Green’s Dictionary of Slang

1. the vagina.

1725		B. Mandeville An Essay upon Whoring iii: From Your stopping up those Drains and Sluices we had to let out Lewdness. Your demolishing those Horn-works and Breast-works of Modesty? Those Ramparts and Ditches within which the Virtue of our Wives and daughters lay so conveniently intrench’d.
c.1850		Peeping Tom (London) 14 54/2: Miss Bunn sends compliments to Mrs Bunt; / Requests she’ll cover up her drain, in front.
1890–1904		Farmer & Henley Sl. and Its Analogues.

2. the throat.

1933

‘William Juniper’ True Drunkard’s Delight 243: The throat, which is also known as [...] drain.