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The phrase "a depth of around" is correct and usable in written English.
It can be used when discussing measurements or estimates related to depth in various contexts, such as geography, construction, or science.
Example: "The lake has a depth of around 30 meters, making it one of the deepest in the region."
Alternatives: "approximately a depth of" or "a depth of about".
Exact(58)
The technical details: microwave ovens use a magnetron (something like a radio transmitter) to generate very short radio waves which penetrate food to a depth of around 2.5cm.
Together with movements observed at two benchmarks on nunataks protruding through the ice cap and seismicity beneath Katla, the horizontal movements at the SOHO and HVOL were interpreted as being due to increased pressure in a magma chamber12, located beneath the caldera at a depth of around 1.5 km b.s.l.13.l.13
The prototype, operated by compressed air, can dig to a depth of around 20cm in 20 seconds.
Crack growth in the top layer was simulated up to a depth of around 95% of its thickness.
The 108-page report describes how Arafat's corpse was located at a depth of around four metres below his mausoleum in Ramallah.
SMIT, for example, recovered the Japanese vessel Ehime Maru in one piece from a depth of around 2,000 feet off the Hawaiian coast in 2001.
The quake hit offshore at 4 18 a.m. at a depth of around 22 miles, the United States Geological Survey said.
The wreck was found 1,600 miles off the Australian coastline at a depth of around 3,700m, following the sonar search in December.
Crucially, they found no evidence for magma pooling at the base of the crust (a depth of around 40km at Springerville), suggesting the traditional model is plain wrong.
Similar(2)
Current EGS exploitation is more likely to be restricted to a depths of around 4.5 km and reservoir temperatures greater than 175 °C.
Until the mid-1990s, says Robin Walker of WesternGeco, an oil-services company, there was a general view that successful offshore oil-drilling operations were limited to a water depth of around 600 metres.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com