How fast can you drain a bath?

Bearing in mind that some people let the bath empty while they ae still in it, what calculation do you have to work out that if they are peeing in the bath at the same time, how much longer will it take to empty and whether they pee like a donkey or have a prostate problem and have a dribble, this all must have a bearing on the emptying time, this could be useful to me for when I am peeing in someones tank while draining off a system and help me to quote properly for the extra time.
 
This is just the sort of real-world complication which has to be factored in. There might be somebody IN the bath :shock:
This would clearly raise the level of the water but in a manner whereby the average depth could no longer be used for calculations. The variation of depth with time would become a multi term polynomial differential equation, which would be different for every occupant.

The question of peeing in the bath is a most interesting one. The volume of the occupant clearly decreases by the exact amount that the volume of, er, liquid in the bath increases. Other normal considerations, such as the evacuation of flatulence during the emptying process, reduce the volume of the body in the water, dependent on the depth of the water at the time of the said evacuation. The deeper the water, the more the gas would have been compressed prior to its escape.

I believe that in future we must have showers only, where the rate of water entering the tray is approximately the same as that of the water leaving it. Though of course in the case of hairy people it becomes er,
um,
 
"The variation of depth with time would become a multi term polynomial differential equation, which would be different for every occupant."

So what your saying is some people are lardys and will take up more volume than rakes.
 

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