1) For the piping diameter changes and flow directions shown below, if the velocity at the input is 5 m/s, the initial density is 1000 kg/m3 and the fluid is incompressible, how much is the velocity at the outlet for each case if the large diameter is 50.8 mm and the small diameter is 25.4 mm? Calculate the volumetric and mass rates for each case. 10 points each.
2) One fundamental problem in manned space travel is that the enormous distances require high velocities to reach an intended destination in a reasonable time, and reaching large velocities also requires large accelerations. Say you are in a spaceship that is floating in outer space at zero velocity and no forces acting on it. If the ship's initial mass is 10000 kgs (including you and its fuel) and it can produce a stream of superheated gases for propulsion coming out of the ship at a velocity of 10 km/s, use the equation for conservation of linear momentum in open systemsdiscussed in class (sum forces + rate of linear momentum in - rate of linear momentum out = d(mv)/dt) to find:
a.- How much is the mass rate for the outlet gases that is needed to get an initial acceleration of one standard gravity, i.e., 9.8 m/s2?
b.- If only 1/3 of the ship's mass can be used for fuel, and assuming the mass rate you obtained in part a remains constant, how long will it take to exhaust the fuel? 5 points.
c.- Assuming that the acceleration is maintained constant by using the constant mass rate you calculated in part a (an assumption that does not hold true in this case), what is the velocity obtained by the time the fuel is exhausted? Calculate the distance traveled during that time, which for constant acceleration can be obtained as a*t2/2, where a is the acceleration and t is the time.