Midterm Learning Module 03: The Energy Equation
5 | Page
Consider a fixed amount of matter contained within a closed boundary. This
matter defines the system. Because the molecules and atoms within the system are
constantly in motion, the system contains a certain amount of energy. For simplicity,
the system contains a unit mass; in turn, denote the internal energy per unit mass.
The region outside the system defines the surroundings. Let an incremental
amount of heat be added to the system from the surroundings. Also, add a work
done on the system by the surroundings. Both heat and work are forms of energy,
and when added to the system, they change the amount of internal energy in the
system.
The energy equation for an inviscid, adiabatic flow:
when:
Example. In a supersonic wind tunnel, the air temperature and pressure in the
reservoir of the wind tunnel are T o = 1000 K and p o = 10 atm, respectively. The static
temperature at the throat and exit T* = 833 K and T e = 300 K. The mass flow through
the nozzle is 0.5 kg/s. For air C p = 1008 J/kg.K. Determine the velocity at the throat,
V*.
Given: T o = 1000 K p o = 10 atm T* = 833 K T e = 300 K
= .5 kg/s C p = 1008 J/kg.K
Required: V*
Solution:
In the reservoir, V o = 0, therefore,
LEARNING MODULE ASSESSMENT
Analyze and solve the following problems based on the topics discussed. You may
write your answers on a sheet of paper and have it photographed or you may have it
encoded. Submit within the given timeframe and to the online platform where this will
be evaluated. Failure to do so will induce a grade with deduction proportional to the
tardiness of submission.
PHILIPPINE STATE COLLEGE OF AERONAUTICS
INSTITUTE OF ENGINEERING AND TECHNOLOGY
Midterm Learning Module 03: The Energy Equation
6 | Page
1. From the given example, determine:
a) Velocity at the exit, V e ;
b) Area of the throat, A*; and
c) Area of the exit, A e .
Answers
Answer:
Midterm Learning Module 03: The Energy Equation
5 | Page
Consider a fixed amount of matter contained within a closed boundary. This
matter defines the system. Because the molecules and atoms within the system are
constantly in motion, the system contains a certain amount of energy. For simplicity,
the system contains a unit mass; in turn, denote the internal energy per unit mass.
The region outside the system defines the surroundings. Let an incremental
amount of heat be added to the system from the surroundings. Also, add a work
done on the system by the surroundings. Both heat and work are forms of energy,
and when added to the system, they change the amount of internal energy in the
system.
The energy equation for an inviscid, adiabatic flow:
when:
Example. In a supersonic wind tunnel, the air temperature and pressure in the
reservoir of the wind tunnel are T o = 1000 K and p o = 10 atm, respectively. The static
temperature at the throat and exit T* = 833 K and T e = 300 K. The mass flow through
the nozzle is 0.5 kg/s. For air C p = 1008 J/kg.K. Determine the velocity at the throat,
V*.
Given: T o = 1000 K p o = 10 atm T* = 833 K T e = 300 K
= .5 kg/s C p = 1008 J/kg.K
Required: V*
Solution:
In the reservoir, V o = 0, therefore,
LEARNING MODULE ASSESSMENT
Analyze and solve the following problems based on the topics discussed. You may
write your answers on a sheet of paper and have it photographed or you may have it
encoded. Submit within the given timeframe and to the online platform where this will
be evaluated. Failure to do so will induce a grade with deduction proportional to the
tardiness of submission.
PHILIPPINE STATE COLLEGE OF AERONAUTICS
INSTITUTE OF ENGINEERING AND TECHNOLOGY
Midterm Learning Module 03: The Energy Equation
6 | Page
1. From the given example, determine:
a) Velocity at the exit, V e ;
b) Area of the throat, A*; and
c) Area of the exit, A e .
Answer:
Midterm Learning Module 03: The Energy Equation
5 | Page
Consider a fixed amount of matter contained within a closed boundary. This
matter defines the system. Because the molecules and atoms within the system are
constantly in motion, the system contains a certain amount of energy. For simplicity,
the system contains a unit mass; in turn, denote the internal energy per unit mass.
The region outside the system defines the surroundings. Let an incremental
amount of heat be added to the system from the surroundings. Also, add a work
done on the system by the surroundings. Both heat and work are forms of energy,
and when added to the system, they change the amount of internal energy in the
system.
The energy equation for an inviscid, adiabatic flow:
when:
Example. In a supersonic wind tunnel, the air temperature and pressure in the
reservoir of the wind tunnel are T o = 1000 K and p o = 10 atm, respectively. The static
temperature at the throat and exit T* = 833 K and T e = 300 K. The mass flow through
the nozzle is 0.5 kg/s. For air C p = 1008 J/kg.K. Determine the velocity at the throat,
V*.
