A tall tank (initially at rest) is propped on wheels and filled with water to an initial depth. The stopper at the bottom of the tank is then removed causing water to jet out and the tank moves the other way due to the rate of change of momentum. Given that the surface (on which the tank moves) is without friction, calculate the distance the tank has moved when the water in the tank has emptied, based on the changing rate of momentum of the water flowing out. Use an excel work sheet for your calculations. The starting parameters are as follows:
1. tank weight = 20 lbs
2. Initial depth = 8 ft.
3. Time needs to be in 1 second increments for your calculations
4. Cross-sectional area of the tank = 1 sq. ft.
5. Diameter of water exit nozzle = 3 inches
6. Specific weight of water = 62.4 pcf
7. Acceleration due to gravity = 32.2 ft/s2
8. Initial tank velocity = 0 fps
Ideally your spread sheet has to include these columns to calculate the final distance traveled:
Time (s), Depth of water (ft.), Wt. of tank and water (lbs), Nozzle velocity (fps), flow rate leaving the nozzle (cfs), depth change (ft.), Tank velocity (fps), Impulse force (lbs), Acceleration (ft/s2), New tank velocity (fps), Distance traveled (ft.)
Use appropriate kinematics equations (for the right ranges) for the new velocity and distance traveled. (Hint: when the impulse becomes a non-negative number set it to zero; then the acceleration becomes zero and the velocity does not change; so use the constant velocity equation to calculate displacement