IO2081 Modelling

Workshop G-W-2: The bathtub

Attention: Fiction case study, for
education only

– Using Euler method to ...
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Modelling Workshop General 2: Solution

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The Modelling Workshop General 2 Solution of the Modelling Course of Industrial Design of the TU Delft

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Modelling Workshop General 2: Solution

  1. 1. IO2081 Modelling Workshop G-W-2: The bathtub Attention: Fiction case study, for education only – Using Euler method to evaluate sensitivity Holes Remove the stopper of the drain in the bathtub to let the water go out of the bathtub . Question We choose: Questions: 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. Drain Drain stopper 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 Force Ref. P-W-F-1 1st step: 2nd step: R-h(t) Sketch Solution for hole = 0.00901: 2 step approach, step=(120-0)/2=60 1st step: w/2 h(t) 2nd step: R Sensitivity at this point The hole diameter = 0.009 meter The hole diameter = 0.00901 meter Page 33

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