Chapter 10
THE FIRST LAW
APPLIED TO
STEADY FLOW PROCESSES
It is not the sun to overtake the moon, nor doth the night outstrip
the day. They float each in an orbit.
− The Holy Qur-ān
In many engineering applications, devices such as turbines, pumps, com-
pressors, heat exchangers and boilers are operated under steady flow con-
ditions for long periods of time. A steady flow process is a process in which
matter and energy flow in and out of an open system at steady rates. More-
over, an open system undergoing a steady flow process does not experience
any change in the mass and energy of the system. Application of the first
law of thermodynamics to steady flow processes is discussed in this chapter.
,212 Chapter 10
10.1 What is Steady?
The term steady implies no change with time. We say that a person
is running at a steady speed of 5 km per hour, as shown in Figure 10.1, if
the speed does not change with time.
✓✏
❡�
✒✑
5 km
✲ per hour
Figure 10.1 A person running at a steady speed of 5 km per hour.
10.2 What is a Steady Flow Process?
A steady flow process is one in which matter and energy flow steadily
in and out of an open system. In a steady flow process, the properties of
the flow remain unchanged with time, that is, the properties are frozen in
time. But, the properties need not be the same in all points of the flow.
It is very common for a beginner to confuse the term steady with the
term equilibrium. But, they are not the same. When a system is at a
steady state, the properties at any point in the system are steady in time,
but may vary from one point to another point. The temperature at the inlet,
for example, may differ from that at the outlet. But, each temperature,
whatever its value, remains constant in time in a steady flow process.
When a system is at an equilibrium state, the properties are steady in
time and uniform in space. By properties being uniform in space, we mean
that a property, such as pressure, has the same value at each and every
point in the system.
An example of steady flow of water through a pipe is shown in Figure
10.2. Pressure measurements taken along the pipe at two different times
, The First Law applied to Steady Flow Processes 213
of a day, shown in the figure, remain the same since the flow is steady.
But, observe that the values of pressure vary along the pipe illustrating the
nonuniform nature of the steady flow.
2.3 bar 2.0 bar 1.7 bar 1.4 bar 1.1 bar
water flows at a ✲ ❄ ❄ ❄ ❄ ❄
steady rate of 0.3 kg/s
(a) measurements taken at 10.00 am
2.3 bar 2.0 bar 1.7 bar 1.4 bar 1.1 bar
water flows at a ✲ ❄ ❄ ❄ ❄ ❄
steady rate of 0.3 kg/s
(b) measurements taken at 2.00 pm
Figure 10.2 An example of steady flow.
10.3 Characteristics of a
Steady Flow Process
A steady flow is one that remains unchanged with time, and therefore
a steady flow has the following characteristics:
• Characteristic 1:
No property at any given location within the system boundary changes
with time. That also means, during an entire steady flow process, the
total volume Vs of the system remains a constant, the total mass ms
, 214 Chapter 10
of the system remains a constant, and that the total energy content
Es of the system remains a constant.
• Characteristic 2:
Since the system remains unchanged with time during a steady flow
process, the system boundary also remains the same.
• Characteristic 3:
No property at an inlet or at an exit to the open system changes
with time. That means that during a steady flow process, the mass
flow rate, the energy flow rate, pressure, temperature, specific (or
molar) volume, specific (or molar) internal energy, specific (or molar)
enthalpy, and the velocity of flow at an inlet or at an exit remain
constant.
• Characteristic 4:
Rates at which heat and work are transferred across the boundary of
the system remain unchanged.
10.4 Mass Balance for a
Steady Flow Process
Since a steady flow process can be considered as a special process expe-
rienced by the open system discussed in Chapter 9, we may start from the
mass balance for open systems, which is given by (9.1). Characteristic 1 of
the steady flow process is that the mass of the open system experiencing
a steady flow process remains constant. This is achieved if the mass flow
rate at the inlet equals the mass flow rate at the exit. Therefore, (9.1)
reduces to
ṁi = ṁe (10.1)
where the subscript i denotes the inlet and the subscript e denotes the exit.
