2. A spherical tank with radius R (=1.5 m) has a hole at the bottom through which water drains out. The flow rate, Q, through the hole is estimated as Q=0.55m² √2gh where r is the hole radius (=0.015 m), g is the gravity constant (=9.81 m/s2), and h is the depth of water. 20 h² (3R-h) 3 The initial height of water For the spherical tank, the volume of water, V, is given by V=- -Qusing Explicit Euler's method (A/= 200 sec), 4th dV is 2.95 m. Solve the mass balance equation = dr order Runge-Kutta method (A/= 200 sec), and ode45 solver. Plot water height (h) vs. time (r) for each Ar for 0 st≤ 5000 sec and confirm that the 4th order RK method is more accurate than Explicit Euler method (we regard the ode45 solution as the true solution). Use ExplicitEuler.m and rk4.m files. Solve the same problem also using Simulink.

2. A spherical tank with radius R (=1.5 m) has a hole at the bottom through which water drains out. The flow rate, Q, through the hole is estimated as Q=0.55m² √2gh where r is the hole radius (=0.015 m), g is the gravity constant (=9.81 m/s2), and h is the depth of water. 20 h² (3R-h) 3 The initial height of water For the spherical tank, the volume of water, V, is given by V=- -Qusing Explicit Euler's method (A/= 200 sec), 4th dV is 2.95 m. Solve the mass balance equation = dr order Runge-Kutta method (A/= 200 sec), and ode45 solver. Plot water height (h) vs. time (r) for each Ar for 0 st≤ 5000 sec and confirm that the 4th order RK method is more accurate than Explicit Euler method (we regard the ode45 solution as the true solution). Use ExplicitEuler.m and rk4.m files. Solve the same problem also using Simulink.

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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Applied Fluid Mechanics

A fluid is a substance that is continuously deformed by the application of shear stress. The rate of deformation of a fluid depends on its viscosity. The fluid tries to flow when it interacts with some other system.

Question

2. A spherical tank with radius R (-1.5 m) has a hole at the bottom through which water drains out. The
flow rate, Q, through the hole is estimated as
Q=0.55m² √2gh
where r is the hole radius (=0.015 m), g is the gravity constant (=9.81 m/s²), and h is the depth of water.
R
For the spherical tank, the volume of water, V, is given by V=
h
h² (3R-h)
3
The initial height of water
-Q using Explicit Euler's method (A/= 200 sec), 4th
dV
is 2.95 m. Solve the mass balance equation H
di
order Runge-Kutta method (A = 200 sec), and ode45 solver. Plot water height (h) vs. time (r) for each
At for 0≤t≤5000 sec and confirm that the 4th order RK method is more accurate than Explicit Euler
method (we regard the ode45 solution as the true solution). Use ExplicitEuler.m and rk4.m files. Solve
the same problem also using Simulink.

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