Free-flowing water on a floor 3

[gregpaul]

Could someone give me a name of a book or of an article, showing how to calculate the speed and depth of water flowing on a floor, in a room where a sprinkler head opened and let water out for several hours ?

Is there also a way to calculate the rate of spreading the water from one room to the other through doors (maybe the water would rise in the room before flowing through the door?) and to determine at each minute, the position of the water on the floor ?

Thank you in advance.

 

[CostasV]

Gregpaul-

Interesting question! Let me rephrase it.

A constant flow (in a rain type expression) of X cm/h of water has met the floor (which has a surface equation of the type z=f(x,y) z=height, x and y are the length and the width coordinates). What is the level of the water (w=g(x,y,t)) as a function of the x,y coordinates and time?

Does this expression makes it easier to answer it?

As you can understand the main factor is the way the floor is constructed. If it is made of tiles, then the space between tiles has a lower relative height and the water may be guided through them to leave the floor.

Actually in a room of 4X5 m there will be differences in height of about 4-5 mm maximum.

The most important for your question is if the maximum height is at the door or not. If it is, then, after a while (time needed for the floor to be flooded) all the sprinkler flow will go to the other rooms or the corridor.

More detailed answer needs precice description of the floor space.

Hope this helps.

Costas

 

[btrueblood]

There are a number of textbooks that will give you equations for the flow of water through open channels. One possibility is _Engineering Fluid Mechanics_ (2nd ed.), Roberson & Crowe, Houghton Mifflin Co., Boston, c. 1980 (but may have been updated since I was in undergrad). You should be able to fairly easily "simulate" your particular room/floor geometry to adapt it to the equation form and get some rough answers.

As far as water "migration" between rooms, this gets a little tricky, since you have to consider capillary (wicking) action along carpets, and along the joinery work at the baseboards, etc. It's amazing how far the damp can spread on a level, carpeted floor that has gotten wet in one area.

Good luck,

Ben T.

 

[unclesyd]

[/b]btrueblood[/b],
Where did you find a level floor?
Or better yet a vertical wall or square corner?

 

[Tremolo]

gregpaul,

If the sprinkler has been operating at a constant flow for several hours, then you can assume that you have an equilibrium flow condition in which the flow out of the room through a doorway is equal to the flow into the room from the sprinkler.

In general, whether the flow is in an open conduit, a closed pipe, across a floor, or through a doorway, the flow is a function of the pressure or water head:

u = sqrt[2*g*h/(1+k)]

where,

u = fluid velocity m/s
g = acceleration due to gravity, 9.81 m/s^2
h = water depth on the floor, m
k = friction losses across the floor and/or doorway loss coefficient
sqrt = mathematical symbol for square root.

If there is a single doorway and the sprinkler has been running for several hours, then the water should be covering the entire room, so just consider the flow restriction through the doorway. In this case, if the sprinkler flow rate is w (kg/s), and the flow area through the doorway is the product of the door width, L (m) and water depth on the floor, h, then you can you can apply the relationship between flow rate and velocity (w = rho*u*A, where rho is density and A=L*h = flow area) and rearrange the preceding equation to calculate h:

h = [w/L/rho]^2/3*[(1+k)/2/g]^1/3

Once the equilibrium head is calculated, you can then calculate the velocity from w = rho*u*A where A=L*h.

TREMOLO.