Conversations With ChatGPT: Air Drag and Surface Topology

Created by Grok.

Eugene: Is it possible to make a material that has a huge amount of drag that could allow a human to float? And what topology of surface has the most drag, a plane? I know that drag is proportional to cross-sectional area and also that there is a coefficient that depends on the surface shape of an object.

ChatGPT: Oh, yes, you can make a material or object with enormous air drag, but it’s a combination of material, surface topology, and shape, not just the “material” itself. Let’s break it down carefully.

Erosion and Deposition

AI image generated by Grok Imagine.

The geometry of a conduit through which any fluid passes affects the velocity profile of that fluid. In the case of a river, on the inside of a bend, water flows slower. On the outside of the bend, water flows faster. Erosion due to faster flow causing a scouring effect is probably responsible for the so-called "Sally Hole" in the riverbed near St Brigid's Well. Eventually there may be landslides as the riverbank is undercut. However, tree roots and other vegetation act as reinforcement, holding the bank together. So it's not necessarily imminent. Meanwhile, on the meander opposite Castlemartin, debris such as bottles and other rubbish accumulate on the inside bend, where water flows slower. Water also flows faster where there's a bottleneck in a watercourse. (You can observe this from the farm trail near the island that's north of the bridge. However, this may be partially due to a gradient in the river bed).
Bernoulli's principle is a law in fluid dynamics which states that an increase in speed occurs simultaneously with a decrease in pressure. It's a principle that's used in engine carburettors. A venturi (a narrowing of the passage in a carburettor through which the fuel/air mixture flows) causes a drop in pressure. That drop in pressure causes fuel to be sucked into the venturi. Small engines such as those used on lawn mowers still use this arrangement for supplying the engine with a fuel/air mixture. However, modern petrol engines on vehicles use fuel injection. (Since the late 1980s, early 1990s I believe).

Engineering Case Study: Weir Calibration at Mill Stream Bridge

Michael Browne from the EPA makes some calibration adjustments at the hydrometric station on the Mill Stream, Kilcullen, Co. Kildare. © Eugene Brennan

If you’ve ever taken a shortcut through the fields to New Abbey graveyard in Kilcullen, you may have noticed a silver-coloured tube beside the bridge where the mass path crosses over the mill stream. There’s also an adjacent vertical scale with numbers on it, rising up out of the stream. This setup is one of over 800 active hydrometric stations located around the country that collect water flow and level data as part of the EPA's National Hydrometric Programme. The stations monitor both surface water (streams and rivers) and groundwater, providing valuable statistics on water movement. The data is used for managing water resources, infrastructure design and monitoring long-term trends for flooding.
The mill stream station was commissioned in October 1999, but only started recording digitally in 2009. Originally a mechanical chart recorder would have been used to record data with a pen on a roll of paper. The recorder would have been driven by a weight, similar to the one in a grandfather clock. This recorder would have been housed inside the stilling chamber if used, although it's more likely that a digital data logger was used at this station from when recordings began in 2009.

What’s a stilling chamber?

This is the metal tube beside the bridge. It shelters the water’s surface, making it less turbulent, ensuring more accurate stream level measurements.

How do hydrometric weirs work?

These structures are used in hydrometrics to measure flow. They can be rectangular, V-notch, broad-crested etc, typically made from concrete or stainless steel sheets. The type used under the mill stream bridge is a concrete flat-V type. A weir causes water to backup behind it and change in level as flow rate varies. Using an equation specific to the shape of the weir, the flow rate can be determined from the water height. In theory, flow rate can be calculated knowing the cross-sectional area of flowing water and measuring its velocity. However, velocity varies within the flow; faster in the middle of a stream and slower towards the edges and bottom due to drag. Therefore, making a velocity measurement at a single point in the flow would be insufficient. Using a weir simplifies the calculations.
Various types of weirs have been studied and empirical equations developed (i.e. by making measurement from models, not analytical derivations) giving flow rate versus water level. Water level can measured using an ultrasonic transducer that emits a high-frequency sound beam and detects its echo. By knowing the transit time of the beam and the speed of sound, distance can be measured to the water surface (similar to the way an ultrasonic measuring tape works). This measurement is then converted to a flow reading, using an equation specific to the type of weir. Alternatively a depth sensor can be used to measure water height.

Telemetry

Measurements are taken every 15 minutes and telemetry data is transmitted every four hours via a GSM modem back to a central station. Although instrumentation can be powered by a solar panel or a small windmill, this station is powered by a battery. To conserve battery power, a compromise has to be made on measurement intervals, and on-time needs to be minimised: the instrumentation wakes briefly, takes a reading and then returns to sleep.

Stilling chamber containing a depth sensor for measuring water level at the Mill Stream hydrometric station, Kilcullen. Co. Kildare. © Eugene Brennan

Calibration of the Weir at the Mill Stream

I met Michael Browne from the EPA a couple of months ago on a walk through the fields to New Abbey graveyard. I was immediately curious, having worked for a company that had designed, manufactured and installed data logging equipment for local authority sewage and water treatment plants. I got chatting with Michael and discovered he was calibrating the weir. This is done every 6 to 8 weeks or so to make sure readings are correct on an ongoing basis. Vegetation can build up on the weir, causing errors in measurement and so it has to be cleaned. Calibrating the weir involves taking actual flow measurements using a portable flow meter and making corresponding readings for the height of water. Necessary adjustments are then made in the instrumentation firmware (embedded software) to the equation that converts height to flow.
I could have talked shop to Michael all day, but I didn't want to take him away too long from his work. Also the cattle had become curious and had come from both fields to investigate, so the place was getting overly crowded and it was time to move on.…
 

An antenna is mounted on top of the stilling chamber for sending data back to a monitoring station. © Eugene Brennan

Archer 2, handheld computer used for calibrating the system. © Eugene Brennan

Carving the Riverbed

Public domain image by Ala Beara via Wikimedia Commons

The Kilcullen Diary's article about water safety made me think about the "Sally Hole" adjacent to St Brigid's Well being one of the danger spots where the river narrows a bit. I'm thinking there's a venturi effect and speed increases (like the way a carburetor works). Possibly this scours the bend, deepening the river bed, hence the Sally Hole? 

Image courtesy OSI (Taillte Éireann)