4. A water tank with the following dimensions is draining. L ho 1 V L =...
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4. A water tank with the following dimensions is draining. L ho 1 V L = (1+x¹) m 1 = 1m a = 5cm b = 5cm g = 9.81 m/s² ho = (80+ x*)cm b a x* is in cm a- What are the essential steps to build a mathematical model that can predict how long it takes to empty a tank? b- Identify if the model is deterministic or stochastic. c- Using the Bernoulli and mass continuity equations, derive the analytical solution and determine how long it will take to empty the tank (see the provided hints). d- Using the Bernoulli and mass continuity equations, derive the 1"-order numerical equation and determine how long it will take to empty the tank (use t=1 s of the interval). e- Draw the curve of each method (on one graph) to correlate the water level (height) to time. f- Calculate the relative true error and relative approximate error for each numerical result (for each interval). g- What type of error (round-off or truncation error) is evaluated by relative true error and relative approximate error? Assumption: • If h = y₁-y₂ is not too large, then we can assume that p₁ = P₂ • For large a tank, we have v₁ << v₂ so we can assume v₁ = 0 • The initial water level is ho • The reduction of water level is continuous • h(t) is the water level at time t • Hints: 1. The total volume of water leaving the tank during At is equal to the total volume of water supplied by the tank during 4t. You need to integrate the equation presented in the lab session to find the analytical solution. Use the given initial condition to find the constant generated after integration. 2. Use Euler's Method to develop 1st order numerical equation having b(t+1) on one side of the equation and the rest on the other side. 4. A water tank with the following dimensions is draining. L ho 1 V L = (1+x¹) m 1 = 1m a = 5cm b = 5cm g = 9.81 m/s² ho = (80+ x*)cm b a x* is in cm a- What are the essential steps to build a mathematical model that can predict how long it takes to empty a tank? b- Identify if the model is deterministic or stochastic. c- Using the Bernoulli and mass continuity equations, derive the analytical solution and determine how long it will take to empty the tank (see the provided hints). d- Using the Bernoulli and mass continuity equations, derive the 1"-order numerical equation and determine how long it will take to empty the tank (use t=1 s of the interval). e- Draw the curve of each method (on one graph) to correlate the water level (height) to time. f- Calculate the relative true error and relative approximate error for each numerical result (for each interval). g- What type of error (round-off or truncation error) is evaluated by relative true error and relative approximate error? Assumption: • If h = y₁-y₂ is not too large, then we can assume that p₁ = P₂ • For large a tank, we have v₁ << v₂ so we can assume v₁ = 0 • The initial water level is ho • The reduction of water level is continuous • h(t) is the water level at time t • Hints: 1. The total volume of water leaving the tank during At is equal to the total volume of water supplied by the tank during 4t. You need to integrate the equation presented in the lab session to find the analytical solution. Use the given initial condition to find the constant generated after integration. 2. Use Euler's Method to develop 1st order numerical equation having b(t+1) on one side of the equation and the rest on the other side.
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a The essential steps to build a mathematical model that can predict how long it takes to empty a tank are as follows Define the relevant variables Identify the variables involved in the problem such ... View the full answer
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Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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