The core of a high-temperature, gas-cooled nuclear reactor has coolant tubes of 20-mm diameter and 780-mm length. Helium enters at 600 K and exits at 1000 K when the flow rate is 8 × 10 − 3 kg / s per tube. (a) Determine the uniform tube wall surface temperature for these conditions. (b) If the coolant gas is air, determine the required how rate if the heat removal rate and tube wall surface temperature remain the same. What is the outlet temperature of the air?
The core of a high-temperature, gas-cooled nuclear reactor has coolant tubes of 20-mm diameter and 780-mm length. Helium enters at 600 K and exits at 1000 K when the flow rate is 8 × 10 − 3 kg / s per tube. (a) Determine the uniform tube wall surface temperature for these conditions. (b) If the coolant gas is air, determine the required how rate if the heat removal rate and tube wall surface temperature remain the same. What is the outlet temperature of the air?
Solution Summary: The author explains the surface temperature of helium, the mass flow rate, and the Reynolds number for the type of flow.
The core of a high-temperature, gas-cooled nuclear reactor has coolant tubes of
20-mm
diameter and 780-mm length. Helium enters at 600 K and exits at 1000 K when the flow rate is
8
×
10
−
3
kg
/
s
per tube.
(a) Determine the uniform tube wall surface temperature for these conditions.
(b) If the coolant gas is air, determine the required how rate if the heat removal rate and tube wall surface temperature remain the same. What is the outlet temperature of the air?
Y
F1
α
В
X
F2
You and your friends are planning to move the log. The log.
needs to be moved straight in the x-axis direction and it
takes a combined force of 2.9 kN. You (F1) are able to exert
610 N at a = 32°. What magnitude (F2) and direction (B) do
you needs your friends to pull?
Your friends had to pull at:
magnitude in Newton, F2
=
direction in degrees, ẞ =
N
deg
100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph
for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Produce an animation of the system for all solutions for the first minute.
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