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JNTU B.Tech III AERODYNAMICS II Previous Question Paper (March - 2021 - R15/R13)
Answer any five questions. All questions carry equal marks.
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How to analyze a thermally perfect gas?
Answer
A thermally perfect gas is defined as a gas that obeys the ideal gas equation of state, where the internal energy and enthalpy are functions of temperature only. To analyze such a gas, the following fundamental relations are applied:
- The equation of state is given by P = ρRT, where P is pressure, ρ is density, R is the specific gas constant, and T is absolute temperature.
- The internal energy (u) and enthalpy (h) are related to temperature via specific heats: du = cv(T)dTanddh = cp(T)dT.
- The specific heats cp and cv are not constant but vary with temperature. They are linked by the relation cp - cv = R.
- For processes involving changes in state, the entropy change is calculated using the temperature-dependent specific heats: ds = cp(T)dT/T - RdP/P.
- In engineering analysis, if the temperature range is small, specific heats are often approximated as constants, allowing for the use of isentropic relations such as T2/T1 = (P2/P1)(γ-1)/γ.
Nitrogen gas is compressed reversibly and isothermally from 100 kPa and 250°C to a final pressure of 300 kPa. Calculate the entropy change associated with this compression process.
Answer
To calculate the entropy change for a reversible isothermal process, we use the property relation for entropy. Since the process is isothermal (T1 = T2), the change in entropy depends solely on the pressure change.
The formula for entropy change is:
Given that the process is isothermal, ln(T2/T1) = ln(1) = 0. Therefore, the equation simplifies to:
For Nitrogen (N2), the molar mass M = 28.01 kg/kmol. The universal gas constant Ru = 8.314 kJ/(kmol·K). The specific gas constant R is:
Substituting the given values (P1 = 100 kPa, P2 = 300 kPa):
The entropy change associated with the compression process is -0.326 kJ/(kg·K).
Air undergoes a change of state isentropically from 300K and 110 kPa to a final pressure of 550 kPa. Assuming ideal gas behavior, determine the change in enthalpy.
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Compute the temperature rise at the nose of an aircraft flying with mach number 2 at an altitude of 10,000 m.
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Derive an expression for Prandtl relation. Consider normal shock relations for a perfect gas to support your answer.
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A normal shock wave forms in an air stream at a static temperature of 22K. If the total temperature is 400K, determine the Mach number and static temperature behind the shock.
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Consider a hypersonic missile flying at Mach 8 at an altitude of 30,000 m where the pressure is 973.3 kg/m2. The nose of the missile is blunt. Calculate the pressure at the stagnation point on the nose.
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Compare subsonic compressible flow and supersonic flow.
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Briefly write about the analysis of wave reflection from a free boundary.
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What are the applications of thin airfoil theory?
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Justify how shock expansion theory explains wave pattern over objects.
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Show that Prandtl Meyer function is a similarity variable.
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Derive an expression for Prandtl Glauert compressibility correction.
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How computational fluid dynamics is useful in analyzing compressible flow over transonic airfoils.
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How the resultant and perturbation velocities vary for supersonic flow along a wave shaped wall?
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Consider a flat plate at an angle of attack in an inviscid supersonic flow. From linear theory, what is the value of the maximum lift-to-drag ratio, and at what angle of attack does it occur?
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