Question

a) A fluid flows from the top of a cylinder to the bottom through a hole....

a) A fluid flows from the top of a cylinder to the bottom through a hole. Given Bernoulli's equation and that the fluid's level is at height y(t) in a cylinder, derive the form dy/dt = −f(y). For Bernoulli’s equation, the kinetic energy term of the fluid’s top surface can be considered zero.

b) The previous differential equation may be integrated as integral from 0 to ∆t dt = integral from 0 to h0 of (1/f(y)) dy. Use this to find the total time ∆t that it takes for all of the fluid to flow out.

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