The international standard atmosphere (ISA) is a reference model for the variation of the properties of...

  

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The international standard atmosphere (ISA) is a reference model for the variation of the properties of the Earth's atmosphere with altitude, which is used to set aviation standards. In the ISA, the atmosphere is divided into several layers with linear temperature distributions. The properties of the first four layers of the ISA are given in the table below: Altitude range (m) 0-11,000 11,000-20,000 20,000-32,000 32,000-47,000 Temperature at bottom (°C) 15.0 Layer Troposphere Tropopause Stratosphere Stratosphere Lapse rate (°C/km) -6.5 0.0 -56.5 1.0 -56.5 2.8 -44.5 The lapse rate is the rate of change of the temperature with altitude within that layer. Thus, the temperature at sea level is 15.0 °C and decreases 6.5 °C for every kilometer over sea level until the altitude reaches 11 km. Between 11 km and 20 km the temperature remains constant (lapse rate is zero). Above 20 km and below 32 km it increases 1.0 °C for every kilometer of altitude, and so on. (a) (11 pts) Derive expressions that can be used to calculate the pressure as a function of altitude for each of the layers of the standard atmosphere in the table above. Using these expressions, plot the pressure, temperature, and air density as a function of altitude for altitudes ranging from 0 to 47 km. (b) (14 pts) Mount Fuji, a stratovolcano located on Honshu Island, is the tallest mountain in Japan, and was added to the UNESCO list of world heritage sites in 2013. It has a nearly perfectly conical shape, with an elevation of 12,388 ft and a diameter at the base of approximately 30 miles. Using the result from part (b), estimate the total vertical force that the atmosphere exerts over Mt. Fuji. Mt. Fuji The international standard atmosphere (ISA) is a reference model for the variation of the properties of the Earth's atmosphere with altitude, which is used to set aviation standards. In the ISA, the atmosphere is divided into several layers with linear temperature distributions. The properties of the first four layers of the ISA are given in the table below: Altitude range (m) 0-11,000 11,000-20,000 20,000-32,000 32,000-47,000 Temperature at bottom (°C) 15.0 Layer Troposphere Tropopause Stratosphere Stratosphere Lapse rate (°C/km) -6.5 0.0 -56.5 1.0 -56.5 2.8 -44.5 The lapse rate is the rate of change of the temperature with altitude within that layer. Thus, the temperature at sea level is 15.0 °C and decreases 6.5 °C for every kilometer over sea level until the altitude reaches 11 km. Between 11 km and 20 km the temperature remains constant (lapse rate is zero). Above 20 km and below 32 km it increases 1.0 °C for every kilometer of altitude, and so on. (a) (11 pts) Derive expressions that can be used to calculate the pressure as a function of altitude for each of the layers of the standard atmosphere in the table above. Using these expressions, plot the pressure, temperature, and air density as a function of altitude for altitudes ranging from 0 to 47 km. (b) (14 pts) Mount Fuji, a stratovolcano located on Honshu Island, is the tallest mountain in Japan, and was added to the UNESCO list of world heritage sites in 2013. It has a nearly perfectly conical shape, with an elevation of 12,388 ft and a diameter at the base of approximately 30 miles. Using the result from part (b), estimate the total vertical force that the atmosphere exerts over Mt. Fuji. Mt. Fuji

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To calculate the pressure at given altitude we need to assumed two things Temperature has standard v... View the full answer