Flow from a tank 11' above ground, 8' diam x 13' long, 6" discharge pipe, gravity fed?

Question

A firefighter friend of mine has this question. If they had a tank 8'diam x 13' long with a 6" diam line from it down to the ground, what would the flow be when they open the valve? The bottom of the tank would be 11' off the ground, it is a gravity fed system. Assume two 90s for fittings, standard cs pipe (if required), I don't need it to the thousandth of a gpm :)

a) What is the flow (gpm) from the tank when full?
b) What is the flow (gpm) from the tank with 1" of level?
c) What is the time to empty the tank completely (starting from full)?

Thanks all.

Answer 1

For the first two questions, the velocity of flow = (2gh)^0.5. Flow = velocity of flow * area of pipe (3.14*0.5^2/4). You have to subtract the head loss for the two bends and length of pipe. This is typically a loss coefficient * the velocity head, h = v^2/2g. All lenth units in feet.

To find the time, you need to integrate the flow vs. time equation.

Answer 2

You probably do not need to do Any fancy math on this one.

The tank holds around 4500 gallons. The pressure at the bottom is something like 8 psi when the tank is full. This is far too little to be used directly for firefighting. It is more likely to be used to fill a tender, or the tank on a pumping engine. If the water is to be dumped into a tank, or to the intake of a pump, the head due to elevation will not be the 8 psi.

If it is dumped into a tank, the fill time will be short, compared to the time it takes to position the vehicle, make the connection and disconnect when the receiving tank is full, or the supply tank is empty.

If the supply tank is connected to a pumper, the pump settings will determine the flow rate and time.

In the fire protection world, we often refine numbers to an extent greater than necessary.

BTW, there will be more fitting losses than you have described. A valve, to be sure, and additional pipe or hose to get the water to a tank or pump.