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?
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Answer:
Explanation:
Given that :
The initial volume of water = 1000.00 mL = 1000000 mm³
The initial temperature of the water = 10° C
The height of the water column h = 1000.00 mm
The final temperature of the water = 70° C
The coefficient of thermal expansion for the glass is ∝ =
The objective is to determine the the depth of the water column
In order to do that we will need to determine the volume of the water.
We obtain the data for physical properties of water at standard sea level atmospheric from pressure tables; So:
At temperature the density of the water is
At temperature the density of the water is
The mass of the water is
Thus; we can say ;
⇒
Thus, the volume of the water after heating to a required temperature of is 1022400 mm³
However; taking an integral look at this process; the volume of the water before heating can be deduced by the relation:
The area of the water before heating is:
The area of the heated water is :
Finally, the depth of the heated hot water is:
Hence the depth of the heated hot water is