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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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