A spherical tank is emptied through a small circular hole at the bottom. The water level, h, measured from the bottom of the tank, can be determined from the solution of the following ODE: dh dt r²√√2gh 2hRh² where R is the radius of the tank, r is the radius of the hole and g = 9.81 m/s². Let R = 4m, r = 0.02m and h = 6m at time t = 0s. Use the midpoint method with step size 10s to find the time required to drain the tank to a level of h =0.5m. Print the result.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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A spherical tank is emptied through a small circular hole at the bottom. The water level, h, measured
from the bottom of the tank, can be determined from the solution of the following ODE:
dh
dt
r²2gh
2hRh²
0.02m
where R is the radius of the tank, r is the radius of the hole and g = 9.81 m/s² . Let R = 4m, r
and h = 6m at time t = Os. Use the midpoint method with step size 10s to find the time required to drain the
tank to a level of h =0.5m. Print the result.
Transcribed Image Text:A spherical tank is emptied through a small circular hole at the bottom. The water level, h, measured from the bottom of the tank, can be determined from the solution of the following ODE: dh dt r²2gh 2hRh² 0.02m where R is the radius of the tank, r is the radius of the hole and g = 9.81 m/s² . Let R = 4m, r and h = 6m at time t = Os. Use the midpoint method with step size 10s to find the time required to drain the tank to a level of h =0.5m. Print the result.
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