Create a mathematical model of the time-dependent volume of water in the container V(t) in terms of the height of water h(t).
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30-Aug-23
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a) If all quantities are expressed in SI units, find the value of ? in
b) Create a mathematical model of the time-dependent volume of water in the container V(t) in terms of the height of water h(t).
c) Find an expression for the time ? that it takes for the container to empty. Check the validity of your expression by calculating ? for a = 1 cm and ho = 30 cm and plotting h(t) from 0 < t < ?.
d) Express h(t) in terms of T, then find an expression for h(t) = dh/dt.
e) Find the volumetric flow rate V(t) = dV/dt [m3S-1] at which water leaves the container. Discuss how the design parameters ?, ho and a affect the outflow in this container.