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Help can only be sought via private Ed Discussion posts or instructor office hours. - In all coding, use only functions covered in class. It will be considered a violation of the Academic Integrity Policy if you use any build-in functions or operators of Matlab that calculate the inverse of a matrix, interpolations, spline, diff, integration, ode, fft, pdes, etc.; - You may reuse functions you yourself developed throughout this semester in this class or from solutions posted on Canvas for this class. 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 g(t) = go+a1 cos(2π f₁t) + b₁ sin(2π f₁t) + a2 cos(2π f₂t) + b₂ sin(2π f₂t), (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) – p√2g(t) (r√max(0, h − h₁) + r‍²¾√√/max(0, h — - ρπι2 where p = 1000 kg/m³. The volume flow rate V(t) of water out of the tank is h2) (2) V(t) ) = π√2g(t) (r}{√/max(0, h(t) − h₁) + r²¾√/max(0, h(t) — h₂) (3) To help determine the model constants in Eq. (1), measurements of the elevator position y(t) are taken every 5s starting at t = 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

Help can only be sought via private Ed Discussion posts or instructor office hours. - In all coding, use only functions covered in class. It will be considered a violation of the Academic Integrity Policy if you use any build-in functions or operators of Matlab that calculate the inverse of a matrix, interpolations, spline, diff, integration, ode, fft, pdes, etc.; - You may reuse functions you yourself developed throughout this semester in this class or from solutions posted on Canvas for this class. 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 g(t) = go+a1 cos(2π f₁t) + b₁ sin(2π f₁t) + a2 cos(2π f₂t) + b₂ sin(2π f₂t), (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) – p√2g(t) (r√max(0, h − h₁) + r‍²¾√√/max(0, h — - ρπι2 where p = 1000 kg/m³. The volume flow rate V(t) of water out of the tank is h2) (2) V(t) ) = π√2g(t) (r}{√/max(0, h(t) − h₁) + r²¾√/max(0, h(t) — h₂) (3) To help determine the model constants in Eq. (1), measurements of the elevator position y(t) are taken every 5s starting at t = 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

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter1: Basic Modes Of Heat Transfer
Section: Chapter Questions
Problem 1.3DP
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Help can only be sought via private Ed Discussion posts or instructor office hours. - In all coding, use only functions covered in class. It will be considered a violation of the Academic Integrity Policy if you use any build-in functions or operators of Matlab that calculate the inverse of a matrix, interpolations, spline, diff, integration, ode, fft, pdes, etc.; - You may reuse functions you yourself developed throughout this semester in this class or from solutions posted on Canvas for this class. 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 g(t) = go+a1 cos(2π f₁t) + b₁ sin(2π f₁t) + a2 cos(2π f₂t) + b₂ sin(2π f₂t), (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) – p√2g(t) (r√max(0, h − h₁) + r‍²¾√√/max(0, h — - ρπι2 where p = 1000 kg/m³. The volume flow rate V(t) of water out of the tank is h2) (2) V(t) ) = π√2g(t) (r}{√/max(0, h(t) − h₁) + r²¾√/max(0, h(t) — h₂) (3) To help determine the model constants in Eq. (1), measurements of the elevator position y(t) are taken every 5s starting at t = 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. Required submission: ☐ Concise report containing description of solution procedure, name of all methods used, hole radius r2, V and its accuracy, and all model constants in Eq. (1), i.e., go, a1, b1, a2, b2, f1, f2; requested graph, and justification/documentation that results have
Transcribed Image Text:Help can only be sought via private Ed Discussion posts or instructor office hours. - In all coding, use only functions covered in class. It will be considered a violation of the Academic Integrity Policy if you use any build-in functions or operators of Matlab that calculate the inverse of a matrix, interpolations, spline, diff, integration, ode, fft, pdes, etc.; - You may reuse functions you yourself developed throughout this semester in this class or from solutions posted on Canvas for this class. 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 g(t) = go+a1 cos(2π f₁t) + b₁ sin(2π f₁t) + a2 cos(2π f₂t) + b₂ sin(2π f₂t), (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) – p√2g(t) (r√max(0, h − h₁) + r‍²¾√√/max(0, h — - ρπι2 where p = 1000 kg/m³. The volume flow rate V(t) of water out of the tank is h2) (2) V(t) ) = π√2g(t) (r}{√/max(0, h(t) − h₁) + r²¾√/max(0, h(t) — h₂) (3) To help determine the model constants in Eq. (1), measurements of the elevator position y(t) are taken every 5s starting at t = 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. Required submission: ☐ Concise report containing description of solution procedure, name of all methods used, hole radius r2, V and its accuracy, and all model constants in Eq. (1), i.e., go, a1, b1, a2, b2, f1, f2; requested graph, and justification/documentation that results have
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