String frameVideo = "<iframe width="100%" height="70%" src="https://www.youtube.com/embed/47yJ2XCRLZs" frameborder="0" allowfullscreen></iframe>";

WebView displayYoutubeVideo = (WebView) findViewById(R.id.mWebView);
String frameVideo = "<iframe width="100%" height="100%" src="https://www.youtube.com/embed/47yJ2XCRLZs" frameborder="0" allowfullscreen></iframe>";
WebSettings webSettings = displayYoutubeVideo.getSettings();
webSettings.setJavaScriptEnabled(true);
displayYoutubeVideo.loadData(frameVideo, "text/html", "utf-8");