Consider a rainfall tank with a hole in the bottom. The change in volume is modelled by dV/dt = fin - fout Volume, V (in Litres). Flow rate in, fin (L/hour). Flow rate out, fout (L/hour). Initially, tank has 50L of water, V(0) = 50 a) Assume rain is getting heavier, such that fin(t) = 10 + t and tank looses 10% of V/hour, such that fout = 0.1V. By direct substitution check that function V(t) = 10(t - 5e-0.1t) satifies the ODE and initial condition. b) Assume hole is getting larger so flow rate out is increasing. fout(V, t) = 0.1(1+0.1t)V. Solve ordinary differential equation for V(t) with this fout. Please use integrating factor method for this step and include initial condition.
Consider a rainfall tank with a hole in the bottom. The change in volume is modelled by dV/dt = fin - fout Volume, V (in Litres). Flow rate in, fin (L/hour). Flow rate out, fout (L/hour). Initially, tank has 50L of water, V(0) = 50 a) Assume rain is getting heavier, such that fin(t) = 10 + t and tank looses 10% of V/hour, such that fout = 0.1V. By direct substitution check that function V(t) = 10(t - 5e-0.1t) satifies the ODE and initial condition. b) Assume hole is getting larger so flow rate out is increasing. fout(V, t) = 0.1(1+0.1t)V. Solve ordinary differential equation for V(t) with this fout. Please use integrating factor method for this step and include initial condition.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Consider a rainfall tank with a hole in the bottom. The change in volume is modelled by dV/dt = fin - fout
Volume, V (in Litres). Flow rate in, fin (L/hour). Flow rate out, fout (L/hour).
Initially, tank has 50L of water, V(0) = 50
a) Assume rain is getting heavier, such that fin(t) = 10 + t and tank looses 10% of V/hour, such that fout = 0.1V. By direct substitution check that function V(t) = 10(t - 5e-0.1t) satifies the ODE and initial condition.
b) Assume hole is getting larger so flow rate out is increasing. fout(V, t) = 0.1(1+0.1t)V. Solve ordinary differential equation for V(t) with this fout. Please use integrating factor method for this step and include initial condition.
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