# Why water from upper level not goes into lower level in this drainage system

In the following typical water drainage system, I'd like to know why waste water from upper floor (let say, from 2nd floor's toilet) does not come to the lower floor's equipment via the common pipes (the 1st floor's sink), according to the equal level principle. In what case would this happen? If the water tends to go through the main pipes but not the branches, is there chance for it to go to the sink?

• What do you think the vents are for? – Peter Shor Jan 12 '14 at 19:55
• Expand a little and that would be a good answer... – Neuneck Jan 12 '14 at 20:15
• I think vents are for preventing gases/air from going inside the house. They do not prevent water from flowing to, let say, sink. – user37262 Jan 13 '14 at 3:29
• I thought vents were for preventing gases/air from going inside the house, and to help the flow by maintaining air pressure. They do not prevent water from flowing to, let say, sink. – user37262 Jan 13 '14 at 3:42

According to me, the air pressure $P_a$ at roof vent would produce an equal pressure $Pa$ below each place which uses water ex bath, sink etc. Now the height of liquid column could be determined by the equation :
$P_{in} - P_a = \rho g h$.
Now if the pressure difference between inside and outiside is less there will be very little water column, I suppose what you are asking for is the water to come out of the drains, this is pretty much what happens during a blockage, the pressure in the drain near blockage reduces from $P_a$ and hence the height of column increases. But the possibility of actually something disgusting turning up in your kitchen sink is low as the pressure would only force the water to move up as column.