chapter 5 thermodynamic
5-1
Chapter 5
MASS AND ENERGY ANALYSIS OF CONTROL
VOLUMES
Conservation of Mass
5-1C Mass, energy, momentum, and electric charge are conserved, and volume and entropy are not conserved during a process.
5-2C Mass flow rate is the amount of mass flowing through a cross-section per unit time whereas the volume flow rate is the amount of volume flowing through a cross-section per unit time.
5-3C The amount of mass or energy entering a control volume does not have to be equal to the amount of mass or energy leaving during an unsteady-flow process.
5-4C Flow through a control volume is steady when it involves no changes with time at any specified position. 5-5C No, a flow with the same volume flow rate at the inlet and the exit is not necessarily steady (unless the density is constant). To be steady, the mass flow rate through the device must remain constant.
PROPRIETARY MATERIAL. © 2008 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.
5-2
5-6E A garden hose is used to fill a water bucket. The volume and mass flow rates of water, the filling time, and the discharge velocity are to be determined.
Assumptions 1 Water is an incompressible substance. 2 Flow through the hose is steady. 3 There is no waste of water by splashing.
Properties We take the density of water to be 62.4 lbm/ft3 (Table A-3E).
Analysis (a) The volume and mass flow rates of water are
V& = AV = (πD 2 / 4)V = [π (1 / 12 ft) 2 / 4](8 ft/s) = 0.04363 ft 3 /s
&
m = ρV& = (62.4 lbm/ft 3 )(0.04363 ft 3 /s) = 2.72 lbm/s
(b) The time it takes to fill a 20-gallon bucket is
Δt =
⎞
⎛ 1 ft 3
20 gal
V
⎟ = 61.3 s
⎜
=
& 0.04363 ft 3 /s ⎜ 7.4804 gal ⎟
V
⎠
⎝
(c) The average discharge velocity of water at the nozzle exit is
Ve =
V&
Ae
=
V&
2
πDe / 4
=
0.04363 ft 3 /s
[π (0.5 / 12 ft) 2 / 4]
= 32 ft/s
Chapter 5
MASS AND ENERGY ANALYSIS OF CONTROL
VOLUMES
Conservation of Mass
5-1C Mass, energy, momentum, and electric charge are conserved, and volume and entropy are not conserved during a process.
5-2C Mass flow rate is the amount of mass flowing through a cross-section per unit time whereas the volume flow rate is the amount of volume flowing through a cross-section per unit time.
5-3C The amount of mass or energy entering a control volume does not have to be equal to the amount of mass or energy leaving during an unsteady-flow process.
5-4C Flow through a control volume is steady when it involves no changes with time at any specified position. 5-5C No, a flow with the same volume flow rate at the inlet and the exit is not necessarily steady (unless the density is constant). To be steady, the mass flow rate through the device must remain constant.
PROPRIETARY MATERIAL. © 2008 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.
5-2
5-6E A garden hose is used to fill a water bucket. The volume and mass flow rates of water, the filling time, and the discharge velocity are to be determined.
Assumptions 1 Water is an incompressible substance. 2 Flow through the hose is steady. 3 There is no waste of water by splashing.
Properties We take the density of water to be 62.4 lbm/ft3 (Table A-3E).
Analysis (a) The volume and mass flow rates of water are
V& = AV = (πD 2 / 4)V = [π (1 / 12 ft) 2 / 4](8 ft/s) = 0.04363 ft 3 /s
&
m = ρV& = (62.4 lbm/ft 3 )(0.04363 ft 3 /s) = 2.72 lbm/s
(b) The time it takes to fill a 20-gallon bucket is
Δt =
⎞
⎛ 1 ft 3
20 gal
V
⎟ = 61.3 s
⎜
=
& 0.04363 ft 3 /s ⎜ 7.4804 gal ⎟
V
⎠
⎝
(c) The average discharge velocity of water at the nozzle exit is
Ve =
V&
Ae
=
V&
2
πDe / 4
=
0.04363 ft 3 /s
[π (0.5 / 12 ft) 2 / 4]
= 32 ft/s