How can I make a technologically correct horizontal watermill clock?

Question

Context

As I was working on some mechanical ideas (and practicing art), I wanted to see how to render time in creative ways. So I decided to make an horizontal watermill akin to a turbine, which has markers on the outside borders and one blade with an arrow pointing outwards to tell the time. Here's my sketch of it here¹, and I've redrawn a very, very basic blueprint you can reuse if you wish to :

Imagine you layed a circular clock on a table. At its centers emerge regularly spaced beams, akin to a watermill's or turbine's and which reach the inner border of the circle (There's just a tiny space between). One of the blade has an arrow pointing outwards, which points some markers in a circle. It's the hour hand. An external pipe gives in water directly into the clock, and another releases it. When you send water, you move these blades, moving the hour hand and changing which time it is.

Problems

As a keen eye like you will see from my sketch, there are most likely mistakes in the drawing. Let's take away dubious proportions and other technical art flaws - that's more drawing skills and focus issues :p -, and let's talk about wheel speed and fluid physics. Here are the two main thoughts I have :

First, my unsophisticated intuition tells me that we're far off regarding the amount of incoming water (~quite big faucet input) in regard to the clock's size. If we think the drawn structure is 2 or 3 m in diameter, the flow seems to be too high to have the speed where the beam is moving at 30°/hour (ie. make a full turn every 12h). Or... Perhaps I messed up what should be the beam's shapes and where the water should come from and the thing isn't moving at all, I don't know. I'm just that bad at whirl-pulling accurate water physics models.

Then, would this thing ever move without overflowing? I mean, contrary to other horizontal turbines I looked at, there's little to no space between the blades and the floor, which means that water cannot evacuate under the blades. The same can be said regarding the space between the blade and the inflow pipe, since when a blade passes by the pipe, the water cannot really use the cylinder's capacity to get rid of the water.

So how can I make this an anatomic... Technologically correct watermill clock?

That is, what troubles are there in the current model - potentially including others which were not highlighted above -, and what can I do to make them more plausible, in regard to real-world physics and following the intentions below? Basically, I want this to be more physically accurate than what I did.

Goals to reach

My watermill clock goal is to tell hours and half hours, rather than minutes or seconds. As such, I don't care much if there are "sudden" jumps in the watermill's movement, as long as you can predict that it's around 11:00 or 11:30. However, the clock should be reliable enough over days : We shouldn't have to recalibrate it every 2 or 3 days.

On top of this, the relationship between time and the watermill should be as direct as possible. That is, unless the concept is critically flawed, avoid the turbine to provide power to other mechanisms and gears, which in turn moves the hour hand like most waterclocks do.

Also, by order of importance :

1. I'm mainly interested in horizontal watermills rather than vertical ones. However, I can allow some light inclination to the structure if it's needed.
2. I'd like to avoid drop-by-drop water input for this to work. I envision the flow to be more like one of a public fountain, an open faucet or shower head, for instance. More is acceptable, but not compulsory :).
3. Tech up to today is available, though no electrical, oil or gaz component are allowed. Also, the simpler you can make it, the better.
4. For the size, it's to be put in public space, so more than 2m in diameter and less than 8m, roughly. The overall structure's height shall not be higher than 1-1.5m (in order for people to read).

Then, less important :

5. We'll presume the water input is constant and at the rate you want. I already have ideas to make the flow constant, so let's only focus on the watermill itself!
6. Material (wood, metal...) is of less importance to me. I'm more interested in mechanisms and the way they should be applied. Still, you can reach a word about it if you find it beneficial :).
7. If it is useful, The inflow and outflow pipes can be moved and rotated. The beams length and shape can change, too, though remember it's a clock and the time should be easily readable.

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¹ : Not directly visible here because I wish to keep some basic rights on this drawing. Please don't reuse without consent.

Answer 1

Let the beams float and provide a circular flow below it

I would let the beams (mill) float freely on the water as shown. Design drawing already comes near.

You have a round container that contains the beams, but some central axis is needed, to keep the floating beams from colliding to the wand of the cylinder while rotating. This axis should add very little friction, to let this work accurately.

I would add a calibration slider at the inlet, which would cause a slightly de-centered mount of the inlet, causing the water under the beams to get a small circular flow component, the floating mill will rotate along. When your water inlet can provide for accurate inflow, the slightly circular flow under the beams will cause the rotation you need.The speed of rotation will depend on the decentered mount of the inlet. When the inlet is at exactly 90 degrees, your beams wheel will not rotate. When it would be, say 87.6 degrees (or whatever), you'd get the 12 hours tempo you need.

Additional advice: make the cylinder wand deeper, or try a transparent lid covering the construct. As it is shown, a design 2-3 meters wide will be susceptible to winds blowing over it. Depending on the direction of the wind, the floating clock beams will deviate.

Answer 2

Pinwheel

Pinwheels turn when they are faced into the wind. Put a pinwheel-like device on the centre of the turbine and make the water enter from above the centre rather than the side. This will ensure a consistent turning rate.

The cool thing about the design is you can vary the depth to vary the rotation rate, since the deeper water provides more resistence. Fine tune the depth further by putting a wad of blue tack in the exit pipe to raise the water level slightly. Remove and further bluetack as required.

Answer 3

VALVES PROVIDE PRESSURE

The walls dividing the compartments have simple, hinged valves that let water through to the right (counter-clockwise), but not to the left (clockwise). Water moving to the right will necessarily push the compartment left (opposite equal forces), until a new compartment is exposed to to the entrance water beam. The water that flows to the right of the entrance compartment exits through a hole in the floor. There may or may not be other holes in the floor as the compartments move clockwise, gradually emptying the water, or it may all flow out as the compartment ultimately moves onto the hole to the right of the entrance beam. For additional pressure, the half-full compartment that moves to the left of the entrance will spout water into the new, empty compartment, until the water levels equalize (when this happens depends on how quickly water can flow through the valves).

Answer 4

Main issue with any water clock is that flow is not constant.

Use Mariotte's bottle for closed loop system, and for open loop use canal that will lower water head to constant level due to excess water flowing over canal's walls.