# One for the mathmaticians

It takes 5 minutes to fill a cylindrical water tank with a constant flow of water from the top

If you turn off the water flow and let the tank drain freely by gravitational force through a pipe on the bottom it takes 10 minutes to empty a fully filled tank.

How long will it take to fill the tank if the bottom pipe is left open?

If you turn off the water flow and let the tank drain freely by gravitational force through a pipe on the bottom it takes 10 minutes to empty a fully filled tank.

How long will it take to fill the tank if the bottom pipe is left open?

because the floor would get very wet!

water flowing out is at half the rate of water coming in (5 mins to fill, 10 mins to empty) - hence net addition of water when you have both water flowing in as well as flowing out is exactly half of what you will have if you were only filling up (and not letting any outflow). Hence it should double the time from 5 mins to 10 mins

Original Poster

no what FP says

Yes but that wouldn't make any difference

It would be the same filling as emptying

Edited by:"Wongy110" 25th Sep 2017No, it would fill at a constant rate which would equate to a full tank at 5mins. However, if you let it fill with an open tap at the bottom, the discharge rate would vary depending on the depth of liquid.

what prize have I won?

please put me out of my misery and pm me the answer!

Original Poster

Why?

because the floor would get very wet!

Original Poster

That much is true

Original Poster

It's not a trick question.

Here's a starting point.

Let

be the fixed height of container,Hbe the current height of water,hbe the cross-sectional area of the cylinder, andAbe the cross-sectional area of the pipe at the bottom.a

It's three-dimensional and in Basingstoke.

If you turn off the water flow".What do I win?.

Edited by:".MUFC." 25th Sep 2017Mmmhhhh, pie.

I'm an armchair mathematician at best, but I still don't think that this is enough to go off if you need the actual answer to the question. Fair enough if you're assuming constant rates in and out, but the output is subject to Toricelli's Law, so surely we need a numerical value for

hto even begin?Original Poster

PM sent

I think so. It depends if you think the word fill means actually turning the tap on also. If you gave some details about running speed etc and then said I ran from A to B and then stopped, how long would it take for me to run to C. You couldn't then say, I never said I started again from B. The fact that you have stated that you are going to be filling or running again means that water will be coming out of the tap and your legs will be moving. Or does it?

I was thinking bernoulli myself. But again don't think there is enough info to go on.

Surely you would just apply Vorderman theory?

Original Poster

So "Infinite", I win lol.

Oh. So, if 'it would never fill up completely', how much water would be showing in the tank then? Would the level be at the top? Bottom? Middle?

Edited by:"deeky" 25th Sep 2017Theresa May was going to give us the correct answer but just at the last minute decided it was not the right thing to do.

Kim Jong-un had the answer but strapped it to his other uncle who was strapped to a Hwasong-14 and just pressed the fire button meanwhile Trumps response was covfefe-((4X3-3'1627)/8)

Jeremy Corbyn is still trying to find the on button for his tablet.

Edited by:"philphil61" 25th Sep 2017"One for the

mathmeticians"Is this a trick question?