(a)
Compute
Answer to Problem 9.43P
Explanation of Solution
Given information:
At section 1,
At section 2,
The area is same but flow is faster than at section 1
The temperature ratio is defined as,
For perfect gas, where
Area change is defined as,
In the above equation,
The velocity at point 2 is defined as,
The density at section 1 is defined as,
For ideal gas,
Calculation:
Calculate the temperature at point 1,
Rearrange,
Substitute,
Calculate the stagnation temperature,
Substitute for known values,
Solve to find
Calculate the area change at point 1,
Since the area is same at point 2, the area change will also be the same
Therefore,
Therefore, according to the table B.1 which represents the isentropic flow of perfect gas
The Mach number at point 2 is equal to,
Now, find the temperature at point 2,
Substitute for known values,
Solve to find
Calculate the velocity at point 2,
Substitute for known values,
Solve to find
Conclusion:
The velocity at point 2 is equal to
(b)
Compute
Answer to Problem 9.43P
Explanation of Solution
Given information:
At section 1,
At section 2,
The area is same but flow is faster than at section 1
For perfect gas, where
Area change is defined as,
In above equation,
Calculation:
Calculate the area change at point 1,
Since the area is same at point 2, the area change will also be the same
Therefore,
Therefore, according to the table B.1 which represents the isentropic flow of perfect gas
The Mach number at point 2 is equal to,
Conclusion:
The Mach number at point 2 is equal to
(c)
Compute
Answer to Problem 9.43P
Explanation of Solution
Given information:
At section 1,
At section 2,
The area is same but flow is faster than at section 1
The temperature ratio is defined as,
Calculation:
Calculate the temperature at point 1,
Rearrange,
Substitute,
Calculate the stagnation temperature,
Substitute for known values,
Solve to find
Calculate the area change at point 1,
Since the area is same at point 2, the area change will also be the same
Therefore,
Therefore, according to the table B.1 which represents the isentropic flow of perfect gas
The Mach number at point 2 is equal to,
Now, find the temperature at point 2,
Substitute for known values,
Solve to find
Conclusion:
The temperature at point 2 is equal to
(d)
To compute: mass flow.
Answer to Problem 9.43P
Explanation of Solution
Given information:
At section 1,
At section 2,
The area is same but flow is faster than at section 1
The mass flow is defined as,
Where,
For ideal gas,
Calculation:
Calculate the velocity at point 1,
Calculate the mass flow,
Substitute,
Solve to find mass flow,
Conclusion:
The mass flow is equal to
(e)
If there is a sonic throat exit and the value.
Answer to Problem 9.43P
Explanation of Solution
Given information:
At section 1,
At section 2,
The area is same but flow is faster than at section 1
Area change is defined as,
In above equation,
Calculation:
According to sub-part a,
We have found that,
The area change is equal to,
But we know,
The area of both sections is equal, but the velocity of the flow differs. Therefore, a throat exist in between section 1 and 2.
Therefore, to find the throat area,
Conclusion:
The throat diameter is equal to
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Chapter 9 Solutions
Fluid Mechanics, 8 Ed
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