Given: T o = 1000 K p o = 10 atm T* = 833 K T e = 300 K
= .5 kg/s C p = 1008 J/kg.K
Required: V*
Solution:
In the reservoir, V o = 0, therefore,
LEARNING MODULE ASSESSMENT
Analyze and solve the following problems based on the topics discussed. You may
write your answers on a sheet of paper and have it photographed or you may have it
encoded. Submit within the given timeframe and to the online platform where this will
be evaluated. Failure to do so will induce a grade with deduction proportional to the
tardiness of submission.
PHILIPPINE STATE COLLEGE OF AERONAUTICS
INSTITUTE OF ENGINEERING AND TECHNOLOGY
Midterm Learning Module 03: The Energy Equation
6 | Page
1. From the given example, determine:
a) Velocity at the exit, V e ;
b) Area of the throat, A*; and
c) Area of the exit, A e .
Answer:
Midterm Learning Module 03: The Energy Equation
5 | Page
Consider a fixed amount of matter contained within a closed boundary. This
matter defines the system. Because the molecules and atoms within the system are
constantly in motion, the system contains a certain amount of energy. For simplicity,
the system contains a unit mass; in turn, denote the internal energy per unit mass.
The region outside the system defines the surroundings. Let an incremental
amount of heat be added to the system from the surroundings. Also, add a work
done on the system by the surroundings. Both heat and work are forms of energy,
and when added to the system, they change the amount of internal energy in the
system.
The energy equation for an inviscid, adiabatic flow:
when:
Example. In a supersonic wind tunnel, the air temperature and pressure in the
reservoir of the wind tunnel are T o = 1000 K and p o = 10 atm, respectively. The static
temperature at the throat and exit T* = 833 K and T e = 300 K. The mass flow through
the nozzle is 0.5 kg/s. For air C p = 1008 J/kg.K. Determine the velocity at the throat,
V*.
Given: T o = 1000 K p o = 10 atm T* = 833 K T e = 300 K
= .5 kg/s C p = 1008 J/kg.K
Required: V*
Solution:
In the reservoir, V o = 0, therefore,
LEARNING MODULE ASSESSMENT
Analyze and solve the following problems based on the topics discussed. You may
write your answers on a sheet of paper and have it photographed or you may have it
encoded. Submit within the given timeframe and to the online platform where this will
be evaluated. Failure to do so will induce a grade with deduction proportional to the
tardiness of submission.
PHILIPPINE STATE COLLEGE OF AERONAUTICS
INSTITUTE OF ENGINEERING AND TECHNOLOGY
Midterm Learning Module 03: The Energy Equation
6 | Page
1. From the given example, determine:
a) Velocity at the exit, V e ;
b) Area of the throat, A*; and
c) Area of the exit, A e .
Answer:
Midterm Learning Module 03: The Energy Equation
5 | Page
Consider a fixed amount of matter contained within a closed boundary. This
matter defines the system. Because the molecules and atoms within the system are
constantly in motion, the system contains a certain amount of energy. For simplicity,
the system contains a unit mass; in turn, denote the internal energy per unit mass.
The region outside the system defines the surroundings. Let an incremental
amount of heat be added to the system from the surroundings. Also, add a work
done on the system by the surroundings. Both heat and work are forms of energy,
and when added to the system, they change the amount of internal energy in the
system.
The energy equation for an inviscid, adiabatic flow:
when:
Example. In a supersonic wind tunnel, the air temperature and pressure in the
reservoir of the wind tunnel are T o = 1000 K and p o = 10 atm, respectively. The static
temperature at the throat and exit T* = 833 K and T e = 300 K. The mass flow through
the nozzle is 0.5 kg/s. For air C p = 1008 J/kg.K. Determine the velocity at the throat,
V*.
Given: T o = 1000 K p o = 10 atm T* = 833 K T e = 300 K
= .5 kg/s C p = 1008 J/kg.K
Required: V*
Solution:
In the reservoir, V o = 0, therefore,
LEARNING MODULE ASSESSMENT
Analyze and solve the following problems based on the topics discussed. You may
write your answers on a sheet of paper and have it photographed or you may have it
encoded. Submit within the given timeframe and to the online platform where this will
be evaluated. Failure to do so will induce a grade with deduction proportional to the
tardiness of submission.
PHILIPPINE STATE COLLEGE OF AERONAUTICS
INSTITUTE OF ENGINEERING AND TECHNOLOGY
Midterm Learning Module 03: The Energy Equation
6 | Page
1. From the given example, determine:
a) Velocity at the exit, V e ;
b) Area of the throat, A*; and
c) Area of the exit, A e .