Redirect to a path after certain content type node creation

Whenever a project is created, edited, it should be redirected to some specific path.

function mymodule_form_alter(&$form, &$form_state, $form_id) {
  switch($form_id) {
    case 'project':
      $form['actions']['submit']['#submit'][] = "mymodule_redirect_on_update";
      break;
    }
}

function mymodule_redirect_on_update($form, &$form_state) {
  global $user;
  $form_state['redirect'] = 'user/' . $user->uid;
  return $form;
}