Question

You have been chosen to be the one of few to go to Mars. On Mars you have a standard 55 gal water drum (height = 35 in, diameter = 23 in) filled with water. You are unlucky that the pump is broken to get the water out. But you are an a NASA astronaut, you find a spike (length = 6.5 in to the point, width = 0.5 in and 0.5 in) and a hammer. You need the water to humidify the pressurized living area. After you find a spike, you are unlucky because your fellow astronaut has been effected by the space travel and the low gravity and is now not functioning right. He has now put holes in the drum without thinking. You have been wondering this whole mission on how your partner made it though training and now you wish they were back on earth. Gravity on Mars is 3.711 m/s2?.

(Part A) Use the Bernoulli Equation to solve for the volumetric flow rate at time t=0 sec, if your partner has put the hole 3 inches from the top.

(Part B) Now do part A with Balance Equations (e.g., mass, linear momentum, angular momentum and energy) and solve for the volumetric flow rate at time t=0 s. Do not set any velocity to zero. Is setting velocity to zero a good assumption?

(Part C) Computational Section: Before you could stop your partner, 3 more holes with the spike (total of 4) have gone down the drum. The first hole is 3 in from the top, second hole is 5 in from the first hole, the third hole is 5 in from the second hole and the last hole is 2 in from the third hole. Viscous effects are negligible. Please attach (1) a graph of water height in the drum versus time and (2) a graph the fluid velocity versus time. (3) Note the time when it stops draining for each hole.

(Part D) Computational Section: Now do part C with the bottom 3 holes created every second. Please attach (1) a graph of water height versus time and (2) a graph the velocity versus time. (3) If you made it back at t=3 sec with a bucket, how much water can you save? (4) Note the time it stops draining for each hole.

Answer 1

Given by the Solution is :