Concept explainers
Helium expands in a nozzle from 0.8 MPa, 500 K, and negligible velocity to 0.1 MPa. Calculate the throat and exit areas for a mass flow rate of 0.34 kg/s, assuming the nozzle is isentropic. Why must this nozzle be converging–diverging?
The throat and exit area of the nozzle.
Answer to Problem 131RP
The throat area of nozzle is
The exit area is
Explanation of Solution
It is given that the initial velocity is negligible. Hence, the inlet properties are equal to the stagnation properties at inlet.
Consider the flow through the nozzle is isentropic. Hence, the stagnation properties at inlet and exit equal.
Write the formula for the critical temperature of the mixture.
Here, the critical temperature of mixture is
Write the formula for the critical pressure of the mixture.
Here, the critical pressure of mixture is
Write the formula for the critical density.
Here, the critical density of mixture is
Write the formula for critical velocity of helium gas through the nozzle.
Here, the superscript
Write the formula for mass flow rate of helium at throat region.
Here, the cross sectional area of the throat is
Rearrange the Equation (V) to obtain
Refer Table A-1, “Molar mass, gas constant, and critical-point properties”.
The gas constant
Refer Table A-2, “Ideal-gas specific heats of various common gases”.
The specific heat ratio
Write the formula of ratio of stagnation pressure to the static pressure at exit of the nozzle.
Here, the actual (static) pressure at the exit of nozzle is
Write the formula of ratio of stagnation temperature to the static temperature at exit of the nozzle.
Here, the actual (static) temperature at the exit of nozzle is
Write the formula for velocity of sound at the exit conditions.
Here, speed of sound at the exit condition is
Write formula for the velocity of helium at exit.
Write the formula for mass flow rate of helium at exit condition.
Here, the exit cross sectional area is
Rearrange the Equation (X) to obtain
Conclusion:
Substitute
Substitute
Substitute
Substitute 1.667 for
Substitute
Equation (VI).
Thus, the throat area of nozzle is
Substitute
Here, the downstream Mach number
Substitute
Substitute
Substitute
Thus, the exit area is
Want to see more full solutions like this?
Chapter 17 Solutions
Thermodynamics: An Engineering Approach
Additional Engineering Textbook Solutions
EBK FUNDAMENTALS OF THERMODYNAMICS, ENH
Manufacturing Engineering & Technology
Engineering Mechanics: Statics
Applied Statics and Strength of Materials (6th Edition)
Vector Mechanics for Engineers: Dynamics
Fundamentals of Heat and Mass Transfer
- Helium 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_forwardHelium enters a converging–diverging nozzle at 0.7 MPa, 800 K, and 100 m/s. What are the lowest temperature and pressure that can be obtained at the throat of the nozzle?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
- Five 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_forwardi need the answer quicklyarrow_forwardSolve it correctly please. I will rate accordinglyarrow_forward
- Air enters a nozzle at 0.5 MPa, 420 K, and a velocity of 110 m/s. 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?arrow_forwardIf 8 kg of oxygen in a closed tank at 200°C and 300 kPa isheated until the pressure rises to 400 kPa, calculate (a) thenew temperature, (b) the total heat transfer, and (c) thechange in entropy.arrow_forwardA large vessel contains compressed air at To = 350 K and Po = 2 bar. A converging-diverging nozzle is attached to the vessel to discharge air. The throat area of the nozzle is 200 cm2. At the exit, the pressure is 20 kPa and the flow is supersonic. Answer the followings:arrow_forward
- I need the answer as soon as possiblearrow_forwardConsider an aircraft engine operating at subsonic conditions with a nozzle that has an exit area of 142in2 and a nozzle inlet/exit area ratio of 2. Engine gases flowing at 30lbm/s enter the nozzle with a pressure of 0.83 bar and avelocity of 144 m/s. The gases expand through the nozzle, exiting at the ambient pressure of 7.25 psia with a velocity of 1320 ft/s. a) For these conditions, what is the force (in units of lbf) trasmitted to the structure holding the nozzle. Provide both direction and magnitude of the force. b) Based on your results, comment on whether the force acting on the nozzle would hlep speed up or slow down a vehicle that used this nozzle as part of a jet propulsion system. I mostly wanted help in part b. Thank you.arrow_forwardA stream of air at 77°F and 1.2 atm absolute flowing at a rate of 225 ft3/h is blown through ducts that pass through the interior of a large industrial motor. The air emerges at 500°F. Calculate the rate atwhich the air is removing heat generated by the motor. What assumption have you made about the pressure dependence of the specific enthalpy of air?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