Answer:
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Explanation:
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Based on the Chvorinov's rule, the diference in the <em>solidification</em> times of the two castings is 14.092 times the <em>solidification</em> time of the prism casting.
<h3>How to apply the Chvorinov's rule for casting processes</h3>
The Chvorinov's rule is an empirical method to estimate the cooling time of a casting in terms of a <em>reference</em> time. This rule states that cooling time (<em>t</em>) is directly proportional to the square of the volume (<em>V</em>), in cubic meters, divided to the surface area (<em>A</em>), in square meters. Now we proceed to model each casting:
<h3>Cylindrical casting</h3>t = C · [0.25π · D² · L/(0.5π · D² + π · D · L)]²
t = C · [0.25 · D · L/(0.5 · D + L)]² (1)
<h3>Prism casting</h3>t' = C · [3 · T² · L/(6 · T · L + 2 · T · L + 6 · T²)]²
t' = C · [3 · T · L/(8 · L + 6 · T)]² (2)
<h3>Relationship between the cross sections of both castings</h3>3 · T² = 0.25π · D² (3)
Where:
- <em>t</em> - Cooling time of the cylindrical casting, in time unit.
- <em>t'</em> - Cooling time of the prism casting, in time unit.
- <em>C</em> - Cooling factor, in time unit per square meter.
- <em>D</em> - Diameter of the cylinder, in meters.
- <em>L</em> - Length of the casting, in meters.
- <em>T</em> - Width of the cross section of the prism casting, in meters.
If we know that <em>D =</em> <em>0.3 m</em>, then the thickness of the prism casting is:
<em>T ≈ 0.153 m</em>
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And (1) and (2) simplified into these forms:
<h3>Cylindrical casting</h3>t = C · {0.25π · (0.3 m) · (0.5 m)/[0.5 · (0.3 m) + 0.5 m]}²
t = 0.0329 · C (1b)
<h3>Prism casting</h3>t' = C · {3 · (0.153 m) · (0.5 m)/[8 · (0.5 m) + 6 · (0.153 m)]}²
t' = 0.00218 · C (2b)
Lastly we find the <em>percentual</em> difference in the solidification times of the two castings by using the following expression:
<em>r = (</em>1 <em>- t'/t) ×</em> 100 %
<em>r = (</em>1 <em>-</em> 0.00218<em>/</em>0.0329<em>) ×</em> 100 %
<em>r =</em> 93.374 %
The <em>cooling</em> time of the <em>prism</em> casting is 6.626 % of the <em>solidification</em> time of the <em>cylindrical</em> casting. The diference in the <em>solidification</em> times of the two castings is 14.092 times the <em>solidification</em> time of the <em>prism</em> casting.
To learn more on solidification times, we kindly invite to check this verified question: brainly.com/question/13536247
Answer:
0.0297M^3/s
W=68.48kW
Explanation:
Hello! To solve this problem, we must first find all the thermodynamic properties at the input (state 1) and the compressor output (state 2), using the thermodynamic tables
Through laboratory tests, thermodynamic tables were developed, these allow to know all the thermodynamic properties of a substance (entropy, enthalpy, pressure, specific volume, internal energy etc ..)
through prior knowledge of two other properties such as pressure and temperature.
state 1
X=quality=1
T=-26C
density 1=α1=5.27kg/m^3
entalpy1=h1=234.7KJ/kg
state 2
T2=70
P2=8bar=800kPa
density 2=α2=31.91kg/m^3
entalpy2=h2=306.9KJ/kg
Now to find the flow at the outlet of the compressor, we remember the continuity equation that states that the mass flow is equal to the input and output.
m1=m2
(Q1)(α1)=(Q2)(α2)
the volumetric flow rate at the exit is 0.0297M^3/s
To find the power of the compressor we use the first law of thermodynamics that says that the energy that enters must be equal to the energy that comes out, in this order of ideas we have the following equation
W=m(h2-h1)
m=Qα
W=(0.18)(5.27)(306.9-234.7)
W=68.48kW
the compressor power is 68.48kW