate them?arrow_forwardA rotating shaft of 20 mm diameter is simply supported. The shaft is loaded with a transverse load of 10 kN as shown in the figure. The shaft is made from AISI 1095 hot-rolled steel. The surface has been machined. The shaft operate at temperature T = 450 °C. Consider a reliability factor of 95%. Determine (a) Calculate the reaction forces R, and R₂ (2 points) (b) Draw the shear force and bending moment diagrams and determine the maximum bending moment and shear force. (6 points) 200 mm 20 mm 10,000 N -50 mm- A Not to scale. (c) Determine the critical location of the shaft and the maximum effective stresses. (3 points) (d) Calculate the safety factor against yielding. Does the shaft undergo local yielding? (2 points) (e) Determined the endurance limit, adjusted as necessary with Marin factors. (12 points) (f) Calculate the fatigue factor of safety based on achieving infinite life. (2 points) (g) If the fatigue factor of safety is less than 1 (hint: it should be for this problem), then…arrow_forward(read image)arrow_forward
- (read image)arrow_forward6: Refer to the figure.Given: W1 = 200 kN/m; W2 = 300 kN/m; L1 = 2 m; L2 = 3 m; L3 = 2 m(a) Calculate the total length L so that the resulting upward pressureq is uniform. (b) draw the shear and moment diagram and determinethe maximum shear, maximum positive and negative bendingmoments.arrow_forwardA six cylinder, four-stroke diesel engine develops a power of 200 kW at 2000 rpm. The bsfc is 0.2 kW/kg h of fuel with 34.9° API. The fuel is injected at an average pressure of 350 bar and the pressure in the combustion chamber is 40 bar. Assuming Ca for injector 0.75 and the atmospheric pressure 1 bar. Determine the period of injection in seconds if the total orifice area required per injector is 0.4876 × 10-6 m².arrow_forward
- Trieed a detailed drawing Win explanatio LL Antsmi 1981x pu + 96252 اه 6. The Pre-combustion chamber design engines employ nozzle type commonly referred to as a ....... a. inward-opening nozzle b. multiple-hole nozzle. c. pintle nozzle. d. none of these. 7. If the temperature of the spark plug tip is less than 350 °C, ......... a. the plug might not work. b. the carbon deposits would increase. 8. Port injection sprays fuel....... c. pre-ignition will occur. d. none of these. a. towards the intake valve. b. in the engine cylinder. c. in the throttle body assembly. d. none of these. 9. When the fuel-air mixture changed from best power to a richer ratio, the spark advance should be........ a. increased. b. decreased. c. left unchanged. d. none of these. d. none of these. 10. Spark plugs are classified as hot plugs and cold plugs depending upon ........ a. spark gap. b. the type of plug c. the operating temperature insulator. range of the electrode tip. ---20125 750 x2.01 SP 5.arrow_forwardA 1. How does the octane number (O.N.) of the fuel a. Higher ignition advance is required for a high O.N. fuel. b. Higher ignition retard is required for a high O.N. fuel. affect spark ing:d. Nou does not affect spark timing. c. The octane number 2. How does the ignition system account for load change? these. of a. The throttle b. The vacuum ignition governor c. The mechanism of d. None of is wide opened. provide additional spark advance at part throttle positions. centrifugal advance does the job. these. 3. In the common rail fuel system the fuel is metered by ........ a. low pressure pump. b. injectors. c. high pressure pump. d. none of these. 4.......... is the time period, measured in degrees of cam rotation, during which the contact points remain closed between each opening. a. Distributor. b. Dwell. c. ECU. d. none of these. 5. The trigger wheel in TCI system replaces the ......... used in a contact breaker distributor. a. pickup coil. b. distributor cam. c. condenser. 750 x2.01…arrow_forwarda い يكا 4 +91- pu Answer the following statements by true or false, giving the reason for your answer: 1. Injection pressure in CI engines should be sufficiently high. 2. The purpose of the condenser in battery ignition system is to prevent spark in the ignition coil assembly. 3. An idling engine requires lean mixture of fuel and air. 4. Factors which decide optimum engine firing order are engine vibration, engine cooling and back pressure. 5. It is the duty of the header to control over speeding during CI engine operation when drastic reduction in load occurs. ---20125 750 x2.01 SParrow_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





