Hello, I am looking for guidance on the best way to implement the falling head orifice equation to calculate the time to empty a pond, in the case where the reservoir surface area is NOT constant.
I'll skip the derivation since hopefully folks are familiar with this equation. The time it takes to drop the water surface from 1 to 2 assuming a constant reservoir surface area is:
where A is the area of the reservoir, h1 is head at the start, h2 is head at the end, C is the coeff of discharge, a is the orifice area, g is gravitational acceleration.
In my case the pond does not have vertical sidewalls and so the reservoir area changes as the head drops- here is where I am looking for feedback. Right now, my approach is calculating incremental drawdown times between elevations, i.e. between 6ft to 5ft, then 5ft to 4ft, etc., and then adding them all up to get the total drawdown time. For each calculation I am using the starting (larger) area in the formula. My question: would using the ending area be more accurate? Or some other approach (i.e. the average area)?
The use of starting, ending, or average area value doesn't make a big difference as long as the elevation is not changing very quickly, but towards the flatter bottom of the pond where the area change between elevations is much greater, the difference is significant between these methods. But which one is most physically accurate?
I'll skip the derivation since hopefully folks are familiar with this equation. The time it takes to drop the water surface from 1 to 2 assuming a constant reservoir surface area is:
Code:
t = 2A * [sqrt(h1) - sqrt(h2)] / [C * a * sqrt(2g)]where A is the area of the reservoir, h1 is head at the start, h2 is head at the end, C is the coeff of discharge, a is the orifice area, g is gravitational acceleration.
In my case the pond does not have vertical sidewalls and so the reservoir area changes as the head drops- here is where I am looking for feedback. Right now, my approach is calculating incremental drawdown times between elevations, i.e. between 6ft to 5ft, then 5ft to 4ft, etc., and then adding them all up to get the total drawdown time. For each calculation I am using the starting (larger) area in the formula. My question: would using the ending area be more accurate? Or some other approach (i.e. the average area)?
The use of starting, ending, or average area value doesn't make a big difference as long as the elevation is not changing very quickly, but towards the flatter bottom of the pond where the area change between elevations is much greater, the difference is significant between these methods. But which one is most physically accurate?
