Derivation of the Emptying Time for a buoyant box to drain

[tjholi]

Homework Statement

I am having trouble deriving the expression from the initial equations. (Calculate the emptying time considering Volume conservation)

Relevant Equations

Q=A*sqrt(b(H-h(t)) And we have dh/dt =Q/S (conservation equation) and we have to obtain h/H = 1-(1-t/te)^2 with te= (2S/A*)(H/b)^1/2

Problem Statement: I am having trouble deriving the expression from the initial equations. (Calculate the emptying time considering Volume conservation)
Relevant Equations: Q=A*sqrt(b(H-h(t)) And we have dh/dt =Q/S (conservation equation) and we have to obtain h/H = 1-(1-t/te)^2 with te= (2S/A*)(H/b)^1/2

I know this is solving a 1st order ODE but I am lost at rearranging prior to solving.
This is not to be submitted, I am revising for an exam)
Thanks for your help
J

 

[Chestermiller]

Can you please provide the exact word-for-word statement of this problem?

 

[tjholi]

Can you please provide the exact word-for-word statement of this problem?

Hey : "To Calculate the emptying time consider volume conservation"

 

[Chestermiller]

Hey : "To Calculate the emptying time consider volume conservation"

Hey, where does buoyancy come in?

 

[tjholi]

Hey, where does buoyancy come in?

Hey Chestermiller, Buoyancy is assumed as it is a model of simplified Displacement ventilation with associated volume flux Q=A*sqrt(b(H-h(t)) with A*being a constant related to the size of the openings.
Thanks