The mass flow rate of a calorically perfect gas (Cp = constant) through a Convergent-Divergent nozzle is given by, m = A Pt R m= y + 1 +²²) 2(x-1) M (1+ (a) Derive the above relation from fundamental principals. Here, P₁, is total (or Stagnation) pressure and T, is total temperature, M is Mach number, A is local area of nozzle. (b) Prove mathematically that the maximum airflow limit occurs when the Mach number is equal to one and obtain below relation. A Pt R (Y+¹) y + 1 2(y-1) √Tt Note: The limiting of the maximum mass flow rate when M =1, is called choking of the flow or Choked flow.
The mass flow rate of a calorically perfect gas (Cp = constant) through a Convergent-Divergent nozzle is given by, m = A Pt R m= y + 1 +²²) 2(x-1) M (1+ (a) Derive the above relation from fundamental principals. Here, P₁, is total (or Stagnation) pressure and T, is total temperature, M is Mach number, A is local area of nozzle. (b) Prove mathematically that the maximum airflow limit occurs when the Mach number is equal to one and obtain below relation. A Pt R (Y+¹) y + 1 2(y-1) √Tt Note: The limiting of the maximum mass flow rate when M =1, is called choking of the flow or Choked flow.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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![The mass flow rate of a calorically perfect gas (C₁ = constant) through a Convergent-Divergent nozzle is given
by,
m =
A Pt
VT₁
M (1+
y +1
YM²) 2(3-1)
(a) Derive the above relation from fundamental principals. Here, P₁, is total (or Stagnation) pressure and T₁ is
total temperature, M is Mach number, A is local area of nozzle.
(b) Prove mathematically that the maximum airflow limit occurs when the Mach number is equal to one and
obtain below relation.
m
A Pt
√√Tt
Note: The limiting of the maximum mass flow rate when M =1, is called choking of the flow or Choked flow.
Hint: https://www.grc.nasa.gov/www/k-12/rocket/mflchk.html
y+1
2(y-1)
√(4¹)
R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69b4eea4-da32-4a3d-a9f6-0631f752eb35%2F6b1632de-1f05-4074-a5a6-26930d78ae33%2Fg3ad8ro_processed.png&w=3840&q=75)
Transcribed Image Text:The mass flow rate of a calorically perfect gas (C₁ = constant) through a Convergent-Divergent nozzle is given
by,
m =
A Pt
VT₁
M (1+
y +1
YM²) 2(3-1)
(a) Derive the above relation from fundamental principals. Here, P₁, is total (or Stagnation) pressure and T₁ is
total temperature, M is Mach number, A is local area of nozzle.
(b) Prove mathematically that the maximum airflow limit occurs when the Mach number is equal to one and
obtain below relation.
m
A Pt
√√Tt
Note: The limiting of the maximum mass flow rate when M =1, is called choking of the flow or Choked flow.
Hint: https://www.grc.nasa.gov/www/k-12/rocket/mflchk.html
y+1
2(y-1)
√(4¹)
R
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