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ES205
Examination II
April 21, 2000
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ES205 Examination II - Problem Solutions - Prof. Phillip J. Cornwell, Exams of Civil Engineering
Solutions to examination ii of es205, including block diagrams, equations for motion determination, and temperature calculations for a hydraulic amplifier and a natural convection heat transfer coefficient meter.
Typology: Exams
Pre 2010
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Name ___________________________ Section _____________________
ES
Examination II
April 21, 2000
Problem Score
Total /
Show all work for credit
AND
Turn in your signed help sheet
ES205 Examination II Problem 1 April 21, 2000
For the system shown below draw a block diagram. The governing equations are shown below (some in Laplace domain and others in time domain).
Op Amp: 1
2 1 R
R
E
Va =−
Loop Eqn.: -Va + IaRa + LasIa+Eb = 0
Back emf: Eb = kbsθ 1
Torque: T 1 = kT Ia
Gears: r 1 θ 1 = r 2 θ 2 T 1 r 2 =T 2 r 1
Load 1: J θ&& 2 + k 1 rL^2 θ 2 − rLk 1 X = T 2
Load 2: (ms^2 +Ds+k 1 +k 2 )X – k 1 rLθ 2 = 0
R 1
R 2
Ra La
ke=kb (^) kT
r 1
r 2
J
rL
m
k 1
k 2
vin (^) +
x
D
SEP
va
θ 1
θ 2
ES205 Examination II Problem 3 April 21, 2000
A natural convection heat transfer coefficient meter is intended for situations where the air temperature T∞ is known but the surrounding surfaces are at an unknown temperature, Tsurr. The two sensors that make up the meter each have a surface area of 1 cm^2 , one has a surface coating of emittance ε 1 = 0.9, and the other has an emittance of ε 2 = 0.1. The rear surface of the sensors is well insulated. When T∞ = 300 K and the test surface is at 320 K, the power inputs required to
maintain the sensors at 320K are W & in^1 (^) = 21. 7 mWand W & in 2 = 8. 28 mW. The Stefan-Boltsman
constant is σ = 5.67x10-8^ W/(m^2 -K^4 ). Determine: a) the temperature of the surroundings and the heat transfer coefficient b) If the power to sensor one is turned off, determine a differential equation for the temperature of the sensor. State your assumptions and what parameters for the system you would need to be given.
Note : Be sure to identify your system or systems and save all numerical substitutions and algebra (or plugging the equations into Maple) until the end of the exam (a list of unknowns and numbered equations for part a) will get you most of the points).
T∞, h
Tsurr
Sensor 1 Sensor 1
Section view of the meter
ES205 Examination II Problem 4 April 21, 2000
A tank of water with a cross section given by y = x^2 , as shown below is connected to a 50- ft- long, 0.5 in ID steel pipe that contains four 90° standard elbows and a gate valve (k 90 ° = 0.95, kgate=0.16, ε = 0.00015 ft, and ν = 0.739x10-5^ ft^2 /s). If the 10 ft long tank is initially filled to a depth of 3 ft and the pipe outlet is 20 ft below the bottom of the tank, determine:
a) the initial flow rate b) a differential equation for the height of fluid in the tank. Assume that the friction factor you determined in part a) is valid for the whole draining process.
x
y
y = x^2
Not drawn to scale
20 ft
3 ft
10 ft