Scottish Scientist
Registered Member
The map shows how and where the biggest-ever pumped-storage hydro-scheme could be built – Strathdearn in the Scottish Highlands.
The scheme requires a massive dam about 300 metres high and 2,000 metres long to impound about 4.4 billion metres-cubed of water in the upper glen of the River Findhorn. The surface elevation of the reservoir so impounded would be as much as 650 metres when full and the surface area would be as much as 40 square-kilometres.
The maximum potential energy which could be stored by such a scheme is colossal – about 6800 Gigawatt-hours – or 280 Gigawatt-days.
There would need to be two pumping stations at different locations – one by the sea at Inverness which pumps sea-water uphill via pressurised pipes to 300 metres of elevation to a water well head which feeds an unpressurised canal in which water flows to and from the other pumping station at the base of the dam which pumps water up into the reservoir impounded by the dam.
To fill or empty the reservoir in a day would require a flow rate of 51,000 metres-cubed per second, the equivalent of the discharge flow from the Congo River, only surpassed by the Amazon!
The power capacity emptying at such a flow rate could be equally colossal. When nearly empty and powering only the lower turbines by the sea, then about 132 GW could be produced. When nearly full and the upper turbines at the base of the dam fully powered too then about 264 GW could be produced.
This represents many times more power and energy-storage capacity than is needed to serve all of Britain’s electrical grid storage needs for backing-up and balancing intermittent renewable-energy electricity generators, such as wind turbines and solar photovoltaic arrays for the foreseeable future, opening up the possibility to provide grid energy storage services to Europe as well.
Canal
The empirical Manning formula relates the properties, such as volume rate, gradient, velocity and depth of a one-directional steady-state water flow in a canal.
For 2-way flow, the canal must support the gradient in both directions and contain the stationary water at a height to allow for efficient starting and stopping of the flow.
The “2-way Power Canal” diagram charts from a spreadsheet model for a 51,000 m3/s flow how the width of the water surface in a 45-degree V-shaped canal varies with the designed maximum flow velocity. The lines graphed are
- Moving width – from simple geometry, for a constant volume flow, the faster the flow velocity, the narrower the water surface width
- Static width – the width of the surface of the stationary water with enough height and gravitational potential energy to convert to the kinetic energy of the flow velocity
- 30km 2-way wider by – using the Manning formula, the hydraulic slope can be calculated and therefore how much higher and deeper the water must begin at one end of a 30km long canal to have sufficient depth at the end of the canal and therefore by how much wider the canal must be
- Canal width – adding the 30km-2-way-wider-by value to the static-width determines the maximum design width of the water surface.
y = 2 √ ( 51000/x) + 0.1529 x^2 + x^8/3/40
where y is the maximum surface water width in the canal and x is the designed maximum flow velocitypredicts a minimum value for the canal width of about 170 metres (plus whatever additional above the waterline freeboard width is added to complete the design of the canal) at a design maximum flow velocity between 10 and 11 metres per second.
Guinness World Records states that the widest canal in the world is the Cape Cod Canal which is “only” 165 metres wide.
So the canal, too, would be the biggest ever!
Canal lining and boulder trap
To maximise the water flow velocity, canals are lined to slow erosion. Concrete is one lining material often used to allow for the highest water flow velocities, though engineering guidelines commonly recommend designing for significantly slower maximum flow velocities than 10 m/s, even with concrete lining.
Designing for a slower maximum flow velocity requires a wider canal to maintain the maximum volume flow rate and is expensive in construction costs.
Water flowing at 10 m/s has the power to drag large – in excess of 10 tonnes – boulders along the bottom of a canal with the potential of eroding even concrete, so I suggest that the bottom 6 metres width of the lining, (3 m either side of the corner of the V) may be specially armoured with an even tougher lining material than concrete and/or include bottom transverse barriers of 2 metres depth to impede the flow along the corner of the V and trap boulders, smaller stones and gravel, in which case the water flow is more precisely modelled for Manning formula calculations as a trapezoidal canal with a bed width equal to the 4 metre width of the top of bottom transverse barrier (“boulder trap”) and a 2-metre smaller depth from the top of the boulder trap to the water surface.
Main Dam
The image shows the location of the main dam at latitude 57°15’16.2″N, decimal 57.254501°, longitude 4°05’25.8″W, decimal -4.090506°.
Assuming the dam would be twice as wide as its height below the dam top elevation of 650 metres, the superficial volume is estimated at 80 million cubic metres, not including the subterranean dam foundations which would be built on the bedrock after clearing away the fluvial sediment.
