Question

Problem 3. Airplanes are launched from aircraft carriers by means of a steam catapult as shown in the figure below. The catapult is a well-insulated cylinder that contains steam and is fitted with a nearly frictionless piston. The piston is connected to the airplane by a cable. As the steam expands, the movement of the piston causes movement of the plane. A catapult design calls for 600 lbm of steam at 2000 psia and 800 °F to be expanded to 50 psia. Will this catapult be adequate to accelerate a 30-ton fighter aircraft from rest to 200 mph? Neglect the mass of the piston head and connecting cables as well as the thrust produced by the planes engines. You may assume that the steams expands reversibly. Assume the steam is an ideal gas. als Sie! (ylinker Pulser Problem 4. Repeat Problem 3 without the ideal gas assumption, meaning that it is true steam.

Answer 1

1/2 = 7. 1396 ft / bm At pi= 2000 psia and T, = 8000f, from Superheated stean Tables the properties are: u = 122001 Btul lom S, = 1.456 Bitul lbm. R Vi = 0.3012 ft3/lbm. the process is adiabatic b = 8,=1.456 Btul lom. R from Saturated bressure tables at b2 = 50 psia and s2 = 10456 Btullbmor, interpolate the valuer: 12 = 0.84 (s = ef to2 ff g] U2 U2 =458 Btulhu 2 = Up+x2 Mfg. - Uz = Up + d2 (ugu The work done by the gas is: W = m(uz-ui) = 6001 958 – 1.220.1) |=- 157260 Blu. Here the negative sign indicates work is done by the gas. The work done on atmosphere is :- Note Patm = 14.7 psia - Warm = tm Pam (12-1) = 14.7 l 144 in = BOOX°)16.8 x (7:1396- 0.3042) I Patra = 2116.8 10/ft? Wam = 8677694.562 lbf.ft in?

Wam = 8677694.59 lbf.ft x 0.60 128507 Bhe 1 lbf.ft = 1115 1044 Bte Net work is in Wnet = Wt Watm = - 157260 + 111 51.44 What = -146ior Btu the kinetic energy to more aircraft is in KE = 1/2 m2 = 12x130x108kg) (200 mph x 0.447 ) imph = 5x30x 10 x 8942 = 119,88X106 J x 1 Bhe KE = 113628.988 B the 1055.06 Since Whet > KE, the cataput can accelerate the fighter aircraft