A heat flux gage of 4−mm diameter is positioned normal to and 1m from the 5−mm−diameter aperture of a blackbody furnace at 1000 K. The diffuse, gray cover shield ( ε = 0.2 ) of the furnace has an outer diameter of 100 mm and its temperature is 350 K. The furnace and gage are located in a large room whose walls have an emissivity of 0.8 and are at 300 K. (a) What is the irradiation on the gage, G g ( W / m 2 ) , considering only emission from the aperture of the furnace? (b) What is the irradiation on the gage due to radiation from the cover and aperture?
A heat flux gage of 4−mm diameter is positioned normal to and 1m from the 5−mm−diameter aperture of a blackbody furnace at 1000 K. The diffuse, gray cover shield ( ε = 0.2 ) of the furnace has an outer diameter of 100 mm and its temperature is 350 K. The furnace and gage are located in a large room whose walls have an emissivity of 0.8 and are at 300 K. (a) What is the irradiation on the gage, G g ( W / m 2 ) , considering only emission from the aperture of the furnace? (b) What is the irradiation on the gage due to radiation from the cover and aperture?
Solution Summary: The author explains the irradiation on the gauge considering only emission from aperture of the furnace.
A heat flux gage of 4−mm diameter is positioned normal to and 1m from the 5−mm−diameter aperture of a blackbody furnace at 1000 K. The diffuse, gray cover shield
(
ε
=
0.2
)
of the furnace has an outer diameter of 100 mm and its temperature is 350 K. The furnace and gage are located in a large room whose walls have an emissivity of 0.8 and are at 300 K.
(a) What is the irradiation on the gage,
G
g
(
W
/
m
2
)
, considering only emission from the aperture of the furnace? (b) What is the irradiation on the gage due to radiation from the cover and aperture?
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
1 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t > 0:
Analytically (hand calculations)
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.
www.m
k₁ = 3
(y₁ = 0).
m₁ = 1
k2=2
(y₂ = 0)
|m₂ = 1
Y2
y 2
System in
static
equilibrium
(Net change in
spring length
=32-31)
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)
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