MAE 110A
Homework 1: Solutions
1/14/2017
H1.1 Consider a 80 kg person. Determine (show all work):
a. mass in lbm (do also in slugs)
b. weight in lbf, if person is at sea level
c. weight in lbf, if person is on top of Mt Everest
d. weight in lbf, if person is on the surface of the moon
Given Data
Conversions
Governing Equations
Analysis
Part a: Determine the mass in lbm and slugs
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Part b: Determine the weight at sea level in
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Part c: Determine the weight at the top Mt. Everest in
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Part d: Determine the weight on the moon in
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Discussion
This problem is focused on understanding mass and force, and their description in English units. The
force due to gravity depends on two factors, the mass and the local acceleration of gravity. In this
particular problem the mass was fixed and the force of gravity varied due to the location of the mass.
The values of used were found using a brief Google search.
References
: A Brief Introduction To Fluid Mechanics 5th Ed by Young
: http://hypertextbook.com/facts/2004/MichaelRobbins.shtml
H1.2: A U-tube mercury manometer is connected to a tank of gas (see text, Figure 1.7). The difference in
mercury levels is 17.5 in. The tank is located in a room where the atmospheric pressure is 14.7 psia.
Assume
. Determine:
a. tank pressure, psig
b. tank pressure, psia
c. tank pressure, kPa (absolute)
Given Data
Conversions
Diagram
Model
Fluid Statics
Governing Equations
(Eq. 1.11)
(Eq. 1.14)
Analysis
Part a: Determine tank pressure in psig
(
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] (
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Part b: Determine tank pressure in psia
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)
(
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Part c: Determine tank pressure in kPa (absolute)
(
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Discussion
A manometer indicates the height of a displaced fluid, in this case mercury, which can be related to the
pressure of the gas within the tank using fluid statics.
H1.3: Gas is contained in a vertical piston-cylinder device. The piston, with a mass of 4.2 kg and crosssectional area of 22
, is in equilibrium with the gas. The outside ambient pressure is 101 kPa.
Determine the (absolute) pressure of the gas (in kPa).
Given Data
Conversions
Diagram
Model
Piston-Cylinder assembly
System is in equilibrium
Governing Equations
∑
,
(Eq. 1.14)
Analysis
Determine the absolute pressure of the gas in
Since the piston is in equilibrium the net force is zero.
∑
∑
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(
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)
(
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)
Discussion
The weight of the piston compresses the gas contained within the cylinder tending to increase the
pressure of the gas. The pressure difference between the gas and atmosphere is maintained by the
piston weight.
H1.4: Consider a simple device or household appliance (e.g., refrigerator, water heater, iron, etc) and do
the following:
Explain its basic operating principle.
Sketch and define system (with dashed line). Identify and indicate significant energy transfers (with
labeled arrows). Be sure to cite any source(s) of information if you use.
Example (Refrigerator)
A refrigerator operates in a thermodynamic cycle. There is heat transfer from a low temperature region
(food compartment) to a high temperature region (surroundings). There are three primary energy
transfers during the four process cycle.
1) The compressor consumes electric power. This is energy entering the system. ( ̇ )
2) The refrigerant loses energy into the room air as it flows through the condenser. This is energy
leaving the system. ( ̇ )
3) A throttling device is used to cause the refrigerant to reduce to a low pressure and temperature.
There is no net energy transfer in the process.
4) The refrigerant absorbs heat (from the food compartment) as it flows through the evaporator.
This is energy entering the system. ( ̇ )
H1.5: Investigate energy consumption in the U.S., Germany, China, Kenya, and one other country (you
choose) through an internet search. Determine the following for each country:
a. total energy consumption (specify in both Btu and kWh (kilowatt-hours))
b. energy consumption per capita
c. total energy consumption breakdown (percentage) by source (e.g., oil, natural gas, renewables,
etc.)
Prepare summary data table and include dates (year) of data. Be sure to cite references (use at least 2).
Comment on any important/interesting findings.
Country
USA
Germany
China
Kenya
Canada
Energy (QuadBtu)
97.7
13.07
119.55
0.27
14.55
Energy Consumption 2014/2015
Energy (TWh) Per capita (kWh) By Source
28.63
91.2
32% Gas, 28%, Oil 21% Coal, 11% Ren
3.83
47.5
30% Ren, 27.5% Other, 23% Lig, 17% Coal
35.03
25.79
66% Coal, 18% Oil, 5% Gas
0.079
1.6
68% Wood, 22% Oil, 10% Other
4.26
121.71
31% Oil, 28% Gas, 26% Hydro, 15% Other
References
https://www.cleanenergywire.org/factsheets/germanys-energy-consumption-and-power-mix-charts
https://www.iea.org/statistics/statisticssearch/
https://yearbook.enerdata.net/
https://en.wikipedia.org/wiki/World_energy_consumption
https://en.wikipedia.org/wiki/List_of_countries_by_total_primary_energy_consumption_and_production
https://www.eia.gov/beta/international/data/browser/#/?pa=000000001&c=ruvvvvvfvtvnvv1urvvvvfvvvvvvfvvvou20evvvvvvvvvnvvuvo&ct=0&
ug=4&vs=INTL.44-2-AFG-QBTU.A&ord=SA&vo=0&v=H&start=1980&end=2014&s=INTL.44-2-DEU-QBTU.A~~INTL.44-2-KEN-QBTU.A~~INTL.44-2USA-QBTU.A~~INTL.44-2-CHN-QBTU.A~~INTL.44-2-CAN-QBTU.A
H1.6: Personal energy audit - part 1. An estimate of your personal energy consumption may be
obtained by considering your energy usage in a number of categories including heating and cooling,
transportation, and lighting/appliances/electronics. Some of these will require some further knowledge
in thermodynamics to do the calculations (we will do in later HWs).
For this assignment, estimate your monthly energy usage for lighting/appliances/electronics. Do the
following:
a. List devices and equipment that you personally use that require electricity, e.g., lamps,
refrigerator, tv, computers, etc. Indicate also the quantity of each.
b. Determine the rate of energy (in Watts) used by each device when it is on. This will be an
indicated power rating of the device, or you could do an internet search for typical values.
c. Estimate how much time (in hrs) you use each device for a typical week.
d. Calculate the energy used for each device (in Watt-hrs) per week and (in kWh) per month.
Determine the total kWh of electricity you use per month for this category.
e. Prepare a summary table that indicates the above information and results.
List any key assumptions made in your estimates.
Devices
Lamp (x12)
TV
Refrigerator
Dishwasher
Washer
Water Cooler
Stove/Oven
Laptop (x2)
Desktop
Vacuum
Power (W)
180
100
100
200
450
100
2000
140
250
1000
Monthly Energy Usage
Weekly Usage (hr) Weekly (Wh)
35
6300
35
3500
84
8400
21
4200
7
3150
7
700
14
28000
28
3920
14
3500
1.75
1750
Totals: 63420
Monthly (kWh)
27
15
36
18
13.5
3
120
16.8
15
0.75
265.05
Assumptions
Average power consumption
Average usage time
Referencees
https://www.energy.gov/energysaver/estimating-appliance-and-home-electronic-energy-use
https://www.daftlogic.com/information-appliance-power-consumption.htm
https://www.easycalculation.com/physics/electromagnetism/power-consumption-table.php