A boiler is being fed by a conical tank seen in the figure. The piping between tanks is through a square duct with sides of length 4 cm. The volume of the water in the tank as a function of height is given by Ch³, where C is a known constant. The average velocity of the water exiting the tank is given by the expression Vavg,tank = K√h, where K can be assumed to be a known constant. The density of liquid water is known to be 1000 kg/m³. h Vavg.tank = K√h 1 cm 2 cm 1 cm Boiler 1.5 m/s 2.0 m/s 1.5 m/s V = 1.13 m³/s Pe = 800 kPa a) What is the equation for the velocity of the water surface in the tank as a function of h (and known constants), (i.e., dh/dt = ....)? Do NOT SOLVE the equation. b) At some instant in time, the velocity profile of the water entering the boiler was found to be approximated by the provided velocity profile in the square duct. What is the mass flow rate of the water entering the boiler at that time? c) At the exit of the boiler, the water is leaving as water vapor at a volumetric flow rate of 1.13 m³/s and a pressure of 800 kPa. What is the temperature of the water vapor? You may assume the water vapor can be treated as an ideal gas with
A boiler is being fed by a conical tank seen in the figure. The piping between tanks is through a square duct with sides of length 4 cm. The volume of the water in the tank as a function of height is given by Ch³, where C is a known constant. The average velocity of the water exiting the tank is given by the expression Vavg,tank = K√h, where K can be assumed to be a known constant. The density of liquid water is known to be 1000 kg/m³. h Vavg.tank = K√h 1 cm 2 cm 1 cm Boiler 1.5 m/s 2.0 m/s 1.5 m/s V = 1.13 m³/s Pe = 800 kPa a) What is the equation for the velocity of the water surface in the tank as a function of h (and known constants), (i.e., dh/dt = ....)? Do NOT SOLVE the equation. b) At some instant in time, the velocity profile of the water entering the boiler was found to be approximated by the provided velocity profile in the square duct. What is the mass flow rate of the water entering the boiler at that time? c) At the exit of the boiler, the water is leaving as water vapor at a volumetric flow rate of 1.13 m³/s and a pressure of 800 kPa. What is the temperature of the water vapor? You may assume the water vapor can be treated as an ideal gas with
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
![A boiler is being fed by a conical tank
seen in the figure. The piping between
tanks is through a square duct with sides
of length 4 cm. The volume of the water
in the tank as a function of height is given
by Ch³, where C is a known
constant. The average velocity of the
water exiting the tank is given by the
expression Vavg,tank = K√h, where K
can be assumed to be a known constant.
The density of liquid water is known to
be 1000 kg/m³.
h
Vavg.tank = K√h
1 cm
2 cm
1 cm
Boiler
1.5 m/s
2.0 m/s
1.5 m/s
V = 1.13 m³/s
Pe = 800 kPa
a) What is the equation for the velocity of the water surface in the tank as a function of h (and known
constants), (i.e., dh/dt = ....)? Do NOT SOLVE the equation.
b)
At some instant in time, the velocity profile of the water entering the boiler was found to be
approximated by the provided velocity profile in the square duct. What is the mass flow rate of
the water entering the boiler at that time?
c) At the exit of the boiler, the water is leaving as water vapor at a volumetric flow rate of 1.13 m³/s
and a pressure of 800 kPa. What is the temperature of the water vapor? You may assume the
water vapor can be treated as an ideal gas with
Rwater = 461.4 J/(kg-K); Ru=8314 J/(kmol-K); Mwater = 18.02 kg/kmol.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6abec00c-0df5-4c95-bf6e-fd605cb914b4%2F7d8e39e2-8b50-4b52-8582-ad69381d1eb6%2Fwx8r2q6_processed.png&w=3840&q=75)
Transcribed Image Text:A boiler is being fed by a conical tank
seen in the figure. The piping between
tanks is through a square duct with sides
of length 4 cm. The volume of the water
in the tank as a function of height is given
by Ch³, where C is a known
constant. The average velocity of the
water exiting the tank is given by the
expression Vavg,tank = K√h, where K
can be assumed to be a known constant.
The density of liquid water is known to
be 1000 kg/m³.
h
Vavg.tank = K√h
1 cm
2 cm
1 cm
Boiler
1.5 m/s
2.0 m/s
1.5 m/s
V = 1.13 m³/s
Pe = 800 kPa
a) What is the equation for the velocity of the water surface in the tank as a function of h (and known
constants), (i.e., dh/dt = ....)? Do NOT SOLVE the equation.
b)
At some instant in time, the velocity profile of the water entering the boiler was found to be
approximated by the provided velocity profile in the square duct. What is the mass flow rate of
the water entering the boiler at that time?
c) At the exit of the boiler, the water is leaving as water vapor at a volumetric flow rate of 1.13 m³/s
and a pressure of 800 kPa. What is the temperature of the water vapor? You may assume the
water vapor can be treated as an ideal gas with
Rwater = 461.4 J/(kg-K); Ru=8314 J/(kmol-K); Mwater = 18.02 kg/kmol.
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