Aerodynamics
Derive the fundamental thrust equation for jet propulsion.
A turbojet aircraft is flying with a velocity of at an altitude of , where the ambient conditions are and . The pressure ratio across the compressor is , and the temperature at the turbine inlet is . Air enters the compressor at and the jet fuel has a heating value of . Assuming ideal operation for all components, and assuming constant specific heats for air at room temperature, determine the velocity of the exhaust gases, the propulsive power, and the rate of fuel consumption.
Derive the fundamental equation of thin airfoil theory and solve it for symmetric airfoil.
Show the typical distribution of pressure coefficient on the upper and the lower surfaces of an airfoil for a zero and non-zero angle of attack.
Explain with appropriate sketches how stall occurs in an airfoil at a high angle of attack.
What is Magnus effect? A cylinder with diameter with a circulation is placed in free stream with uniform velocity of . Calculate the value of when both the stagnation points coincide on the body. Also calculate the lift acting on the cylinder. Take .
A Rankine oval of long and high is immersed in a stream of , as in Fig. 6(b). Determine the velocity at point A and the location of point B where a particle approaching the stagnation point achieves its maximum deceleration.

Find the velocity distribution and shear stress for the following cases by the exact solution of Navier-Stokes equations: Plane Poiseuille flow and Plane Couette flow. The x-momentum equation is given as:
The viscous, incompressible flow between the parallel plates shown in Fig. 7(b) is caused by both the motion of the top plate and a pressure gradient . Find the required pressure to achieve a zero net volume flow rate across a cross-section.

Define stability of an aircraft. Explain positive dynamic stability with necessary sketches.
What are the purposes of flaps in an aircraft? Name with neat sketches different types of flaps used in airplane.
In a tornado as shown in Fig. 8(c), the circulation is and that the pressure at is which is less than the far-field pressure. Assuming sea-level density of air, calculate the sink strength, the pressure at , and the angle at which the streamlines cross the circle at .
