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The theoretical maximum velocity (in m/s) of air expanding from a reservoir at 700 K is __________ (accurate to two decimal places). Specific heat of air at constant pressure is 1005 J/(kg-K)
Correct answer is '1185.00 to 1186.50'. Can you explain this answer?
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The theoretical maximum velocity (in m/s) of air expanding from a rese...
Given:
- Temperature of the air reservoir (T) = 700 K
- Specific heat of air at constant pressure (Cp) = 1005 J/(kg-K)
To find:
- The theoretical maximum velocity of air expanding from the reservoir in m/s, accurate to two decimal places.
Explanation:
The theoretical maximum velocity of air expanding from the reservoir can be determined using the isentropic flow equation. The isentropic flow equation relates the velocity of a fluid to its temperature, pressure, and specific heat at constant pressure.
1. Calculate the sonic velocity:
The sonic velocity (a) of air at a given temperature can be calculated using the equation:
a = sqrt(gamma * R * T)
Where:
- gamma is the ratio of specific heats (Cp/Cv) for air, which is approximately 1.4
- R is the specific gas constant for air, approximately 287 J/(kg-K)
Substituting the given values, we can calculate the sonic velocity:
a = sqrt(1.4 * 287 * 700) = 347.62 m/s
2. Calculate the Mach number:
The Mach number (M) is defined as the ratio of the velocity of the fluid to the sonic velocity. It can be calculated using the equation:
M = V/a
Where:
- V is the velocity of the fluid
3. Calculate the theoretical maximum velocity:
The Mach number is related to the velocity of the fluid through the isentropic flow equation:
M = (1 / sqrt(1 - (V/a)^2))
Rearranging the equation, we can solve for V:
(V/a)^2 = 1 - (1/M)^2
V = a * sqrt(1 - (1/M)^2)
Substituting the given values, we can calculate the theoretical maximum velocity:
V = 347.62 * sqrt(1 - (1/1)^2) = 347.62 m/s
Final answer:
The theoretical maximum velocity of air expanding from the reservoir is 347.62 m/s, accurate to two decimal places.
- Temperature of the air reservoir (T) = 700 K
- Specific heat of air at constant pressure (Cp) = 1005 J/(kg-K)
To find:
- The theoretical maximum velocity of air expanding from the reservoir in m/s, accurate to two decimal places.
Explanation:
The theoretical maximum velocity of air expanding from the reservoir can be determined using the isentropic flow equation. The isentropic flow equation relates the velocity of a fluid to its temperature, pressure, and specific heat at constant pressure.
1. Calculate the sonic velocity:
The sonic velocity (a) of air at a given temperature can be calculated using the equation:
a = sqrt(gamma * R * T)
Where:
- gamma is the ratio of specific heats (Cp/Cv) for air, which is approximately 1.4
- R is the specific gas constant for air, approximately 287 J/(kg-K)
Substituting the given values, we can calculate the sonic velocity:
a = sqrt(1.4 * 287 * 700) = 347.62 m/s
2. Calculate the Mach number:
The Mach number (M) is defined as the ratio of the velocity of the fluid to the sonic velocity. It can be calculated using the equation:
M = V/a
Where:
- V is the velocity of the fluid
3. Calculate the theoretical maximum velocity:
The Mach number is related to the velocity of the fluid through the isentropic flow equation:
M = (1 / sqrt(1 - (V/a)^2))
Rearranging the equation, we can solve for V:
(V/a)^2 = 1 - (1/M)^2
V = a * sqrt(1 - (1/M)^2)
Substituting the given values, we can calculate the theoretical maximum velocity:
V = 347.62 * sqrt(1 - (1/1)^2) = 347.62 m/s
Final answer:
The theoretical maximum velocity of air expanding from the reservoir is 347.62 m/s, accurate to two decimal places.
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The theoretical maximum velocity (in m/s) of air expanding from a reservoir at 700 K is __________ (accurate to two decimal places). Specific heat of air at constant pressure is 1005 J/(kg-K)Correct answer is '1185.00 to 1186.50'. Can you explain this answer?
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The theoretical maximum velocity (in m/s) of air expanding from a reservoir at 700 K is __________ (accurate to two decimal places). Specific heat of air at constant pressure is 1005 J/(kg-K)Correct answer is '1185.00 to 1186.50'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The theoretical maximum velocity (in m/s) of air expanding from a reservoir at 700 K is __________ (accurate to two decimal places). Specific heat of air at constant pressure is 1005 J/(kg-K)Correct answer is '1185.00 to 1186.50'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The theoretical maximum velocity (in m/s) of air expanding from a reservoir at 700 K is __________ (accurate to two decimal places). Specific heat of air at constant pressure is 1005 J/(kg-K)Correct answer is '1185.00 to 1186.50'. Can you explain this answer?.
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