Professor Gordon Holloway and his student, Jason Bettle, of the University of New Brunswick obtained the following tabulated data for blow-dow n airflow through a converging- diverging nozzle similar in shape to Fig. P3.22. The supply tank pressure and temperature were 29 psig and 74°F, respectively. Atmospheric pressure was 14.7 psia. Wall pressures and centerline stagnation pressures were measured in the expansion section, which was a frustrum of a cone The nozzle throat is at v = 0.
item) | 0 | 1.5 | 3 | 4.5 | 6 | 7.5 | 9 |
Diameter (cm) | 1.00 | 1.098 | 1.195 | 1.293 | 1.390 | 1.488 | 1.585 |
PwaiKpsig) | 7.7 | -2.6 | -4.9 | -7.3 | -6.5 | -10.4 | -7.4 |
PsMglMIKHI (psig) | 29 | 26.5 | 22.5 | 18 | 16.5 | 14 | 10 |
Use the stagnation pressure data to estimate the local Mach number. Compare the measured Mach numbers and wall pressures with the predictions of one-dimensional theory. For.v > 9 cm. the stagnation pressure data was not thought by Holloway and Bettle to be a valid measure of Mach number. What is the probable reason?
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Fluid Mechanics
- Air (k= 1.40, R = 0.287 kJ/kg.K) flows into a converging nozzle from a large tank, as shown in the figure below. Diameter at section 2 is fixed, D2 = 8 cm. Assume steady, isentropic flow. Use 4 significant figures in problem-solving and answers. Large Tank Exit Plane Ideal Gas k=1.40 R= 0.287 kJkg.K a) When the back pressure, P, = 310 kPa (abs), Vi = 804 km/hr Ti = 775.2 K V2 = 1256 km/hr P2 = 379.6 kPa (abs) Determine : Exit velocity, V, = ?, Exit density, p.= ?, Exit diameter, D. = ?, Mass flow rate, ṁ = ? b) When the back pressure, Ps = 200 kPa (abs) and De = as calculated in part a) Determine : Exit pressure, P. = ? Exit temperature, Te = ? Exit velocity, V. =? Exit density, p. = ? Mass flow rate, m = ? Section 2 velocity, V2 = ? Section 1 diameter, Di = ? %3Darrow_forward1. Air, with stagnation conditions of 800 kPa and 100 °C, ex pands isentropically to a section of a duct where A₁ = 20 cm² and p₁ = 47 kPa. Compute ( a ) Ma₁ , ( b ) the throat area , and ( c ) m . At section 2 between the throat and section 1, the area is 9 cm². (d) Estimate the Mach number at sec tion 2. Plz sketch and solve itarrow_forwardWhere necessary, assume air as an ideal gas and consider R = 287J/(kg.K), Cp = 1005 J/(kg.K), Cv = 718 J/(kg.K). A nozzle is a device that is used to increase the velocity of a fluidby varying the cross-sectional area. At the last section of a jetengine (Fig Q1.a, section 5), air with a mass flow rate of 50 kg/s ata pressure of 500 kPa and a temperature of 600 K enters a nozzlewith an inlet cross-sectional area of 5 m2. The exit area of thenozzle is 20% of its inlet area. The air leaves the nozzle at avelocity of 300 m/s. The nozzle is not well-insulated and duringthis process, 5 kJ/kg heat is lost. (iv) Determine the temperature of the air as it leaves the nozzle.(v) Calculate the pressure of the air as it leaves the nozzle.arrow_forward
- Air at P1 = 1 MPa, T1 = 600 °C and V1 = 150 m/s enters a converging nozzle. The exit area is A2 = 50 cm2 and the back pressure is P2 = 0.7 MPa. What is the mass flow rate (kg/s) through the nozzle? What the is Mach number at the nozzle exit? What would be the flow rate you calculate if you assumed isothermal flow?arrow_forwardA constant area adiabatic wind tunnel is to be designed to provide a test section of air flowing at M=3, pressure of 7 kPa and temperature of 255 K. The air is forced through the tunnel by isentropic nozzle having a stagnation pressure of 300 kPa. Find the area ratio of the nozzle. [Answ. 4.94]arrow_forward4.17 Consider a flat plate with a chord length (from leading to trailing edge) of 1 m. The free-stream flow properties are M, = 3, p1 = 1 atm, and T¡ = 270 K. Using shock-expansion theory, tabulate and plot on graph paper these properties as functions of angle of attack from 0 to 30° (use increments of 5°): %3D а. Pressure on the top surface b. Pressure on the bottom surface Temperature on the top surface с. d. Temperature on the bottom surface Lift per unit span е.arrow_forward
- A typical carbon dioxide tank for a paintball gun holdsabout 12 oz of liquid CO2. The tank is fi lled no more thanone-third with liquid, which, at room temperature, maintainsthe gaseous phase at about 850 psia. (a) If a valve isopened that simulates a converging nozzle with an exitdiameter of 0.050 in, what mass fl ow and exit velocityresults? (b) Repeat the calculations for helium.arrow_forwardThe mass flow rate of a calorically perfect gas (C₁ = constant) through a Convergent-Divergent nozzle is given by, m = A Pt VT₁ M (1+ y +1 YM²) 2(3-1) (a) Derive the above relation from fundamental principals. Here, P₁, is total (or Stagnation) pressure and T₁ is total temperature, M is Mach number, A is local area of nozzle. (b) Prove mathematically that the maximum airflow limit occurs when the Mach number is equal to one and obtain below relation. m A Pt √√Tt Note: The limiting of the maximum mass flow rate when M =1, is called choking of the flow or Choked flow. Hint: https://www.grc.nasa.gov/www/k-12/rocket/mflchk.html y+1 2(y-1) √(4¹) Rarrow_forwardAir, at po = 160 lbf/in2 and To = 300 °F, fl ows isentropicallythrough a converging–diverging nozzle. At section 1,where A1 = 288 in2, the velocity is V1 = 2068 ft/s. Calculate(a) Ma1, (b) A*, (c) p1, and (d ) the mass flow, in slug/s.arrow_forward
- Design the 2D steady MOC contour for a super sonic nozzle assuming that the expansion section is a simple corner of some fixed angle, with the straightening section being designed to produce uniform outflow. The inflow for your nozzle is to be M = 1, gamma = 1.4, P = 101325, T = 300K, incoming flow area of 1m, with 1m depth into the page. The exit Mach number of your design is to be M = 3. Note to execute this properly you will need to compute v (nu) as a function of M, and viceversa. Please use Matlab for results.arrow_forwardQ2: The large compressed-air tank shown in the figure bellow exhausts from a nozzle at an exit velocity of Ve= 235 m/s. Assuming isentropic flow, compute: a) the exit Mach number. b) the pressure in the tank. (take; k = 1.396, Cp = 917 J/Kg.k and R = 260 J/Kg.k) air at 30 °C V. tank conditions remain constant Pain = 101 kPaarrow_forwardQ2: The large compressed-air tank shown in the figure bellow exhausts from a nozzle at an exit velocity of V235 m/s. Assuming isentropic flow, compute: a) the exit Mach number. b) the pressure in the tank. (take; k = 1.396, C, = 917 J/Kg.k and R = 260 J/Kg.k) air at 30 C tank conditions Pan= 101 LPaarrow_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