Maths A-level Question, Rates of change involving a cylindrical vessel.
What do we know (IN) dv/dt = o.4π(OUT) dv/dt = 0.2π(h)0.5 Initial height of water in vessel is 2.25m Diameter = 4m a) Show that at time t minutes after that tap has been opened, the height h m of the water in the tank satisfies the differential equation 20dh/dt = 2-(h)0.5
dh/dt = dv/dt x dh/dv (1)-By writing this equation we can remove the unwanted element dv which describes the volume of water in the tank.-Where volume = πr2hV = 4πhTherefore, dv/dh = 4π-Now insert what we know into (1) (0.4π-o.2π(h)0.5) x 1/4π = dh/dt -Simplify and isolate.
20dh/dt = 2 - (h)0.5
b)/c) move on to rearranging the differential equation to make an integral where by the time taken to fill the tank can be integrated in terms of h. Resulting in the calculation of the time taken to fill the tank.
