Need help solving math problem using integration
1 answer:
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Answer:
1) q=18414.93 W
2) C=12920$
Explanation:
Given data:
pipe length L=25m
pipe diameter D=100mm =0.1 m
air temperature =
=25
°C.....= 298.15k
pipe surface temp =150
°C.....=423.15k
surface emissivity e= 0.8
boiler efficiency η=0.90
natural gas price Cg=$0.02 per MJ
1) Total heat loss and radiation heat loss combined
q=
q=б(
^4-
^4)]....... (1)
б=5.67×10^-8 W/m^2K^4 (boltzmann constant)
area A =L.Dπ=25×0.1π=7.85 m^2
putting all these values in eq (1)
q=18414.93 W
2) suppose boiler is operating non stop annual energy loss will be
E=q.t
=18414.93.3600.24.365
=5.81×10^11 J
to find furnace energy consumption
Ef =E/η
=6.46×10^5 MJ
annual cost
C=Cg. Ef
=12920$
Answer:
Q= 4.6 × 10⁻³ m³/s
actual velocity will be equal to 8.39 m/s
Explanation:
density of fluid = 900 kg/m³
d₁ = 0.025 m
d₂ = 0.05 m
Δ P = -40 k N/m²
C v = 0.89
using energy equation
under ideal condition v₁² = 0
v₂² = 88.88
v₂ = 9.43 m/s
hence discharge at downstream will be
Q = Av
Q =
Q =
Q= 4.6 × 10⁻³ m³/s
we know that
hence , actual velocity will be equal to 8.39 m/s
Answer with Explanation:
The crown will be pure if it's specific gravity is 19.3
Now by definition of specific gravity it is the ratio between the weight of an object to the weight of water of equal volume
Since it is given that the weight of the crown is 11.8 N we need to find it's volume
Now According to Archimedes principle when the crown is immersed into water the water shall exert a force in upwards direction on the crown with a magnitude equaling to weight of the water displaced by the crown
Mathematically this is the difference between the weight of the crown in air and weight when immersed in water
Thus Buoyant force is
Now by Archimedes principle This force equals in magnitude to the weight of water of same volume as of the crown
Thus the specific gravity of the crown equals
As we see that the specific gravity of the crown material is less than that of pure gold hence we conclude that it is impure.