The installers want to extend the vent pipe in Barleycorn Cottage’s garden quite high into the air but I don’t want it to look too obstructive. They have check levels from the proposed water in the forebay to get the level that the water will be in the vent pipe. However it occurred to me that when the system is running the water level in the vent pipe must be lower due to friction losses in the pipe.
To Estimate the flow rate in the leat we used Manning’s Equation:-
v = (√S) x R0.667
Where: v = velocity of flow
S = slope
R = Hydraulic mean radius = A Cross sectional area of flow / P Wetted Perimeter
n = Roughness Coefficient
For the leat with 0.3m water flowing:-
S = 200m long with a fall of 1.7m = 200/1.7 = 0.0085
A = 1.5m wide by 0.3m deep = 0.45m2
P = 1.5m wide + 0.3m * 2 for each side = 2.1m
R = A/P = 0.45m2 / 2.1m = 0.214 m
n = 0.07 for a shallow channel with short vegetation.
Then:- v = (√.0085) x 0.2140.667 = 0.471
Thus Flow rate = v*A = 0.212 m3/sec = 212 litres/sec.
The drop in the penstock pipe from the forebay to where the vent pipe is is 0.3m and the Roughness Coefficient for plastic pipes is 0.11. I selected a 0.5m diameter pipe knowing that this was larger than required (In case I apply to increase the abstraction licence for a greater flow in the future) So if we apply the above calculation to the flow in the penstock we get a maximum flow of about 350l/sec. However the Turbine is designed for a flow rate of 187l/sec. Working back through the figures for this flow rate we find we would need a 9cm fall. It seems logical to me therefore that, with the normal operating flow through the turbine of 187l/sec, the water level at the vent pipe should be 9cm lower than that in the forebay.
We’ve decide that, before finishing off the vent pipe, we will get the turbine running and see what the actual working water level is.
If you don’t hear any more about this on the blog then you can assume I’ve either given up my foray into hydraulic engineering or am carrying on further research into the work carried out by Mr Manning.