3-21
3-57E The combustion efficiency of a furnace is raised from 0.7 to 0.8 by tuning it up. The annual energy and cost savings
as a result of tuning up the boiler are to be determined.
Assumptions The boiler operates at full load while operating.
3-22
3-58E Problem 3-57E is reconsidered. The effects of the unit cost of energy and combustion efficiency on the annual
energy used and the cost savings as the efficiency varies from 0.7 to 0.9 and the unit cost varies from $4 to $6 per million
Btu are the investigated. The annual energy saved and the cost savings are to be plotted against the efficiency for unit costs
of $4, $5, and $6 per million Btu.
Analysis The problem is solved using EES, and the solution is given below.
3-24
3-61 A room is cooled by circulating chilled water through a heat exchanger, and the air is circulated through the heat
exchanger by a fan. The contribution of the fan-motor assembly to the cooling load of the room is to be determined.
Assumptions The fan motor operates at full load so that fload = 1.
3-62 A hydraulic turbine-generator is to generate electricity from the water of a lake. The overall efficiency, the turbine
efficiency, and the shaft power are to be determined.
Assumptions 1 The elevation of the lake and that of the discharge
site remains constant. 2 Irreversible losses in the pipes are
negligible.
Properties The density of water can be taken to be
= 1000
kg/m3. The gravitational acceleration is g = 9.81 m/s2.
3-26
3-65 Problem 3-64 is reconsidered. The effect of wind velocity and the blade span diameter on wind power
generation as the velocity varies from 5 m/s to 20 m/s in increments of 5 m/s, and the diameter varies from 20 m to 120 m in
increments of 20 m is to be investigated.
3-27
3-66 Water is pumped from a lake to a storage tank at a specified rate. The overall efficiency of the pump-motor unit and
the pressure difference between the inlet and the exit of the pump are to be determined.
Assumptions 1 The elevations of the tank and the lake remain constant. 2 Frictional losses in the pipes are negligible. 3 The
changes in kinetic energy are negligible. 4 The elevation difference across the pump is negligible.
Properties We take the density of water to be
= 1000 kg/m3.
3-28
3-67 A large wind turbine is installed at a location where the wind is blowing steadily at a certain velocity. The electric
power generation, the daily electricity production, and the monetary value of this electricity are to be determined.
Assumptions 1 The wind is blowing steadily at a constant
uniform velocity. 2 The efficiency of the wind turbine is
independent of the wind speed.
Properties The density of air is given to be
= 1.25
kg/m3.
3-68 The available head of a hydraulic turbine and its overall efficiency are given. The electric power output of this turbine
is to be determined.
Assumptions 1 The flow is steady and incompressible. 2 The
elevation of the reservoir remains constant.
Wind
Wind
turbine
3-30
3-71 The mass flow rate of water through the hydraulic turbines of a dam is to be determined.
3-72 A pump is pumping oil at a specified rate. The pressure rise of oil in the pump is measured, and the motor efficiency is
specified. The mechanical efficiency of the pump is to be determined.
Assumptions 1 The flow is steady and incompressible. 2 The elevation difference across the pump is negligible.
3-31
Review Problems
3-73 The weight of the cabin of an elevator is balanced by a counterweight. The power needed when the fully loaded cabin
is rising, and when the empty cabin is descending at a constant speed are to be determined.
frictiontotal WWW
3-74 A decision is to be made between a cheaper but inefficient natural gas heater and an expensive but efficient natural gas
heater for a house.
Assumptions The two heaters are comparable in all aspects other than the initial cost and efficiency.
3-32
3-75E The energy contents, unit costs, and typical conversion efficiencies of various energy sources for use in water heaters
are given. The lowest cost energy source is to be determined.
Assumptions The differences in installation costs of different water heaters are not considered.
3-76 A home owner is considering three different heating systems for heating his house. The system with the lowest energy
cost is to be determined.
Assumptions The differences in installation costs of different heating systems are not considered.
3-33
3-77 It is estimated that 570,000 barrels of oil would be saved per day if the thermostat setting in residences in winter were
lowered by 6F (3.3C). The amount of money that would be saved per year is to be determined.
Assumptions The average heating season is given to be 180 days, and the cost of oil to be $40/barrel.
3-78 Caulking and weather-stripping doors and windows to reduce air leaks can reduce the energy use of a house by up to
10 percent. The time it will take for the caulking and weather-stripping to pay for itself from the energy it saves is to be
determined.
Assumptions It is given that the annual energy usage of a house is $1100 a year, and the cost of caulking and weather–
3-79E The work required to compress a gas in a gas spring is to be determined.
Assumptions All forces except that generated by the gas spring will be neglected.
Analysis When the expression given in the problem statement is substituted into the work integral relation, and advantage is
taken of the fact that the force and displacement vectors are collinear, the result is
Btu 0.0160
ftlbf 169.778
Btu 1
ft)lbf 45.12(
ftlbf 45.12
in 12
ft 1
in) 2(in) 7(
4.11
inlbf 200
)(
1
Constant
Constant
0.40.4
1.4
1
1
1
2
2
1
2
1
kk
k
xx
k
dx
x
FdsW
x
F
3-34
3-80E A man pushes a block along a horizontal plane. The work required to move the block is to be determined considering
(a) the man and (b) the block as the system.
Analysis The work applied to the block to overcome the friction is found by using the work integral,
Btu 2.57
ftlbf 169.778
Btu 1
ft)lbf 2000(
ftlbf 2000
ft) 100)(lbf 100)(2.0(
)(
2
1
12
2
1
xxfWFdsW
The man must then produce the amount of work
3-81 A TV set is kept on a specified number of hours per day. The cost of electricity this TV set consumes per month is to
be determined.
Assumptions 1 The month is 30 days. 2 The TV set consumes its rated power when on.
3-82E The power required to pump a specified rate of water to a specified elevation is to be determined.
Properties The density of water is taken to be 62.4 lbm/ft3 (Table A-3E).
Analysis The required power is determined from
kW 11.3
ft/slbf 737.56
kW 1
)ft/slbf 8342(ft/slbf 8342
ft/slbm 32.174
lbf 1
gal/min 15,850
/sft 315.35
)()(
2
2
3
3
1212 zzgzzgmW
V
x
W
fW
fW
3-36
3-85 The available head, flow rate, and efficiency of a hydroelectric turbine are given. The electric power output is to be
determined.
Assumptions 1 The flow is steady. 2 Water levels at the reservoir and the discharge site remain constant. 3 Frictional losses
in piping are negligible.
Properties We take the density of water to be = 1000 kg/m3 = 1 kg/L.
3-38
3-87 The pump of a water distribution system is pumping water at a specified flow rate. The pressure rise of water in the
pump is measured, and the motor efficiency is specified. The mechanical efficiency of the pump is to be determined.
Assumptions 1 The flow is steady. 2 The elevation difference across the pump is
negligible. 3 Water is incompressible.
3-88 … 3-93 Design and Essay Problems
15 kW