Workshop G-W-2: The bathtub
Attention: Fiction case study, for
– Using Euler method to evaluate sensitivity
Remove the stopper of the drain in the bathtub to let the water go out of the bathtub .
1. Predict the remaining height of water at 120 seconds in the draining;
2. Manufacturing errors lead to systematic variation of the size of the holes in the drain.
This will affect the flow rate. Evaluate the sensitivity of the height of the water at 120
seconds regarding the diameter of the holes.
1. the shape of the bath tub is a half-cylinder (the cross section of the bath tub is
a half-circle) where the radius is 0.33 m;
2. the length of the bathtub is 1.2 m;
3. the initial height of water in the bath-tub is 20 cm;
4. there are 6 holes (same size, 9 mm in diameter) in the drain;
5. the discharging coefficient is 0.6 for all holes;
6. to use the Euler method to solve the questions (2 steps).
Courtesy of http://www.simplybathtubs.com/whirlpool-bathtubs/whitebathtub-with-claw-feet.html
Solution for hole = 0.009: 2 step approach, step=(120-0)/2=60
Solution for hole = 0.00901: 2 step approach, step=(120-0)/2=60
Sensitivity at this point
The hole diameter = 0.009 meter
The hole diameter = 0.00901 meter