To my understanding, Pi Hakhirot has yet to be properly identified. Some say that "pi" refers to the Egyptian word "house", so it would mean "The House of Khirot" and Khirot may refer to the name of a place somewhere along the Nile that has the root KhRT (חר"ת) in it. According to Wikipedia, William Smith identified it with ...
The Shem miShmuel answers your question, he says:
ואדמו"ר זצללה"ה הכהן הגדול מאלכסנדר אמר כי לשון טבע הוא מלשון טובע
בנהר, שאדם צריך שמירה שלא יטבע בגשמיות
Translation (I do not know how to translate the abbreviated titles):
"...said: Because the word טבע (nature) is from the word טובע
(drowning) in a stream, that a person needs gaurding in ...
This website notes a connection and writes as follows:
The term טבע to denote “nature” is derived from:
Prov. 8:25– Before the mountains were sunk within the water;
Metz. David… sunk in the sense of established/planted;
Ibn Ezra… as in: on what were its sockets sunk (הטבעו), or who laid its cornerstone (Job 38:6).
RSRH Ex. 15:4(paraphrased) – טבע means ...
The Midrash explains that until that time, they had lived on water taken from amongst the rocks of the Yam Suf. Rabbeinu Bachaye quotes Rabbeinu Chananel who explains that though the Torah writes that the Jews walked in the desert for three days, they didn't actually go without water for three days, but rather they walked three day's journey in one day. (...