jquery selector to count the number of visible table rows?

You can use the :visible selector and .length like this:

var numOfVisibleRows = $('tr:visible').length;

If the <table> itself isn’t visible on the screen (:visible returns false if any parent is hidden, the element doesn’t have to be hidden directly), then use .filter(), like this:

var numOfVisibleRows = $('tr').filter(function() {
  return $(this).css('display') !== 'none';
}).length;