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Unformatted text preview: Y(s) = G(s).X(s)
Y ( s) = 11
1 + τs s 1 + τs s s A = τ 2 B = − τ C =1 τ2
Y ( s) =
1 + τs s s
Y ( t ) = τe − t / τ − τ + t
(a) the difference between the indicated temperature and bath temperature
at t = 0.1 min = X(0.1)_ Y(0.1)
= 0.1 - (0.2e-0.1/0.2 - 0.2+0.1) since T = 0.2 given
= 0.0787 deg C
(b) t = 1.0 min
X(1) - Y(1) = 1- (0.2e-1/0.2 - 0.2 +1) = 0.1986
(c) Deviation D = -Y(t) +X(t)
= -τe-t/T+T =τ (-e-t/T+1)
For maximum value dD/dT = τ (-e-t/T+(_-1/T) = 0
-e-t/ = 0
as t tend to infinitive
D = τ (-e-t/T+(_-1/T) = τ =0.2 deg C 5.2 A mercury thermometer bulb in ½ in . long by 1/8 in diameter. The
glass envelope is very thin. Calculate the time constant in water flowing
at 10 ft / sec at a temperature of 100 deg F. In your solution , give a
summary which includes
(a) Assumptions used.
(b) Source of data
(c) Results T = mCp/hA = ( ρAL)C p
h ( A + πDL) Calculation of NU d = Re d = Pr = hD
= CRem (Pr) n
K Dvρ µ Cpµ
K = (1 / 8 * 2.54 * 10 −2 )(10 * 0.3048)103
10 −3 = 4.2 KJ / KgK Source data: Recently, Z hukauskas has given c,m ,ξ,n values.
For Re = 967704
C = 0.26 & m = 0.6
NuD = hD/K = 0.193 (9677.4)*(6.774X10-3) = 130
.h = 25380 5.3 Given a system with the transfer function Y(s)/X(s) = (T1s+1)/(T2s+1).
Find Y(t) if X(t) is a unit step function. If T1/T2 = s. Sktech Y(t) Versus
t/T2. Show the numerical values of minimum, maximum and ultimate values
that may occur during the transient. Check these using the initial value
and final value theorems of chapter 4. Y ( s) = T1s + 1
T2 s + 1 X(s) =unit step function = 1 X(s) = 1/s ...
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This note was uploaded on 11/13/2011 for the course COP 4355 taught by Professor Koslov during the Spring '10 term at University of Florida.
- Spring '10