## Question

###### Part (Based off week 6 workshop content ) Cousider Vrater tank with hole of arca in its Di. through this hole, The tank will drain Tale proportional to the height oi tlc wuter (as this influcnces the pressure). Torricelli $ Law descrilxuse this proce $Vzgh() ,where:h(t)the height of water in the tank tme in m,the cross-sectional area of the tank in m?,the area of the hole in the hottom of the tank in m? 9.81 m/s? the acceleration gravity:For the following questions, use A = 10 m?,0.1 m?_h(0) 10

Part (Based off week 6 workshop content ) Cousider Vrater tank with hole of arca in its Di. through this hole, The tank will drain Tale proportional to the height oi tlc wuter (as this influcnces the pressure). Torricelli $ Law descrilxuse this proce $ Vzgh() , where: h(t) the height of water in the tank tme in m, the cross-sectional area of the tank in m?, the area of the hole in the hottom of the tank in m? 9.81 m/s? the acceleration gravity: For the following questions, use A = 10 m?, 0.1 m?_ h(0) 10 u_ Solve the ODE using sepmration variables: Use first order Taylor series show' that when Torricelli's law: linearised about the initial height, 2h(o) (h() ~ h(O)) Solve the linearised ODE using the integrating factor method, Plot your solutions to Q1 and Q3 in the same figure: Discuss the accuracy of the linearised ODE solution. Plec se Gnsbe C1 l Luestions