A jet engine for a supersonic transport (SST) propels the airplane at Mach 3 at an altitude of 50,000 ft where the temperature i
s 217°K and the ambient pressure is 0.115 atm. The maximum temperature that the advanced turbine blades can handle is 1900°K. The engine operates at a compressor pressure ratio that allows the engine to achieve maximum work. The temperature at the entrance to the compressor is 595.7K. Assume that γ = 1.4 and Cp = 1004 J/kg-°K throughout the engine. If the engine inlet isentropically slows down the incoming freestream air such that the Mach number of the flow just upstream of the compressor is 0.3,
a) How many stages should the aircraft engine compressor have if the compression pressure ratio of each stage is 1.2? b) Please plot the cycle on a T-s diagram labeling only the temperature at each point? c) What is the thermal efficiency of the engine? d) What is the absolute highest possible thermal efficiency one can expect from a machine operating within the range of temperatures involved in this problem? e) What is the amount of heat per unit mass of working fluid that is needed to be generated by the combustion of fuel in the engine burner?
a) How many stages should the aircraft engine compressor have if the compression pressure ratio of each stage is 1.2? b) Please plot the cycle on a T-s diagram labeling only the temperature at each point? c) What is the thermal efficiency of the engine? d) What is the absolute highest possible thermal efficiency one can expect from a machine operating within the range of temperatures involved in this problem? e) What is the amount of heat per unit mass of working fluid that is needed to be generated by the combustion of fuel in the engine burner?
1 answer:
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Answer:
0.024 m = 24.07 mm
Explanation:
1) Notation
= tensile stress = 200 Mpa
= plane strain fracture toughness= 55 Mpa
= length of a surface crack (Variable of interest)
2) Definition and Formulas
The Tensile strength is the ability of a material to withstand a pulling force. It is customarily measured in units (F/A), like the pressure. Is an important concept in engineering, especially in the fields of materials and structural engineering.
By definition we have the following formula for the tensile stress:
(1)
We are interested on the minimum length of a surface that will lead to a fracture, so we need to solve for
Multiplying both sides of equation (1) by
(2)
Sequaring both sides of equation (2):
(3)
Dividing both sides by we got:
(4)
Replacing the values into equation (4) we got:
3) Final solution
So the minimum length of a surface crack that will lead to fracture, would be 24.07 mm or more.