The throat and exit areas of the nozzle for given mass flow rates and also the reason the nozzle must be of converging-diverging type.
Answer to Problem 127P
The throat area of the nozzle is
The exit area of the nozzle is
The exit Mach number comes out to be greater than the 1, hence the nozzle must be of converging-diverging type.
Explanation of Solution
Given:
Ambient temperature at inlet
Stagnation Pressure
Exit pressure
Mass flow rate
Calculation:
Properties of helium,
R is gas constant,
Stagnation temperature of helium at inlet is given by
Stagnation pressure of helium at inlet is given by
The flow is considered to be isentropic, so the stagnation temperature and stagnation pressure remain same throughout the nozzle.
Now the critical temperature is given by
And critical pressure is given by
The critical density is given by
Inlet velocity is given by
Exit area of throat is given by
Pressure at the exit of nozzle is given as
Temperature at nozzle exit is given by
Density at exit of nozzle is given by
Velocity at exit of nozzle is given by
Area of exit at nozzle is given by
Conclusion:
Therefore, the throat area of the nozzle is
The exit area of the nozzle is
The exit Mach number comes out to be greater than 1, hence the nozzle must be of converging-diverging type.
Want to see more full solutions like this?
Chapter 12 Solutions
Fluid Mechanics: Fundamentals and Applications
- Air enters a nozzle at 0.5 MPa, 420 K, and . Approximating the flow as isentropic, determine the pressure and temperature of air at a location where the air velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area? assuming the entrance velocity is negligible.arrow_forwardFive kilograms of a perfect gas expands polytropically from a pressure of 1 MPa and temperature of 300 °C to a pressure of 0,2 MPa and a temperature 165 °c. If the specific heat capacities are C, = 1,011 and C, = 0,777 kJ/kgK, draw P-V of the process and calculate: 1. (a) Characteristic gas constant Change of entropy Change of internal energy polytropic index of expansion Work done Heat flow during expansion of the gas (f)arrow_forwardThe stopping pressure of the air flow at the inlet of a pipe with an inner diameter of 20 cm is 1.1 atm, the static pressure It is 1 atm and its temperature is 285°K, and the Mach number at its exit is 0.6. Average friction inside the pipe Since the coefficient is 0.005, the length of the pipe, the stopping pressure at the outlet, the static pressure and the Calculate the temperature.arrow_forward
- Consider subsonic Fanno flow of air with an inlet Mach number of 0.70. If the Mach number increases to 0.90 at the duct exit as a result of friction, will the (a) stagnation temperature T0, (b) stagnation pressure P0, and (c) entropy s of the fluid increase, decrease, or remain constant during this process?arrow_forwardHelium enters a nozzle at 0.5 MPa, 600 K, and a negligible entrance velocity. Assuming isentropic flow, determine the pressure and temperature of helium at a location where the velocity equals the speed of sound. What is the ratio of the area at this location to the entrance area?arrow_forwardAir enters a nozzle at 200 KPa, 360 K and a velocity of 180 meter per second . Assuming isentropic or adiabatic flow, if the pressure and temperature of air at a location where the air velocity equals the speed of sound, the Mach number at the nozzle inlet is Blank 1. The properties of air are : k = 1.4; Cp = 1005 J/kg-K; R = 287 J/kg-K. ***EXPRESS YOUR ANSWER in TWO (2) DECIMAL PLACE and WITHOUT UNITS****arrow_forward
- Steam enters a nozzle at 377°C, 1.6 MPa, and a steadyspeed of 200 m/s and accelerates isentropically until it exitsat saturation conditions. Estimate the exit velocity andtemperature.arrow_forward3. Air enters a converging-diverging nozzle at 1.50 MPa and 900 K with a negligible velocity. The flow is steady, one-dimensional, and isentropic with k =1.4. For an exit Mach number of Ma = 2.4 and a throat area of 15 cm2, determine (a) the T, P and p in the throat, (b) the T, P and p in the exit plane, including the exit area, and (c) the mass flow rate through the nozzlearrow_forwardA vessel containing 63.8 kg of water is left out where it evaporates completely. Assuming the temperature remains con- stant at C, what is the change in entropy? The latent heat of vaporization of water at 20°C is 585 cal/g. Answer in units of kcal/K.arrow_forward
- Thermodynamics (Ideal Gas) air enters an ideal nozzle at a pressure of 45 psig with a temperature of 1,340F. The pressure at the nozzle exit is 14.925 psia. If the mass flow rate of air is 8 lm/min, determine the required exit diameter in cm?arrow_forwardIs it possible to accelerate a gas to supersonic velocity in a converging nozzle?arrow_forwardi just need final answer The tank is filled with air at 20°C and 139 kPa in stationary condition. Air is leaving the tank with flowing in anozzle under steady-state condition. The flow is under isentropic and subsonic condition. The nozzle exit area is28,1 cm2. After leaving from the nozzle, air strikes a vertical plate. Define the force [N] required to hold the platestationary. (Note: Assume Pe=1 atm, kor=1.4, Ric=287 J/kg.K)arrow_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