THE FIRST LAW
APPLIED TO
STEADY FLOW PROCESSES
It is not the sun to overtake the moon, nor doth the night outstrip
the day. They float each in an orbit.
− The Holy Qur-ān
In many engineering applications, devices such as turbines, pumps, com-
pressors, heat exchangers and boilers are operated under steady flow con-
ditions for long periods of time. A steady flow process is a process in which
matter and energy flow in and out of an open system at steady rates. More-
over, an open system undergoing a steady flow process does not experience
any change in the mass and energy of the system. Application of the first
law of thermodynamics to steady flow processes is discussed in this chapter.
,212 Chapter 10
10.1 What is Steady?
The term steady implies no change with time. We say that a person
is running at a steady speed of 5 km per hour, as shown in Figure 10.1, if
the speed does not change with time.
✓✏
❡�
✒✑
5 km
✲ per hour
Figure 10.1 A person running at a steady speed of 5 km per hour.
10.2 What is a Steady Flow Process?
A steady flow process is one in which matter and energy flow steadily
in and out of an open system. In a steady flow process, the properties of
the flow remain unchanged with time, that is, the properties are frozen in
time. But, the properties need not be the same in all points of the flow.
It is very common for a beginner to confuse the term steady with the
term equilibrium. But, they are not the same. When a system is at a
steady state, the properties at any point in the system are steady in time,
but may vary from one point to another point. The temperature at the inlet,
for example, may differ from that at the outlet. But, each temperature,
whatever its value, remains constant in time in a steady flow process.
When a system is at an equilibrium state, the properties are steady in
time and uniform in space. By properties being uniform in space, we mean
that a property, such as pressure, has the same value at each and every
point in the system.
An example of steady flow of water through a pipe is shown in Figure
10.2. Pressure measurements taken along the pipe at two different times
, The First Law applied to Steady Flow Processes 213
of a day, shown in the figure, remain the same since the flow is steady.
But, observe that the values of pressure vary along the pipe illustrating the
nonuniform nature of the steady flow.
2.3 bar 2.0 bar 1.7 bar 1.4 bar 1.1 bar
water flows at a ✲ ❄ ❄ ❄ ❄ ❄
steady rate of 0.3 kg/s
(a) measurements taken at 10.00 am
2.3 bar 2.0 bar 1.7 bar 1.4 bar 1.1 bar
water flows at a ✲ ❄ ❄ ❄ ❄ ❄
steady rate of 0.3 kg/s
(b) measurements taken at 2.00 pm
Figure 10.2 An example of steady flow.
10.3 Characteristics of a
Steady Flow Process
A steady flow is one that remains unchanged with time, and therefore
a steady flow has the following characteristics:
• Characteristic 1:
No property at any given location within the system boundary changes
with time. That also means, during an entire steady flow process, the
total volume Vs of the system remains a constant, the total mass ms
, 214 Chapter 10
of the system remains a constant, and that the total energy content
Es of the system remains a constant.
• Characteristic 2:
Since the system remains unchanged with time during a steady flow
process, the system boundary also remains the same.
• Characteristic 3:
No property at an inlet or at an exit to the open system changes
with time. That means that during a steady flow process, the mass
flow rate, the energy flow rate, pressure, temperature, specific (or
molar) volume, specific (or molar) internal energy, specific (or molar)
enthalpy, and the velocity of flow at an inlet or at an exit remain
constant.
• Characteristic 4:
Rates at which heat and work are transferred across the boundary of
the system remain unchanged.
10.4 Mass Balance for a
Steady Flow Process
Since a steady flow process can be considered as a special process expe-
rienced by the open system discussed in Chapter 9, we may start from the
mass balance for open systems, which is given by (9.1). Characteristic 1 of
the steady flow process is that the mass of the open system experiencing
a steady flow process remains constant. This is achieved if the mass flow
rate at the inlet equals the mass flow rate at the exit. Therefore, (9.1)
reduces to
ṁi = ṁe (10.1)
where the subscript i denotes the inlet and the subscript e denotes the exit.
