Problem Description (CCOs #1, 2, 3, 4, 5, 6, 7, 8, 11, 12) A water tank of radius R = 1.8m with two outlet pipes of radius r₁ = 0.05m and r2 installed at heights h₁ = 0.13m and h₂ = 1m, is mounted in an elevator moving up and down causing a time dependent acceleration g(t) that must be modeled as = 90+ a1 cos(2ƒ₁t) + b₁ sin(2Ã₁t) + a2 cos(2π f₂t) + b₂ sin(2π f₂t), g(t) = (1) Figure 1: Water tank inside an elevator The height of water h(t) in the tank can be modeled by the following ODE, dh dt = f(t) - - PT √√2g(t) (r√✓/max(0, h − h₁) + r¾¾√/max(0, h — h₂) PπR² where p = 1000 kg/m³. The volume flow rate V (t) of water out of the tank is V(t) = π √2g(t) (r²√/max(0, h(t) − h₁) + r²¾√/max(0, h(t) – h₂)) (2) (3) To help determine the model constants in Eq. (1), measurements of the elevator position y(t) are taken every 5s starting att = Os until 2000s. The measured position data is available on Canvas in the Matlab file ydat.mat. The mass flow rate f(t) in kg/s into the tank is measured every 10s starting at Os and ending at 2500s and is available on Canvas in the Matlab file fdat.mat. At t = 0s, the height of water in the tank is h(t = 0s) = 3.3m. Task: For the given measured data, find the outlet pipe radius r2 such that the volume of water leaving the tank from Os < t < 2500s is V = 165m³ ±1. 10-6m³ if 0m < r2 < 0.06m. For this r2, graph V(t) from Os < t < 2500s.
Problem Description (CCOs #1, 2, 3, 4, 5, 6, 7, 8, 11, 12) A water tank of radius R = 1.8m with two outlet pipes of radius r₁ = 0.05m and r2 installed at heights h₁ = 0.13m and h₂ = 1m, is mounted in an elevator moving up and down causing a time dependent acceleration g(t) that must be modeled as = 90+ a1 cos(2ƒ₁t) + b₁ sin(2Ã₁t) + a2 cos(2π f₂t) + b₂ sin(2π f₂t), g(t) = (1) Figure 1: Water tank inside an elevator The height of water h(t) in the tank can be modeled by the following ODE, dh dt = f(t) - - PT √√2g(t) (r√✓/max(0, h − h₁) + r¾¾√/max(0, h — h₂) PπR² where p = 1000 kg/m³. The volume flow rate V (t) of water out of the tank is V(t) = π √2g(t) (r²√/max(0, h(t) − h₁) + r²¾√/max(0, h(t) – h₂)) (2) (3) To help determine the model constants in Eq. (1), measurements of the elevator position y(t) are taken every 5s starting att = Os until 2000s. The measured position data is available on Canvas in the Matlab file ydat.mat. The mass flow rate f(t) in kg/s into the tank is measured every 10s starting at Os and ending at 2500s and is available on Canvas in the Matlab file fdat.mat. At t = 0s, the height of water in the tank is h(t = 0s) = 3.3m. Task: For the given measured data, find the outlet pipe radius r2 such that the volume of water leaving the tank from Os < t < 2500s is V = 165m³ ±1. 10-6m³ if 0m < r2 < 0.06m. For this r2, graph V(t) from Os < t < 2500s.
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter1: Fundamentals Of C++ Programming
Section: Chapter Questions
Problem 4PP
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Transcribed Image Text:Problem Description (CCOs #1, 2, 3, 4, 5, 6, 7, 8, 11, 12)
A water tank of radius R = 1.8m with two outlet pipes of radius r₁ = 0.05m and r2 installed at heights h₁ = 0.13m
and h₂ = 1m, is mounted in an elevator moving up and down causing a time dependent acceleration g(t) that must be
modeled as
= 90+ a1 cos(2ƒ₁t) + b₁ sin(2Ã₁t) + a2 cos(2π f₂t) + b₂ sin(2π f₂t),
g(t) =
(1)
Figure 1: Water tank inside an elevator
The height of water h(t) in the tank can be modeled by the following ODE,
dh
dt
=
f(t) - - PT √√2g(t) (r√✓/max(0, h − h₁) + r¾¾√/max(0, h — h₂)
PπR²
where p = 1000 kg/m³. The volume flow rate V (t) of water out of the tank is
V(t) = π √2g(t) (r²√/max(0, h(t) − h₁) + r²¾√/max(0, h(t) – h₂))
(2)
(3)
To help determine the model constants in Eq. (1), measurements of the elevator position y(t) are taken every 5s starting
att = Os until 2000s. The measured position data is available on Canvas in the Matlab file ydat.mat. The mass
flow rate f(t) in kg/s into the tank is measured every 10s starting at Os and ending at 2500s and is available on Canvas
in the Matlab file fdat.mat. At t = 0s, the height of water in the tank is h(t = 0s) = 3.3m.
Task:
For the given measured data, find the outlet pipe radius r2 such that the volume of water leaving the tank from
Os < t < 2500s is V = 165m³ ±1. 10-6m³ if 0m < r2 < 0.06m. For this r2, graph V(t) from Os < t < 2500s.
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