# Calculating discharge from a reservoir as the head of water decreases

Due to the dry weather we've been experiencing in the UK I need to calculate the discharge rate from some reservoirs for work and how the dropping water level will result in a reduced head and so a reduction in discharge.

The information I have is:

Maximum height of water in the reservoir is: 10.52m

Diameter of the pipe: 0.3m

length of the pipe: 450m

fall of piper from the reservoir to discharge: 14m

Pipe material: cement lined iron ductile

I've calculated the flow rate due to gravity alone using hazen-williams but this doesn't take into account the head of water and so the discharge flow is far lower than the reality. I'm unsure of how to incorporate pressure into the calculations.

Help would be greatly appreciated

• This looks like a homework question. In order for such questions to be answered in this site, we need you to add details describing the precise problem you're having. What have you tried to solve this yourself? Please edit your question to include this information.
– Wasabi
Jul 5 at 13:13
• For a reservoir, the discharge velocity v = sqrt(2*g*h), in which "h" is the head, and the discharge velocity varies with varies in the head.
– r13
Jul 5 at 20:34
• Thank you! Using v = sqrt(2*g*h) I should then be able to calculate the flow rate with the area of the the pipe but how do I incorporate the roughness coefficient and the slope of the pipe into the calculation?
– Sean
Jul 5 at 21:09