browser - How to detect private browsing in iOS 11+ Safari as well as older versions of Safari?

I need to detect if user is on private mode in Safari both in older versions as well as Safari on IOS 11. Is there a test that would cover both?

Update: Here is a pen that attempts to combine the storage and openDatabase try-catch blocks based on jeprubio's solution below

var isPrivate = false;

// Check private in iOS < 11
var storage = window.sessionStorage;
try {
  console.log('first try for storage')
    storage.setItem("someKeyHere", "test");
    storage.removeItem("someKeyHere");
} catch (e) {
  console.log('first catch')

    if (e.code === DOMException.QUOTA_EXCEEDED_ERR && storage.length === 0) {
        isPrivate = true;
   } 
}

// Check private in iOS 11: https://gist.github.com/cou929/7973956#gistcomment-2272103
try {
  console.log('second try for opendb');
   window.openDatabase(null, null, null, null);
} catch (e) {

  console.log('second catch');
   isPrivate = true;
}

console.log('isPrivate: ' + isPrivate)

alert((isPrivate ? 'You are' : 'You are not')  + ' in private browsing mode');

https://codepen.io/anon/pen/zpMZjp

In Safari new versions (11+) normal browser mode, that does not error on openDatabase test on the console but enters the second catch and isPrivate gets set to true. So, in Safari 11+ non-private mode is also detected as private mode.