Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
3.0k views
in Physics by (49.1k points)
closed by

A cylindrical furnace has height (H) and diameter (D) both 1 m. It is maintained at temperature 360 K. The air gets heated inside the furnace at constant pressure Pa and its temperature becomes T = 360 K. The hot air with density ρ rises up a vertical chimney of diameter d = 0.1 m and height h = 9 m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density ρa = 1.2 kg m−3, pressure Pa and temperature Ta = 300 K enters the furnace. Assume air as an ideal gas, neglect the variations in ρ and T inside the chimney and the furnace. Also ignore the viscous effects.

[Given: The acceleration due to gravity g = 10 ms−2 and π = 3.14]

(1) Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is ______ g ms−1 .

(2) When the chimney is closed using a cap at the top, a pressure difference \(\Delta\)P develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air, due to the stoppage of air flow, are negligible then the value of \(\Delta\)P is ______ N m−2.

1 Answer

+1 vote
by (48.0k points)
selected by
 
Best answer

(1) Applying Bernoulli’s theorem between top and bottom points of furnace:

(2) Let V' be the speed of air in chimney.

⇒ By continuity equation,

πd2 . V = πd2 . V' 

⇒ V' = 100V = 1000 m/s 

Also, pressure difference \(\Delta\)

= pV'2 . area

= 7850 N/m2

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...