How to calculate the tides for lake?

Assuming I have a lake on Earth shaped simply like an oval or circle with a consistent bottom slope and of otherwise arbitrary dimensions, how do I figure out what the resultant tidal range will be? In my setting sculpted lakes with specific tidal ranges are being used as part of an ancient and long lasting system for irrigation, providing water pressure, providing decorative ambience, and even telling time.

I will not tolerate handwavium for this and want to actually calculate even if imperfectly what a described lake will produce in terms of tidal range.

The lakes are sculpted from preexisting lake in a process across many generations to produce useful movement of water between different areas.

The weather in the area is fairly stable and predictable.

• I would be very surprised if a body a water which could properly be called a lake had noticeable tides. For example, in the American Great Lakes the maximum tidal range is about 2 inches (5 centimeters), which is smaller than ordinary ripples. In the Black Sea the maximum tidal range is about 7 inches (18 cm), again smaller than ordinary waves and thus not noticeable in practice. (And in both cases those maximum tidal ranges occur only in select places and only twice per lunar month.) In a lake, water level variation due to wind and changes in atmospheric pressure is vastly more important. Commented May 18 at 6:41
• That is enough for my purposes, though more would have been better. The examples are helpful. Commented May 18 at 11:39
• How accurate does your model need to be? The largest three largest frequencies come from planet rotation, lunar orbit, andbsolar orbit. If you want more accuracy, the rest of the terms are typically nonlinear and resonant effects that will be hard to predict. Historically we measure these terms rather than predict them Commented May 18 at 16:22
• I do not know the specific answer to your question, but your lakes would have to be very large indeed as even the Med has very limited tides in most areas. The tidal depth is influenced by both the Moon and the Sun and even the basic calculation would be complex as the Earth and the Moon both have elliptical orbits and the Moon does not orbit the Earth exactly in the plane of the ecliptic. The shape and depth of water will effect the water level changes as will the air pressure, wind speed and weather conditions and these later last three items will probably swamp any tidal effects in any lake Commented May 18 at 22:29
• Cort Ammon, it can have several centimeters of leeway and feel free to ignore air pressure and weather so that they can be considered later. Long ago volcanic activity in a mountain range produced a series of basins that flooded and became most of the lakes while the largest formed in a U shaped glacial valley when the opening into the valley became blocked by the sides caving in and part of the land uplifting which resulted in a several kilometer deep lake. The area is now much more geologically calm but boasts impressive lakes. Not actually our Earth but close. Commented May 21 at 8:55