MAE 101B – Summer Session II 2006

Homework Assignment #4

Due Friday September1

  1. Air is cooled at constant pressure from 858 K and 4.5 MPa (gage) to 15oC. Show the process on a T-s diagram. Calculate the change in specific entropy if air behaves as an ideal gas. Evaluate the heat transferred per unit mass if the process is reversible.
  1. In a closed system, a gas undergoes a cycle made up of the following processes: 1-2 reversible isothermal compression, 2-3 reversible constant volume heating, 3-4 reversible constant pressure expansion, and 4-1 reversible adiabatic expansion. (a) Sketch p-v and T-s diagrams of the cycle. (b) State whether each of the following quantities is positive, zero, negative, or indeterminate in sign:
  1. A jet transport aircraft cruises at M = 0.85 at 12.5 km altitude on a standard day. Evaluate the stagnation pressure sensed by a probe on the aircraft. What speed would be calculated from the incompressible Bernoulli equation? By what percentage is this speed in error compared to the true speed of the aircraft?
  1. Air enters a long, insulated duct at M1 = 0.2, T1 = 286 K, and p1 = 98.5 kPa (abs). Downstream the properties are M2 = 0.6, T2 = 268.9 K, and p2 = 31.3 kPa (abs). (Four significant figures are given to minimize roundoff errors.) Evaluate local isentropic stagnation conditions (a) at the inlet section and (b) at the outlet section. Calculate the change in specific entropy along the duct. Plot static and stagnation state points on a T-s diagram.
  1. A bicycle tire is inflated to 800 kPa (gage); at a temperature of 37oC. Find critical T and p. Then find the speed of sound within the tire at these critical conditions.
  1. An airplane cruises overhead, at 3 km, at M = 1.35. The air temperature is 303 K and there is a 10 m/s headwind. (a) What is the speed of the aircraft? (b) What is the time between seeing the aircraft overhead and hearing it?

Problems from Fox and McDonald:

  1. 11.2
  2. 11.8
  3. 11.12
  4. 11.56