Thermal energy generated by the electrical resistance of a 5-mm-diameter and 4-m-long bare cable is dissipated to the surroundin
g air at 20°C. The voltage drop and the electric current across the cable in steady operation are measured to be 60 V and 1.5 A, respectively. Disregarding radiation, estimate the surface temperature of the cable. Evaluate air properties at a film temperature of 60°C and 1 atm pressure. Is this a good assumption?
1 answer:
Answer:
surface temperature = 128.74⁰c
Explanation:
Given data
diameter of cable = 5 mm = 0.005 m
length of cable = 4 m
T∞ ( surrounding temperature ) = 20⁰c
voltage drop across cable ( dv )= 60 V
current across cable = 1.5 A
attached to this answer is the comprehensive analysis and solution to the problem.
The assumption made is not a good one since the calculated Ts ( surface temperature ) is very much different from the assumed Ts
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Answer:
the elongation of the metal alloy is 21.998 mm
Explanation:
Given the data in the question;
K = σT/ (εT)ⁿ
given that metal alloy true stress σT = 345 Mpa, plastic true strain εT = 0.02,
strain-hardening exponent n = 0.22
we substitute
K = 345 /
K = 815.8165 Mpa
next, we determine the true strain
(εT) = (σT/ K)^1/n
given that σT = 412 MPa
we substitute
(εT) = (412 / 815.8165 )^(1/0.22)
(εT) = 0.04481 mm
Now, we calculate the instantaneous length
=
given that = 480 mm
we substitute
=
×
= 501.998 mm
Now we find the elongation;
Elongation =
we substitute
Elongation = 501.998 mm - 480 mm
Elongation = 21.998 mm
Therefore, the elongation of the metal alloy is 21.998 mm