Water in a cylindrical container is hanging by a rod from the ceiling at point O shown in the figure.
The container is initially full, and initially displaced 20 degree . There is a hole in the bottom where water
pours out and the top of the container is open to the atmosphere. As the container swings it empties
and the water level h decreases.
The cylindrical tank has a diameter D and length b of 4 cm and 0.5 m, respectively. The distance
from the ceiling to the bottom of the tank L is 5 m. The hole diameter d in the bottom of the tank is
1 mm. The combined rod and empty container's center of gravity is identified by cg and its mass is
0.0063 kg.
You are to develop a model. Use a control volume analysis of mass, linear momentum, and
angular momentum to predict the change in its period as a function of time, the number of swings
it makes before it empties, and the time it takes to empty. You are to make the following
assumptions:
i. Water is incompressible and has a density of 998 kg/m3.
ii. The linear momentum in the container's axis direction is negligible such that the
hydrostatic pressure in the tank and the centrifugal force are balanced by the fluid
momentum exiting the container.
iii. No friction between the fluid and container walls.
iv. Water's free surface remains perpendicular to the container's axis.
v. No pressure drop through hole.
In addition to the results to be determined listed above, you should address the following issues:
a. Does the period increase or decrease as the water exits the container? Explain.
b. Does it take longer to drain if the container is swinging or stationary. Explain.
c. How does the e ffect of the initial angle ΓΈ have on the time to empty. Explain.
1 answer