Hydro power question

I am trying to calculate how fast water will exit from a tank using this website: http://www.efunda.com/formulae/fluids/draining_tank.cfm#calc

I am using these values:

Depth of spout: 10 meters
Fluid Density: 1 kg / litre
Spout Exit Diameter: 4 cm
Discharge Coefficent: 0.98

The flow rate calculates to 17.2 litres / second

My question is this. If I connected a 5 meter pipe to the exit spout on the tank, and aimed that pipe straight down a 5 meter drop, does the "Spout Depth" in the formula above then become 15 meters, increasing the flow rate to 21.1 litres /second?

Thanks

Brad Hughes wrote:My question is this. If I connected a 5 meter pipe to the exit spout on the tank, and aimed that pipe straight down a 5 meter drop, does the "Spout Depth" in the formula above then become 15 meters, increasing the flow rate to 21.1 litres /second?

Thanks

I'm not certain I have the right picture in my head, but, let's assume the the 5 meter pipe is not provided. Instead, the water free falls by 5 meters. In this case, it's clear that the flow rate through the system does not change. Now, let's add a 5 meter pipe with a very large diameter (say, a foot). In this case, the flow rate of 17.2 liters per second is so low that this large pipe affects the system as if there is no pipe at all. Therefore, the flow rate remains unchanged. Only when the pipe diameter becomes small enough to provide additional back pressure on the system will the flow rate change, and it can only decrease.

Brad Hughes : I second what Marcos is saying. Without the math, only increasing the total height of the tank to give you another 5'
of standing water will increase the 'head', and give you more pressure ! And the smaller the pipe the greater the friction loss !
I hope this helps Big AL

Thanks guys

I was thinking along the lines of having a 5 meter pipe connected to the spout the same diameter as the spout, pointing straight down, and on the bottom end of the pipe a closed valve holding the water back. When that valve is opened would the spout depth then not have increased by 5 meters? Essentially giving 5 more meters of head?

I struggle with this concept lol

Brad : Yes BUT, the spout would have to be of a very large diameter, in effect making your barrel deeper not taller !

Try this on for size, ask a volunteer fireman, usually they have 1.5 '' fire hose and 3.0'' fire hose, even though the 3''hose is only 2 Xs the diameter of the 1.5'' hose
it will flow 4Xs the water (at the same pressure ) as the 1.5'' -due to higher friction loss in the flow for the smaller hose! Hope this clears things up a little ! Big AL !

Thanks I think I am starting to understand now.

Brad Hughes wrote:Thanks guys

I was thinking along the lines of having a 5 meter pipe connected to the spout the same diameter as the spout, pointing straight down, and on the bottom end of the pipe a closed valve holding the water back. When that valve is opened would the spout depth then not have increased by 5 meters? Essentially giving 5 more meters of head?

I struggle with this concept lol

All else equal, if you decrease the difference in fluid pressure across a component, then the flow rate will go down. When there is no component downstream the spout, then the pressure downstream is atmospheric. It's clear that adding a component downstream the spout must increase this pressure to greater than atmospheric as long as there is any flow. The pressure drop across a component is generally proportional to the square of the flow rate, so the pressure drops get significant as flow rate increases. So, adding a length of pipe introduces back pressure at the outlet of the spout => the differential pressure across the spout decreases => the flow rate decreases. Now, when a valve is added to the end of the pipe, then the flow rate decreases even more, and for the same reason.

You are correct that you get 5 more meters of head, but only under static conditions. The head changes with changes in flow rate, and some components affect this more than others.