After completing the ENGR 315 hands-on project Sparky decided to create a symbolic solution for the time it takes for water to drain from the bottle. Sparky will compare the times to a YouTube video of the hands-on project. Sparky’s bottle is 4 inches in diameter and contains three holes of equal size (not what was required by the hands-on experiment). The hole size of diameter (dhole) is in inches and the holes are L inches apart. There is Ltop inches was water above the top hole at the start of the experiment (as shown in the figure). Neglecting viscous effects (orifice coefficient) and considering the flow conditions to be quasi-steady (consistent with the hands-on experiment) create a symbolic solution for the time it takes for water to stop draining from the top hole. The density (ρ) and specific weight (γ) of the water are 1.94 slugs/ft3 and 62.4 lbf/ft3, respectively. The height of water above the first hole is h, which varies with time. The flow through each hole is the velocity from Torricelli’s Law. The problem is solved symbolically by equating the mass through all three holes to the time rate of change of mass associated with the decreasing mass of water in the bottle. The symbolic solution has an integral that can only be integrated numerically, which you are not required to and should not try to solve. Since the symbolic equation is an integral the limits of integration should be defined as part of the symbolic solution.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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After completing the ENGR 315 hands-on project Sparky decided to create a symbolic solution for the time it takes for water to drain from the bottle. Sparky will compare the times to a YouTube video of the hands-on project. Sparky’s bottle is 4 inches in diameter and contains three holes of equal size (not what was required by the hands-on experiment). The hole size of diameter (dhole) is in inches and the holes are L inches apart. There is Ltop inches was water above the top hole at the start of the experiment (as shown in the figure). Neglecting viscous effects (orifice coefficient) and considering the flow conditions to be quasi-steady (consistent with the hands-on experiment) create a symbolic solution for the time it takes for water to stop draining from the top hole. The density (ρ) and specific weight (γ) of the water are 1.94 slugs/ft3 and 62.4 lbf/ft3, respectively. The height of water above the first hole is h, which varies with time. The flow through each hole is the velocity from Torricelli’s Law. The problem is solved symbolically by equating the mass through all three holes to the time rate of change of mass associated with the decreasing mass of water in the bottle. The symbolic solution has an integral that can only be integrated numerically, which you are not required to and should not try to solve. Since the symbolic equation is an integral the limits of integration should be defined as part of the symbolic solution.

Surface at t = 0
- 4 in.-
2 in.
2 in.
2 in.
0.15 in.

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